JP2005310190A - Method and apparatus for interpolating image - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To solve the problem that misunderstanding are likely to occur with electronic communications because of difficulty in conveying feelings. <P>SOLUTION: A key frame storage part 16 holds a plurality of key frames depicting facial expressions. An intermediate frame position acquiring part 14 acquires the position of an intermediate frame depicting an intermediate facial expression, based on its relationship with the other key frames. A matching processor 18 calculates matching between the key frames surrounding the intermediate frame. An intermediate frame generating part 22 generates the intermediate frame according to the matching result. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to an image interpolation technique, and more particularly to a digital image interpolation method and apparatus, and an image processing method and apparatus.

    The Internet has spread widely in the general society, and now the Internet is actively used for business and academic purposes. Factors for widespread use include lower prices of personal computers (PCs) and mobile phones, and enhancement of network infrastructure. As a result, personal information transmission and information collection became easier, and e-mail was recognized as a useful communication tool for everyone. E-mails can be easily sent at any time because they do not limit the other party's time like telephone calls, and their contents are often closer to conversation than letters.

  Until communication using such electronic media appeared, letters and facsimiles using paper media were the mainstream equivalents. However, it is not suitable for conversational use such as frequently exchanging short messages with a specific partner, and in that sense, it is inferior in terms of convenience compared to e-mail.

  However, even if the utterances made in the sense of conversation are documented as they are, the inflections and visual emotional expressions that are actually added in the conversation do not necessarily appear in the text and may cause misunderstandings to the other party. . The other person can't catch emotions either audibly or visually, and only infer their intentions in context. Therefore, if the content of the utterance may cause misunderstanding for the other party, even if it is an e-mail, a considerable amount of nerves must be used for the sentence.

  On the other hand, there are cases where so-called emoticons are used as a method of conveying emotions to the other party in electronic mail. Although this emoticon has been devised in a wide variety, it is insufficient as a means of conveying complicated emotions.

  The present invention has been made in view of such circumstances, and an object thereof is to provide an image interpolation and processing technique for expressing complex emotions with images.

  Although the present invention relates to image interpolation or processing techniques, the techniques are not necessarily limited to still image processing. For example, a moving image generation process and a compression technique thereof are also realized in the same manner, and of course, it falls within the scope of the application of the present invention.

One embodiment of the present invention relates to an image interpolation method. This method includes the following steps.
(1) A step of acquiring a first image pair composed of two key frames each including a face photographed with an arbitrary expression as a subject, and first corresponding point information between the two key frames. (2) Optional A step of acquiring a second image pair composed of two key frames each including a face captured with the expression of (2) and a second corresponding point information between the two key frames. (3) Positional relationship between a first axis determined temporally or spatially between two key frames and a second axis determined temporally or spatially between two key frames of the second image pair, first corresponding point information, And a step of generating an intermediate frame in which an intermediate facial expression should be projected by using the second corresponding point information.

  (1) In (2), both the first corresponding point information and the second corresponding point information may be obtained by matching key frames. In (3), biaxial interpolation may be performed using the first axis and the second axis. As an example, a key frame obtained from two viewpoints p1 (0, 0) and p2 (0, 100) is used as a first image pair, and another two viewpoints p3 (100, 0) and p4 (100, 100) are used. The obtained key frame is set as the second image pair. A straight line connecting points p1 and p2 corresponds to the first axis, and a straight line connecting points p3 and p4 corresponds to the second axis.

  When an image viewed from the viewpoint p ′ = (50, 50) is obtained as an intermediate frame, first, a frame from the viewpoint (0, 50) is generated based on the corresponding point information between the first image pair. Next, another frame from the viewpoint (100, 50) is generated based on the corresponding point information between the second image pair. Subsequently, these two frames are interpolated, that is, in this case, internally divided by 1: 1, and a desired intermediate frame is generated. Here, in order to perform interpolation in both vertical and horizontal directions, in general, the first image pair and the second image pair may be determined so that the first axis and the second axis do not come on the same straight line.

  In this example, the first axis and the second axis are spatially determined between two key frames, but there is another example in which the first axis and the second axis are temporally determined. For example, two key frames obtained at time t = t0 and t1 from one viewpoint P are set as a first image pair, and two key frames obtained at time t = t0 and t1 from another viewpoint Q are set as a second image pair. And In this case, a straight line connecting the point defined by (P, t0) and the point defined by (P, t1) in the first image pair becomes the first axis, and similarly (Q, t0) in the second image pair. A straight line connecting the point defined by (Q) and the point defined by (Q, t1) is the second axis. Therefore, if the intermediate frame is, for example, an image from the point ((P + Q) / 2, (t0 + t1) / 2), an intermediate image of two axes may be generated and then interpolated. In the following, neither time nor space is considered as a special parameter in the four dimensions.

  The method further includes a step of arranging a plurality of acquired key frames in a matrix at predetermined intervals and displaying the same on a screen, and a step of allowing a user to specify an arbitrary point on the screen. The specified point and each key Interpolation may be performed based on the positional relationship of the frames. The two key frames of the first image pair and the two key frames of the second image pair may be face images captured with different expressions of the same person. The “interpolation” may be not only interpolation but also extrapolation. For example, an intermediate frame is generated by extrapolation even when the user designates an arbitrary point outside a matrix in which a plurality of images are arranged. The term “matrix” is not intended to limit the arrangement of a plurality of key frames to a matrix, but for example, three key frames may be arranged in a triangular shape, or more key frames may be arranged. You may arrange | position in arbitrary forms so that they may not be located on a straight line.

  One of the two key frames of the first image pair and one of the two key frames of the second image pair are shared, and based on a triangle with the first and second axes as two sides The interpolation may be performed. Also, the two key frames of the first image pair and the two key frames of the second image pair are not shared, and the interpolation is based on a quadrilateral having two sides opposite to each other, the first axis and the second axis. May be performed. When detecting the first and second corresponding point information, the process performs a pixel-by-pixel matching calculation based on the correspondence between the singular points detected by two-dimensional search in each of the two key frames. Also good. The detecting step is to perform multi-resolution matching by extracting the singular points of each of the two key frames, and then performing matching calculation in units of images between the same resolution levels, and then calculating the matching results at different resolution levels. In this case, the pixel unit correspondence at the finest resolution level may be finally obtained.

  Another aspect of the present invention relates to an image interpolation apparatus. This device stores a plurality of key frames each containing a face captured with an arbitrary facial expression as a subject, and temporal or spatial positional information of the intermediate frame on which an intermediate facial expression is to be projected. Interpolating the intermediate frame based on the unit acquired in relation to the frame, the corresponding point information determined for each of the first image pair and the second image pair each consisting of two key frames, and the position information A first axis that is temporally or spatially defined between the two key frames of the first image pair and a temporal axis that is temporally or spatially defined between the two key frames of the second image pair. Those image pairs are selected so that the two axes do not come on the same straight line. The apparatus may further include a matching processor that generates corresponding point information.

  The above-described matching method using singular points is an application of the technique (hereinafter referred to as “premise technique”) previously proposed by the present applicant in Japanese Patent No. 2927350, and is suitable for the detecting step. However, the base technology does not touch on vertical and horizontal interpolation. With the new technique of the present invention, for example, a face image having an intermediate expression can be generated from a plurality of face images having different expressions.

  It may further include a unit that arranges a plurality of key frames in a matrix at predetermined intervals and displays them on the screen, and a user interface for inputting designation regarding the temporal or spatial position of the intermediate frame from the outside. The two key frames of the first image pair and the two key frames of the second image pair may be face images captured with different expressions of the same person.

  A plurality of corresponding point files describing corresponding points between key frames may be prepared or acquired, and a new corresponding point file may be generated by performing a mixing process therebetween. The “mixing process” is, for example, bilinear interpolation. In order to obtain the corresponding point file, a matching processor described later may be used. A process of generating an intermediate frame between the key frames by interpolation based on the new corresponding point file thus generated may be further included.

  Yet another embodiment of the present invention also relates to an image interpolation method. This method includes a step of displaying a plurality of images corresponding to various facial expressions to the user, a step of obtaining an instruction regarding the mixing of the images from the user, and an expression that did not originally exist according to the instructions. Generating a corresponding new image, and the instruction is acquired in a form including a blending ratio of the plurality of images at the time of mixing. The blending ratio may be determined from the relationship between the display position of the images on the screen on which a plurality of images are displayed and the action position at which the user inputs an instruction on the screen.

  Yet another aspect of the present invention relates to an image editor. This image editor has a function for displaying a plurality of images corresponding to various facial expressions to the user, a function for obtaining an instruction regarding mixing of those images from the user, and an expression that did not exist at the beginning according to the instructions. And a function for generating a new image corresponding to the information, and the instruction is acquired in a form including a mixture ratio of a plurality of images at the time of mixing.

  Yet another embodiment of the present invention also relates to an image interpolation method. This method generates a new image corresponding to a facial expression that did not originally exist by performing interpolation processing on at least three images corresponding to various facial expressions.

  In the present invention, the prerequisite technology is not essential. Further, the present invention also includes those in which the above configurations and processes are arbitrarily replaced, a part or all of expressions are replaced or added between the method and the apparatus, or expressions are changed to computer programs, recording media, and the like. It is effective as

  First, the multi-resolution singularity filter technique used in the embodiment and the image matching process using the technique will be described in detail as a “premise technique”. These techniques are the techniques for which the present applicant has already obtained Patent No. 2927350, and are most suitable for combination with the present invention. In the present invention, a mesh is provided on an image, and a large number of pixels are represented by the lattice points. Therefore, the present invention has a high application effect on a pixel-by-pixel matching technique such as the premise technique. However, the image matching technique that can be employed in the embodiment is not limited to this.

The image data encoding and decoding technology using the prerequisite technology will be specifically described below with reference to FIG.
[Background of prerequisite technology]
The automatic matching of two images, that is, the correspondence between image areas and pixels, is one of the most difficult and important themes in computer vision and computer graphics. For example, if matching is possible between images from different viewpoints for an object, an image from another viewpoint can be generated. If the matching between the right eye image and the left eye image can be calculated, photogrammetry using a stereoscopic image is also possible. When the face image model and other face images are matched, characteristic face parts such as eyes, nose and mouth can be extracted. For example, when matching is accurately performed between images of a human face and a cat's face, the morphing can be completely automated by automatically generating the intermediate images.

  However, in general, a corresponding point between two images has to be designated by a person one by one, which requires a lot of work. In order to solve this problem, many corresponding point automatic detection methods have been proposed. For example, there is an idea of reducing the number of corresponding point candidates by using an epipolar line. However, even in that case, the processing is extremely complicated. In order to reduce complexity, it is assumed that the coordinates of each point in the left-eye image are usually in the same position in the right-eye image. However, if such a restriction is provided, it becomes very difficult to perform matching that simultaneously satisfies the global feature and the local feature.

  In volume rendering, a series of cross-sectional images are used to construct a voxel. In this case, it is generally assumed that the pixels in the upper cross-sectional image correspond to the pixels at the same location in the lower cross-sectional image, and a pair of these pixels is used for the interpolation calculation. Since such a very simple method is used, an object constructed by volume rendering tends to be unclear when the distance between successive cross sections is long and the cross-sectional shape of the object changes greatly.

  There are many matching algorithms that use edge detection, such as stereoscopic photogrammetry. However, in this case, since the number of corresponding points obtained as a result is small, the disparity value must be interpolated in order to fill the gap between matched corresponding points. In general, it is difficult for all edge detectors to determine if this really suggests the presence of an edge when the pixel brightness changes within the local window they use. The edge detector is essentially a high-pass filter, and picks up noise at the same time as the edge.

  As another method, optical flow is known. When two images are given, the optical flow detects the movement of an object (rigid body) in the image. At that time, it is assumed that the luminance of each pixel of the object does not change. In the optical flow, the motion vector (u, v) of each pixel is calculated together with some additional conditions such as the smoothness of the vector field of (u, v). However, the optical flow cannot detect a global correspondence between images. Only the local change in the luminance of the pixel is noticed, and when the displacement of the image is large, the error of the system becomes remarkable.

  Many multi-resolution filters have been proposed to recognize the global structure of an image. They are classified into linear filters and nonlinear filters. A wavelet is an example of the former, but linear filters are generally not very useful for image matching. This is because information on the luminance of pixels having extreme values gradually becomes unclear together with their position information. FIG. 1A and FIG. 1B show the results of applying an averaging filter to a face image. As shown in the figure, the luminance of the pixels having extreme values gradually fades by averaging, and the position shifts due to the averaging. As a result, the brightness and position information of the eyes (minimum brightness points) is ambiguous at such a coarse resolution level, and correct matching cannot be calculated at this resolution. Thus, while providing a coarse resolution level is for global matching, the matching obtained here does not accurately correspond to the true features of the image (eyes, ie, local minima). Even if the eyes appear clearly at a finer resolution level, the error introduced when performing global matching is no longer irreversible. It has already been pointed out that the stereo information in the texture area is lost by applying a smoothing process to the input image.

  On the other hand, there is a one-dimensional “sieve” operator as a nonlinear filter which has recently been used in the field of topography. This operator adds a smoothing process to an image while preserving the causal relationship between the scale and space by selecting a minimum value (or maximum value) within a one-dimensional window of a predetermined size. The resulting image is the same size as the original image, but is simpler because small wave components have been removed. This operator can be classified as a “multi-resolution filter” in a broad sense in terms of reducing image information, but in reality it does not layer images while changing the resolution of the image like a wavelet. (Ie, not a multi-resolution filter in a narrow sense) and cannot be used to detect correspondence between images.

[Problems that the underlying technology is trying to solve]
In summary, the following issues are recognized.
1. There have been few image processing methods for accurately grasping image characteristics with relatively simple processing. In particular, there have been few effective proposals relating to an image processing method capable of extracting information while maintaining information on characteristic points, for example, pixel values and positions.
2. When automatically detecting corresponding points based on image features, there are generally drawbacks such as complicated processing and low noise resistance. In addition, it is necessary to set various restrictions in processing, and it is difficult to achieve matching that simultaneously satisfies the global feature and the local feature.
3. Even when a multi-resolution filter is introduced to recognize the global structure or features of an image, if the filter is a linear filter, the pixel luminance information and position information become ambiguous. As a result, it was easy to grasp the corresponding points inaccurately. The one-dimensional sieving operator which is a non-linear filter cannot be used to detect corresponding points between images because the images are not hierarchized.
4). As a result, in order to grasp the corresponding points correctly, there was no effective means other than relying on manual designation after all.

  The base technology has been made for the purpose of solving these problems, and provides a technology that enables accurate understanding of image characteristics in the field of image processing.

[Means for prerequisite technology to solve problems]
For this purpose, an aspect of the base technology proposes a new multi-resolution image filter. This multi-resolution filter extracts singularities from the image. Therefore, it is also called a singular point filter. A singular point is a point having an image feature. For example, in a certain area, the pixel value (pixel value refers to any numerical value related to the image or pixel, such as color number, luminance value, etc.) is the maximum point, the minimum point where the pixel value is minimum, There is a saddle point that minimizes the direction of. The singularity may be a topological concept. However, it may have any other characteristics. It is not an essential problem for the underlying technology what kind of property is considered a singularity.

  In this aspect, image processing using a multi-resolution filter is performed. First, in the detection step, a singular point is detected by performing a two-dimensional search on the first image. Next, in the generating step, the detected singular point is extracted to generate a second image having a resolution lower than that of the first image. The singularity of the first image is inherited in the second image. Since the second image has a lower resolution than the first image, it is suitable for grasping the global characteristics of the image.

  Another aspect of the base technology relates to an image matching method using a singular point filter. In this aspect, matching is performed between the start point image and the end point image. The start point image and the end point image are names given for convenience for distinguishing two images, and there is no essential difference.

  In this aspect, in the first step, a singular point filter is applied to the start point image to generate a series of start point hierarchical images having different resolutions. In the second step, a singular point filter is applied to the end point image to generate a series of end point layer images having different resolutions. The starting point hierarchical image and the ending point hierarchical image are image groups obtained by hierarchizing the starting point image and the ending point image, respectively, and are each composed of at least two images. Next, in the third step, matching between the start point hierarchical image and the end point hierarchical image is calculated in the resolution level layer. According to this aspect, the feature of the image related to the singular point is extracted and / or clarified by the multi-resolution filter, so that matching is facilitated. There is no particular requirement for matching conditions.

  Still another aspect of the base technology relates to matching of the start point image and the end point image. In this aspect, an evaluation formula is provided in advance for each of a plurality of matching evaluation items, the evaluation formulas are integrated to define a comprehensive evaluation formula, and an optimum matching is searched by focusing on the vicinity of the extreme value of the comprehensive evaluation formula. . The overall evaluation formula may be defined as the sum of the evaluation formulas after multiplying at least one of the evaluation formulas by the coefficient parameter. In this case, either the comprehensive evaluation formula or one of the evaluation formulas is almost extremal. The parameter may be determined by detecting a state. The reason that “near the extreme value” or “takes almost the extreme value” is because it may contain some errors. Some errors are not a problem over the base technology.

  Since the extreme value itself also depends on the parameter, there is a room for determining an optimum parameter based on the behavior of the extreme value, that is, how the extreme value changes. This aspect takes advantage of that fact. According to this aspect, a way to automate the determination of parameters that are difficult to adjust by nature is opened.

[Embodiment of prerequisite technology]
First, the elemental technology of the prerequisite technology is described in detail in [1], and the processing procedure is specifically described in [2]. We will report the results of the experiment in [3].

[1] Details of element technology [1.1] Introduction A new multi-resolution filter called a singular point filter is introduced to accurately calculate matching between images. No prior knowledge of objects is required. The calculation of matching between images is calculated at each resolution while proceeding through the resolution hierarchy. At that time, the resolution hierarchy is sequentially traced from the coarse level to the fine level. The parameters required for the calculation are set completely automatically by dynamic calculations similar to the human visual system. There is no need to manually identify corresponding points between images.

  The base technology can be applied to, for example, fully automatic morphing, object recognition, stereoscopic photogrammetry, volume rendering, and generation of a smooth moving image from a small number of frames. When used for morphing, a given image can be automatically transformed. When used for volume rendering, an intermediate image between cross sections can be accurately reconstructed. The same applies to the case where the distance between the cross sections is long and the cross-sectional shape changes greatly.

[1.2] Hierarchy of Singularity Filter The multi-resolution singularity filter according to the base technology can preserve the brightness and position of each singularity included in an image while reducing the resolution of the image. Here, the width of the image is N, and the height is M. Hereinafter, for simplicity, it is assumed that N = M = 2 ⁿ (n is a natural number). The section [0, N] ＮR is described as I. The pixel of the image at _{(i, j)} is described as p _{(i, j)} (i, jεI).

Here, a multi-resolution hierarchy is introduced. The hierarchized image group is generated by a multi-resolution filter. The multi-resolution filter performs a two-dimensional search on the original image to detect singular points, and generates another image having a lower resolution than the original image even if the detected singular points are extracted. . Here, the size of each image at the m-th level is 2 ^m × 2 ^m (0 ≦ m ≦ n). The singularity filter recursively constructs the following four types of new hierarchical images in a direction descending from n.

ただしここで、

Where

とする。以降これら４つの画像を副画像（サブイメージ）と呼ぶ。ｍｉｎ_{ｘ≦ｔ≦ｘ＋１}、ｍａｘ_{ｘ≦ｔ≦ｘ＋１}をそれぞれα及びβと記述すると、副画像はそれぞれ以下のように記述できる。

And Hereinafter, these four images are called sub-images. If min _{x ≦ t ≦ x + 1} and max _{x ≦ t ≦ x + 1} are described as α and β, respectively, the sub-images can be described as follows.

P ^{(m, 0)} = α (x) α (y) p ^{(m + 1,0)}
P ^{(m, 1)} = α (x) β (y) p ^{(m + 1,1)}
P ^{(m, 2)} = β (x) α (y) p ^{(m + 1, 2} )
P ^{(m, 3)} = β (x) β (y) p ^{(m + 1,3)}
That is, these are considered to be like tensor products of α and β. Each sub-image corresponds to a singular point. As is clear from these equations, the singularity filter detects a singularity for each block composed of 2 × 2 pixels in the original image. At this time, a point having the maximum pixel value or the minimum pixel value is searched for in two directions of each block, that is, vertical and horizontal. As the pixel value, luminance is adopted in the base technology, but various numerical values relating to the image can be adopted. The pixel with the maximum pixel value in both directions is the maximum point, the pixel with the minimum pixel value in both directions is the minimum point, the maximum pixel value in one of the two directions, and the minimum pixel value in the other direction Are detected as saddle points.

  The singularity filter reduces the resolution of the image by representing the image (4 pixels here) of the block with the image (1 pixel here) of the singularity detected inside each block. From the theoretical point of view of singularities, α (x) α (y) preserves the minimum point, β (x) β (y) preserves the maximum point, α (x) β (y) and β (x) α (y) preserves saddle points.

  First, the singular point filtering process is separately performed on the start point (source) image and the end point (destination) image to be matched, and a series of images, that is, a start point hierarchical image and an end point hierarchical image are generated. Four types of start point hierarchical images and end point hierarchical images are generated corresponding to the types of singular points.

Thereafter, matching between the start point layer image and the end point layer image is performed within a series of resolution levels. First, a minimum point is matched using p ^{(m, 0)} . Next, based on the result, saddle points are matched using p ^{(m, 1)} , and other saddle points are matched using p ^{(m, 2)} . Finally, the maximum points are matched using p ^{(m, 3)} .

FIGS. 1C and 1D show the sub-image p ^{(5, 0)} of FIGS. 1A and 1B, respectively. Similarly, FIG. 1 (e) and FIG. 1 (f) are p ^(5,1) , FIG. 1 (g) and FIG. 1 (h) are p ^(5,2) , FIG. 1 (i) and FIG. j) represents p ^{(5, 3)} , respectively. As can be seen from these figures, the sub-image facilitates the matching of the feature portions of the image. First, the eye becomes clear by p ^{(5, 0)} . This is because the eyes are the minimum brightness points in the face. According to p ^{(5, 1)} , the mouth becomes clear. This is because the mouth is low in luminance in the horizontal direction. According to p ^{(5, 2)} , the vertical lines on both sides of the neck become clear. Finally, p ^{(5, 3)} clarifies the brightest point on the ears and cheeks. This is because these are the maximum points of luminance.

  The feature of the image can be extracted by using the singular point filter. For example, by comparing the features of the image captured by the camera with the features of several objects that have been recorded in advance, the subject reflected in the camera is identified. can do.

[1.3] Calculation of mapping between images The pixel at the position (i, j) of the start point image is written as p ⁽ⁿ⁾ _{(i, j),} and the pixel at the position (k, l) of the end point image is also q ^{( n)} _{Describe by (k, l)} . Let i, j, k, lεI. Defines the energy of mapping between images (described later). This energy is determined by the difference between the luminance of the pixel of the start point image and the luminance of the corresponding pixel of the end point image, and the smoothness of the mapping. First, a mapping f ^{(m, 0)} : p ^{(m, 0)} → q ^{(m, 0)} between p ^{(m, 0)} and q ^{(m, 0)} having the minimum energy is calculated. Based on f ^{(m, 0)} , a mapping f ^{(m, 1)} between p ^{(m, 1} ) and q ^{(m, 1)} having the minimum energy is calculated. This procedure continues until the computation of the mapping f ^{(m, 3)} between p ^{(m, 3)} and q ^{(m, 3)} is complete. Each map f ^{(m, i)} (i = 0, 1, 2,...) Is called a sub-map. For convenience of calculation of f ^{(m, i)} , the order of i can be rearranged as follows: The reason why the rearrangement is necessary will be described later.

ここでσ（ｉ）∈｛０，１，２，３｝である。

Here, σ (i) ε {0, 1, 2, 3}.

[1.3.1] Bijection When the matching between the start point image and the end point image is expressed by mapping, the mapping should satisfy the bijection condition between the two images. This is because there is no conceptual superiority or inferiority between the two images, and the pixels of each other should be connected bijectively and injectively. However, unlike the usual case, the map to be constructed here is a bijective digital version. In the base technology, a pixel is specified by a grid point.

The mapping from the start point sub-image (sub-image provided for the start-point image) to the end-point sub-image (sub-image provided for the end-point image) is f ^{(m, s)} : I / 2 ^nm− I / 2 ^{n −m} → I / 2 ^nm × I / 2 ^nm (s = 0, 1,...) Here, f ^{(m, s)} (i, j) = (k, l) indicates that p ^{(m, s)} _{(i, j)} of the start point image is q ^{(m, s)} _{(k, l )} of the end point image. ₎ . For simplicity, a pixel q _{(k, l )} is described as q _{f (i, j)} when f (i, j) = (k, l) holds.

  The definition of bijection is important when data is discrete, such as pixels (grid points) handled in the base technology. Here, it is defined as follows (i, i ', j, j', k, l are all integers). First, each square region denoted by R in the plane of the starting point image,

を考える（ｉ＝０，…，２^ｍ−１、ｊ＝０，…，２^ｍ−１）。ここでＲの各辺（エッジ）の方向を以下のように定める。

(I = 0,..., 2 ^m −1, j = 0,..., 2 ^m −1). Here, the direction of each side (edge) of R is determined as follows.

この正方形は写像ｆによって終点画像平面における四辺形に写像されなければならない。ｆ^{（ｍ，ｓ）}（Ｒ）によって示される四辺形、

This square must be mapped to a quadrilateral in the endpoint image plane by mapping f. f ^{(m, s)} A quadrilateral indicated by (R),

は、以下の全単射条件を満たす必要がある。

Must meet the following bijective conditions:

1. The edges of the quadrilateral f ^{(m, s)} (R) do not intersect each other.
2. The edge directions of f ^{(m, s)} (R) are equal to those of R (clockwise in the case of FIG. 2).
3. As a relaxation condition, retraction is allowed.

This is because unless there is any relaxation condition, the only map that completely satisfies the bijection condition is the unit map. Here ^{f (m, s)} the length of one edge of the (R) is 0, i.e. ^{f (m, s)} (R) may become a triangle. However, it should not be a figure with an area of 0, that is, one point or one line segment. When FIG. 2 (R) is the original quadrilateral, FIG. 2 (A) and FIG. 2 (D) satisfy the bijection condition, but FIG. 2 (B), FIG. 2 (C), FIG. ) Is not satisfied.

In an actual implementation, the following conditions may be further imposed to easily guarantee that the mapping is surjective. That is, each pixel on the boundary of the start point image is mapped to a pixel occupying the same position in the end point image. That is, f (i, j) = (i, j) (where i = 0, i = 2 ^m −1, j = 0, j = 2 ^m −1). Hereinafter, this condition is also referred to as “additional condition”.

[1.3.2] Mapping energy [1.3.2.1] Pixel luminance cost Defines the energy of mapping f. The purpose is to find a map that minimizes energy. The energy is mainly determined by the difference between the luminance of the pixel in the start point image and the luminance of the corresponding pixel in the end point image. That is, the energy C ^{(m, s)} _{(i, j) at} the point (i, j) of the map f ^{(m, s)} is determined by the following equation.

ここで、Ｖ（ｐ^{（ｍ，ｓ）} _{（ｉ，ｊ）}）及びＶ（ｑ^{（ｍ，ｓ）} _{ｆ（ｉ，ｊ）}）はそれぞれ画素ｐ^{（ｍ，ｓ）} _{（ｉ，ｊ）}及びｑ^{（ｍ，ｓ）} _{ｆ（ｉ，ｊ）}の輝度である。ｆのトータルのエネルギーＣ^{（ｍ，ｓ）}は、マッチングを評価するひとつの評価式であり、つぎに示すＣ^{（ｍ，ｓ）} _{（ｉ，ｊ）}の合計で定義できる。

Here, V (p ^{(m, s)} _{(i, j)} ) and V (q ^{(m, s)} _{f (i, j)} ) are pixels p ^{(m, s)} _{(i, j)} and q ^{( m, s)} is the brightness of _{f (i, j)} . The total energy C ^{(m, s)} of f is one evaluation formula for evaluating matching, and can be defined by the sum of C ^{(m, s)} _{(i, j)} shown below.

［１．３．２．２］滑らかな写像のための画素の位置に関するコスト
滑らかな写像を得るために、写像に関する別のエネルギーＤｆを導入する。このエネルギーは画素の輝度とは関係なく、ｐ^{（ｍ，ｓ）} _{（ｉ，ｊ）}およびｑ^{（ｍ，ｓ）} _{ｆ（ｉ，ｊ）}の位置によって決まる（ｉ＝０，…，２^ｍ−１，ｊ＝０，…，２^ｍ−１）。点（ｉ，ｊ）における写像ｆ^{（ｍ，ｓ）}のエネルギーＤ^{（ｍ，ｓ）} _{（ｉ，ｊ）}は次式で定義される。

[1.3.2.2] Cost of pixel location for smooth mapping In order to obtain a smooth mapping, another energy Df for mapping is introduced. This energy is independent of the luminance of the pixel and is determined by the position of p ^{(m, s)} _{(i, j)} and q ^{(m, s)} _{f (i, j)} (i = 0,..., 2 ^m −1). , J = 0,..., 2 ^m −1). The energy ^D (i, j) mapping in ^{f (m, s) (m} , s) (i, j) is defined by the following equation.

ただし、係数パラメータηは０以上の実数であり、また、

However, the coefficient parameter η is a real number of 0 or more, and

とする。ここで、

And here,

であり、ｉ’＜０およびｊ’＜０に対してｆ（ｉ’，ｊ’）は０と決める。Ｅ_０は（ｉ，ｊ）及びｆ（ｉ，ｊ）の距離で決まる。Ｅ_０は画素があまりにも離れた画素へ写影されることを防ぐ。ただしＥ_０は、後に別のエネルギー関数で置き換える。Ｅ_１は写像の滑らかさを保証する。Ｅ_１は、ｐ_{（ｉ，ｊ）}の変位とその隣接点の変位の間の隔たりを表す。以上の考察をもとに、マッチングを評価する別の評価式であるエネルギーＤ_ｆは次式で定まる。

And f (i ′, j ′) is determined to be 0 for i ′ <0 and j ′ <0. E ₀ is determined by the distance between (i, j) and f (i, j). E ₀ prevents the pixel from being mapped to a pixel that is too far away. However, E ₀ is replaced later with another energy function. E ₁ ensures the smoothness of the mapping. E ₁ represents the distance between the displacement of p _{(i, j) and} the displacement of its neighboring points. Based on the above consideration, the energy D _f is another evaluation equation for evaluating the matching is determined by the following equation.

［１．３．２．３］写像の総エネルギー
写像の総エネルギー、すなわち複数の評価式の統合に係る総合評価式はλＣ^{（ｍ，ｓ）} _ｆ＋Ｄ^{（ｍ，ｓ）} _ｆで定義される。ここで係数パラメータλは０以上の実数である。目的は総合評価式が極値をとる状態を検出すること、すなわち次式で示す最小エネルギーを与える写像を見いだすことである。

[1.3.2.3] Total energy of mapping The total energy of mapping, that is, a comprehensive evaluation formula relating to the integration of a plurality of evaluation formulas is defined by λC ^{(m, s)} _f + D ^{(m, s)} _f . Here, the coefficient parameter λ is a real number of 0 or more. The purpose is to detect a state in which the comprehensive evaluation formula takes an extreme value, that is, to find a map that gives the minimum energy shown by the following formula.

λ＝０及びη＝０の場合、写像は単位写像になることに注意すべきである（すなわち、全てのｉ＝０，…，２^ｍ−１及びｊ＝０，…，２^ｍ−１に対してｆ^{（ｍ，ｓ）}（ｉ，ｊ）＝（ｉ，ｊ）となる）。後述のごとく、本前提技術では最初にλ＝０及びη＝０の場合を評価するため、写像を単位写像から徐々に変形していくことができる。仮に総合評価式のλの位置を変えてＣ^{（ｍ，ｓ）} _ｆ＋λＤ^{（ｍ，ｓ）} _ｆと定義したとすれば、λ＝０及びη＝０の場合に総合評価式がＣ^{（ｍ，ｓ）} _ｆだけになり、本来何等関連のない画素どうしが単に輝度が近いというだけで対応づけられ、写像が無意味なものになる。そうした無意味な写像をもとに写像を変形していってもまったく意味をなさない。このため、単位写像が評価の開始時点で最良の写像として選択されるよう係数パラメータの与えかたが配慮されている。

Note that when λ = 0 and η = 0, the mapping is a unit mapping (ie, all i = 0,..., 2 ^m −1 and j = 0,..., 2 ^m −1). F ^{(m, s)} (i, j) = (i, j)). As will be described later, since the base technology first evaluates the case of λ = 0 and η = 0, the mapping can be gradually changed from the unit mapping. If the position of λ in the comprehensive evaluation formula is changed and defined as C ^{(m, s)} _f + λD ^{(m, s)} _f , the comprehensive evaluation formula is C ^{(m, s)} It becomes only _f , and the pixels which are not related in any way are associated with each other simply because the luminance is close, and the mapping becomes meaningless. Even if the map is transformed based on such a meaningless map, it does not make any sense. For this reason, consideration is given to how the coefficient parameter is given so that the unit map is selected as the best map at the start of evaluation.

  The optical flow also considers the difference in pixel brightness and the smoothness as in this base technology. However, the optical flow cannot be used for image conversion. This is because only local movement of the object is considered. A global correspondence can be detected by using a singularity filter according to the base technology.

[1.3.3] Determination of mapping by introducing multi-resolution A mapping f _min that gives minimum energy and satisfies the bijection condition is obtained using a multi-resolution hierarchy. The mapping between the start sub-image and the end sub-image is calculated at each resolution level. Starting from the top of the resolution hierarchy (the coarsest level), the mapping of each resolution level is determined taking into account the mappings of the other levels. The number of mapping candidates at each level is limited by using higher or coarser level mappings. More specifically, when determining a mapping at a certain level, a mapping obtained at one coarser level is imposed as a kind of constraint condition.

  First,

が成り立つとき、ｐ^{（ｍ−１，ｓ）} _{（ｉ’，ｊ’）}、ｑ^{（ｍ−１，ｓ）} _{（ｉ’，ｊ’）}をそれぞれｐ^{（ｍ，ｓ）} _{（ｉ，ｊ）}、ｑ^{（ｍ，ｓ）} _{（ｉ，ｊ）}のｐａｒｅｎｔと呼ぶことにする。［ｘ］はｘを越えない最大整数である。またｐ^{（ｍ，ｓ）} _{（ｉ，ｊ）}、ｑ^{（ｍ，ｓ）} _{（ｉ，ｊ）}をそれぞれｐ^{（ｍ−１，ｓ）} _{（ｉ’，ｊ’）}、ｑ^{（ｍ−１，ｓ）} _{（ｉ’，ｊ’）}のｃｈｉｌｄと呼ぶ。関数ｐａｒｅｎｔ（ｉ，ｊ）は次式で定義される。

P ^{(m-1, s)} _{(i ′, j ′)} , q ^{(m−1, s)} _{(i ′, j ′)} are converted to p ^{(m, s)} _{(i, j)} , q, respectively. ^{(M, s)} Called parent of _{(i, j)} . [X] is a maximum integer not exceeding x. Also, p ^{(m, s)} _{(i, j)} and q ^{(m, s)} _{(i, j)} are respectively converted to p ^{(m-1, s)} _{(i ′, j ′)} and q ^{(m−1, s).} _This is called _{(i ', j')} child. The function parent (i, j) is defined by the following equation.

ｐ^{（ｍ，ｓ）} _{（ｉ，ｊ）}とｑ^{（ｍ，ｓ）} _{（ｋ，ｌ）}の間の写像ｆ^{（ｍ，ｓ）}は、エネルギー計算を行って最小になったものを見つけることで決定される。ｆ^{（ｍ，ｓ）}（ｉ，ｊ）＝（ｋ，ｌ）の値はｆ^{（ｍ−１，ｓ）}（ｍ＝１，２，…，ｎ）を用いることによって、以下のように決定される。まず、ｑ^{（ｍ，ｓ）} _{（ｋ，ｌ）}は次の四辺形の内部になければならないという条件を課し、全単射条件を満たす写像のうち現実性の高いものを絞り込む。

The mapping f ^{(m, s)} between p ^{(m, s)} _{(i, j)} and q ^{(m, s)} _{(k, l} ⁾ is determined by performing an energy calculation to find the smallest one. Is done. The value of f ^{(m, s)} (i, j) = (k, l) is determined as follows by using f ^{(m−1, s)} (m = 1, 2,..., n). The First, q ^{(m, s)} _{(k, l)} imposes a condition that it must be inside the following quadrilateral, and narrows down the most realistic maps that satisfy the bijection condition.

ただしここで、

Where

である。こうして定めた四辺形を、以下ｐ^{（ｍ，ｓ）} _{（ｉ，ｊ）}の相続（inherited）四辺形と呼ぶことにする。相続四辺形の内部において、エネルギーを最小にする画素を求める。

It is. The quadrilateral thus determined will be referred to as an inherited quadrilateral of p ^{(m, s)} _{(i, j)} hereinafter. Find the pixel that minimizes the energy inside the inherited quadrilateral.

FIG. 3 shows the above procedure. In the figure, the A, B, C, and D pixels of the start point image are mapped to the end point images A ′, B ′, C ′, and D ′, respectively, at the (m−1) th level. The pixel p ^{(m, s)} _{(i, j)} is mapped to the pixel q ^{(m, s)} _{f (m) (i, j)} existing inside the inherited quadrilateral A′B′C′D ′. There must be. With the above consideration, the mapping from the (m-1) th level mapping to the mth level mapping is performed.

The energy E ₀ defined above is replaced by the following equation in order to calculate the submapping f ^{(m, 0} ) at the m-th level.

また、副写像ｆ^{（ｍ，ｓ）}を計算するためには次式を用いる。

Further, the following equation is used to calculate the submapping f ^{(m, s)} .

こうしてすべての副写像のエネルギーを低い値に保つ写像が得られる。式２０により、異なる特異点に対応する副写像が、副写像どうしの類似度が高くなるように同一レベル内で関連づけられる。式１９は、ｆ^{（ｍ，ｓ）}（ｉ，ｊ）と、第ｍ−１レベルの画素の一部と考えた場合の（ｉ，ｊ）が射影されるべき点の位置との距離を示している。

This gives a map that keeps the energy of all submaps low. According to Equation 20, the sub-maps corresponding to different singular points are related within the same level so that the similarity between the sub-maps becomes high. Equation 19 shows the distance between f ^{(m, s)} (i, j) and the position of the point where (i, j) should be projected when considered as a part of the pixel of the (m-1) th level. ing.

If there is no pixel satisfying the bijection condition inside the inherited quadrilateral A′B′C′D ′, the following measures are taken. First, a pixel whose distance from the boundary line of A′B′C′D ′ is L (initially L = 1) is examined. If the one with the minimum energy satisfies the bijection condition, this is selected as the value of f ^{(m, s)} (i, j). L is increased until such a point is found or until L reaches its upper limit L ^(m) max. L ^(m) max is fixed for each level m. If such a point is not found at all, a mapping in which the area of the quadrilateral to be converted becomes zero by temporarily ignoring the third condition of bijection is recognized, and f ^{(m, s)} (i , J). If a point that satisfies the condition is still not found, the bijection first and second conditions are then removed.

  An approximation method using multiple resolutions is essential to determine the global correspondence between images while avoiding the mapping being affected by image details. Unless an approximation method based on multi-resolution is used, it is impossible to find a correspondence between distant pixels. In that case, the size of the image must be limited to a very small size, and only an image with small change can be handled. Furthermore, since the normal mapping requires smoothness, it is difficult to find the correspondence between such pixels. This is because the energy of mapping from pixel to pixel at a distance is high. According to the approximation method using multi-resolution, an appropriate correspondence between such pixels can be found. This is because these distances are small at the upper level (coarse level) of the resolution hierarchy.

[1.4] Automatic determination of optimal parameter values One of the main drawbacks of existing matching techniques is the difficulty in adjusting parameters. In most cases, the parameter adjustment is performed manually, and it is extremely difficult to select an optimum value. According to the method according to the base technology, the optimum parameter value can be determined completely automatically.

The system according to the base technology includes two parameters, λ and η. In short, λ is the weight of the difference in luminance of the pixels, and η is the stiffness of the mapping. The initial values of these parameters are 0. First, η is fixed at η = 0 and λ is gradually increased from 0. When the value of λ is increased and the value of the comprehensive evaluation formula (Equation 14) is minimized, the value of C ^{(m, s)} _f for each submapping generally decreases. This basically means that the two images must be better matched. However, when λ exceeds the optimum value, the following phenomenon occurs.

1. Pixels that should not be associated with each other are erroneously associated with each other simply because the luminance is close.
2. As a result, the correspondence between the pixels becomes strange and the mapping starts to be broken.

3. As a result, D ^{(m, s)} _f in Equation 14 tends to increase rapidly.
4). As a result, since the value of Equation 14 tends to increase rapidly, f ^{(m, s)} changes to suppress the rapid increase in D ^{(m, s)} _f , and as a result, C ^{(m, s)} _f Will increase.
Therefore, a threshold value at which C ^{(m, s)} _f changes from decreasing to increasing is detected while maintaining the state that Equation 14 takes the minimum value while increasing λ, and λ is set as the optimum value at η = 0. Next, η is increased little by little to check the behavior of C ^{(m, s)} _f , and η is automatically determined by the method described later. Λ is also determined corresponding to η.

  This method is similar to the operation of the focus mechanism of the human visual system. In the human visual system, the left and right eyes are matched while moving one eye. When an object can be clearly recognized, its eyes are fixed.

[1.4.1] Dynamic determination of λ λ is increased from 0 by a predetermined step size, and the submapping is evaluated each time the value of λ changes. As in Equation 14, the total energy is defined by λC ^{(m, s)} _f + D ^{(m, s)} _f . D ^{(m, s)} _{f in} Equation 9 represents smoothness, theoretically becomes the minimum in the case of unit mapping, and both E ₀ and E ₁ increase as the mapping is distorted. Since E ₁ is an integer, the minimum step size of D ^{(m, s)} _f is 1. Therefore, if the current change (decrease amount) of λC ^{(m, s)} _{(i, j)} is not greater than 1, the total energy cannot be reduced by changing the mapping. This is because D ^{(m, s)} _f increases by 1 or more as the mapping changes, so that the total energy does not decrease unless λC ^{(m, s)} _{(i, j)} decreases by 1 or more.

Under this condition, it is shown that C ^{(m, s)} _{(i, j)} decreases in the normal state as λ increases. A histogram of C ^{(m, s)} _{(i, j} ) is described as h (l). h (l) is the number of pixels whose energy C ^{(m, s)} _{(i, j)} is l ² . In order to satisfy λl ² ≧ 1, for example, consider the case of l ² = 1 / λ. When λ changes from λ ₁ to λ ₂ by a small amount,

で示されるＡ個の画素が、

A pixels indicated by

のエネルギーを持つより安定的な状態に変化する。ここでは仮に、これらの画素のエネルギーがすべてゼロになると近似している。この式はＣ^{（ｍ，ｓ）} _ｆの値が、

Changes to a more stable state with the energy of. Here, it is approximated that the energy of these pixels is all zero. This equation shows that the value of C ^{(m, s)} _f is

だけ変化することを示し、その結果、

Show that only changes, and as a result,

が成立する。ｈ（ｌ）＞０であるから、通常Ｃ^{（ｍ，ｓ）} _ｆは減少する。しかし、λが最適値を越えようとするとき、上述の現象、つまりＣ^{（ｍ，ｓ）} _ｆの増加が発生する。この現象を検出することにより、λの最適値を決定する。

Is established. Since h (l)> 0, C ^{(m, s)} _f usually decreases. However, when λ is about to exceed the optimum value, the phenomenon described above, that is ^, an increase in C ^{(m, s)} _f occurs. By detecting this phenomenon, the optimum value of λ is determined.

  When H (h> 0) and k are constants,

と仮定すれば、

Assuming

が成り立つ。このときｋ≠−３であれば、

Holds. At this time, if k ≠ -3,

となる。これがＣ^{（ｍ，ｓ）} _ｆの一般式である（Ｃは定数）。

It becomes. This is a general formula of C ^{(m, s)} _f (C is a constant).

When detecting the optimum value of λ, the number of pixels that violate the bijection condition may be inspected for further safety. Here, when determining the mapping of each pixel, it is assumed that the probability of breaking the bijection condition is p ₀ . in this case,

が成立しているため、全単射条件を破る画素の数は次式の率で増加する。

Therefore, the number of pixels that violate the bijection condition increases at the rate of the following equation.

従って、

Therefore,

は定数である。仮にｈ（ｌ）＝Ｈｌ^ｋを仮定するとき、例えば、

Is a constant. If h (l) = Hl ^k is assumed, for example,

は定数になる。しかしλが最適値を越えると、上の値は急速に増加する。この現象を検出し、Ｂ_０λ^{３／２＋ｋ／２}／２^ｍの値が異常値Ｂ_{０ｔｈｒｅｓ}を越えるかどうかを検査し、λの最適値を決定することができる。同様に、Ｂ_１λ^{３／２＋ｋ／２}／２^ｍの値が異常値Ｂ_{１ｔｈｒｅｓ}を越えるかどうかを検査することにより、全単射の第３の条件を破る画素の増加率Ｂ_１を確認する。ファクター２^ｍを導入する理由は後述する。このシステムはこれら２つの閾値に敏感ではない。これらの閾値は、エネルギーＣ^{（ｍ，ｓ）} _ｆの観察では検出し損なった写像の過度の歪みを検出するために用いることができる。

Becomes a constant. However, when λ exceeds the optimum value, the above value increases rapidly. By detecting this phenomenon, it is possible to determine whether the value of B ₀ λ _3/2 ^{+ k /} _2/2 ^m exceeds the abnormal value B _0thres and determine the optimum value of λ. Similarly, by checking whether the value of B ₁ λ _3/2 ^{+ k /} _2/2 ^m exceeds the abnormal value B _1thres , the pixel increase rate B ₁ that violates the third condition of bijection is confirmed. . The reason why factor 2 ^m is introduced will be described later. This system is not sensitive to these two thresholds. These thresholds can be used to detect excessive distortion of the map that was missed by observation of energy C ^{(m, s)} _f .

In the experiment, when calculating the submapping f ^{(m, s)} , if λ exceeds 0.1, the calculation of f ^{(m, s)} is stopped and the calculation shifts to the calculation of f ^{(m, s + 1)} . This is because a difference of only “3” in the luminance level of 255 pixels affects the submapping calculation when λ> 0.1, and it is difficult to obtain a correct result when λ> 0.1. .

[1.4.2] Histogram h (l)
The examination of C ^{(m, s)} _f does not depend on the histogram h (l). It can be affected by h (l) during inspection of bijection and its third condition. When (λ, C ^{(m, s)} _f ) is actually plotted, k is usually near 1. In the experiment, k = 1 was used, and B ₀ λ ² and B ₁ λ ² were examined. If the true value of k is less than 1, B ₀ λ ² and B ₁ λ ² do not become constants and gradually increase according to the factor λ ^{(1−k) / 2} . If h (l) is a constant, for example, the factor is λ ^1/2 . However, these differences can be absorbed by setting the threshold B _0thres correctly.

Here, it is assumed that the starting point image is a circular object having a center (x ₀ , y ₀ ) and a radius r as in the following equation.

一方、終点画像は、次式のごとく中心（ｘ_１，ｙ_１）、半径がｒのオブジェクトであるとする。

On the other hand, the end point image is assumed to be an object having a center (x ₁ , y ₁ ) and a radius r as in the following equation.

ここでｃ（ｘ）はｃ（ｘ）＝ｘ^ｋの形であるとする。中心（ｘ_０，ｙ_０）及び（ｘ_１，ｙ_１）が十分遠い場合、ヒストグラムｈ（ｌ）は次式の形となる。

Where c (x) has the form of c ^(x) = x ^k. When the centers (x ₀ , y ₀ ) and (x ₁ , y ₁ ) are sufficiently far away, the histogram h (l) has the form:

ｋ＝１のとき、画像は背景に埋め込まれた鮮明な境界線を持つオブジェクトを示す。このオブジェクトは中心が暗く、周囲にいくに従って明るくなる。ｋ＝−１のとき、画像は曖昧な境界線を持つオブジェクトを表す。このオブジェクトは中心が最も明るく、周囲にいくに従って暗くなる。一般のオブジェクトはこれらふたつのタイプのオブジェクトの中間にあると考えてもさして一般性を失わない。したがって、ｋは−１≦ｋ≦１として大抵の場合をカバーでき、式２７が一般に減少関数であることが保障される。

When k = 1, the image shows an object with a sharp border embedded in the background. This object has a dark center and becomes brighter as you go around. When k = -1, the image represents an object with an ambiguous boundary. This object is brightest at the center and darkens as you move around. Even if you think that a general object is in between these two types of objects, you won't lose generality. Therefore, k can cover most cases with −1 ≦ k ≦ 1, and it is guaranteed that Equation 27 is generally a decreasing function.

Note that, as can be seen from Equation 34, r is affected by the resolution of the image, i.e., r is proportional to 2 ^m . For this purpose, a factor of 2 ^m was introduced in [1.4.1].

[1.4.3] Dynamic determination of η The parameter η can be automatically determined by the same method. First, η = 0, and the final map f ⁽ⁿ⁾ and energy C ⁽ⁿ⁾ _f at the finest resolution are calculated. Subsequently, η is increased by a certain value Δη, and the final mapping f ⁽ⁿ⁾ and energy C ⁽ⁿ⁾ _f at the finest resolution are calculated again. This process is continued until the optimum value is obtained. η indicates the rigidity of the mapping. This is because the weight of the following equation.

ηが０のとき、Ｄ^（ｎ） _ｆは直前の副写像と無関係に決定され、現在の副写像は弾性的に変形され、過度に歪むことになる。一方、ηが非常に大きな値のとき、Ｄ^（ｎ） _ｆは直前の副写像によってほぼ完全に決まる。このとき副写像は非常に剛性が高く、画素は同じ場所に射影される。その結果、写像は単位写像になる。ηの値が０から次第に増えるとき、後述のごとくＣ^（ｎ） _ｆは徐々に減少する。しかしηの値が最適値を越えると、図４に示すとおり、エネルギーは増加し始める。同図のＸ軸はη、Ｙ軸はＣ_ｆである。

When η is 0, D ⁽ⁿ⁾ _f is determined regardless of the immediately preceding submapping, and the current submapping is elastically deformed and excessively distorted. On the other hand, when η is a very large value, D ⁽ⁿ⁾ _f is almost completely determined by the immediately preceding submapping. At this time, the sub-mapping is very rigid and the pixels are projected to the same location. As a result, the map becomes a unit map. When the value of η increases gradually from 0, C ⁽ⁿ⁾ _f gradually decreases as described later. However, when the value of η exceeds the optimum value, the energy starts to increase as shown in FIG. In the figure, the X axis is η, and the Y axis is C _f .

In this way, an optimum value of η that minimizes C ⁽ⁿ⁾ _f can be obtained. However, as a result of various factors affecting the calculation as compared with the case of λ, C ⁽ⁿ⁾ _f changes with small fluctuations. In the case of λ, the submapping is only recalculated once every time the input changes by a small amount, but in the case of η, all the submappings are recalculated. For this reason, it is not possible to immediately determine whether or not the obtained value of C ⁽ⁿ⁾ _f is minimum. If a candidate for the minimum value is found, it is necessary to search for the true minimum value by setting a finer section.

[1.5] Supersampling When determining the correspondence between pixels, in order to increase the degree of freedom ^, the range of f ^{(m, s)} can be expanded to R × R (R is a set of real numbers). In this case, the luminance of the pixel of the end point image is interpolated, and a non-integer point,

における輝度を持つｆ^{（ｍ，ｓ）}が提供される。つまりスーパーサンプリングが行われる。実験では、ｆ^{（ｍ，ｓ）}は整数及び半整数値をとることが許され、

F ^{(m, s)} with luminance at is provided. That is, super sampling is performed. In the experiment, f ^{(m, s)} is allowed to take integer and half integer values,

は、

Is

によって与えられた。

Given by.

[1.6] Normalization of luminance of pixels of each image When the start point image and the end point image include very different objects, it is difficult to use the luminance of the original pixel as it is for calculation of mapping. This is because the luminance difference C ^{(m, s)} _f becomes too large due to the large difference in luminance, making it difficult to perform correct evaluation.

  For example, consider the case of matching a human face and a cat face. The cat's face is covered with hair and contains very bright and very dark pixels. In this case, the sub-image is first normalized in order to calculate the sub-mapping between the two faces. That is, the brightness of the darkest pixel is set to 0, the brightest is set to 255, and the brightness of the other pixels is obtained by linear interpolation.

[1.7] Implementation An inductive method is used in which the calculation proceeds linearly according to the scan of the starting point image. First, the value of f ^{(m, s)} is determined for the top leftmost pixel (i, j) = (0, 0). Next, the value of each f ^{(m, s)} (i, j) is determined while i is incremented by one. When the value of i reaches the width of the image, the value of j is increased by 1 and i is returned to 0. Thereafter, f ^{(m, s)} (i, j) is determined as the start point image is scanned. If the correspondence of pixels is determined for all points, one mapping f ^{(m, s)} is determined.

There _{p (i, j)} corresponding point _{q f (i, j)} for the In is Kimare, then _{p (i, j + 1)} of the corresponding point _{q f (i, j + 1} ) is determined. At this time, the position of q _{f (i, j + 1)} is limited by the position of q _{f (i, j)} in order to satisfy the bijection condition. Therefore, the priority is higher in this system as the corresponding points are determined first. If (0,0) always has the highest priority, additional deflections are added to the final mapping required. In the base technology, in order to avoid this state, f ^{(m, s)} is determined by the following method.

  First, when (s mod 4) is 0, the starting point is (0, 0) and i and j are gradually increased. When (s mod 4) is 1, the right end point of the uppermost row is used as a starting point, and i is decreased and j is increased. When (s mod 4) is 2, the starting point is the rightmost point in the bottom row, and i and j are determined while decreasing. When (s mod 4) is 3, the left end point of the bottom row is used as a starting point, and i is increased and j is decreased. Since the sub-mapping concept, that is, the parameter s does not exist at the nth level with the finest resolution, two directions are calculated continuously assuming that s = 0 and s = 2.

In an actual implementation, by giving a penalty to a candidate that violates the bijection condition, f ^{(m, s)} (i, j ⁾ satisfying the bijection condition from the candidates (k, l) as much as possible. ) (M = 0, ..., n) was chosen. Candidate energy D (k, l) that violates the third condition is multiplied by φ, while candidates that violate the first or second condition are multiplied by ψ. This time, φ = 2 and ψ = 100000 were used.

In order to check the bijection condition described above, the following test was performed when (k, l) = f ^{(m, s)} (i, j) was determined as an actual procedure. That is, it is confirmed whether or not the z component of the outer product of the following equation is 0 or more for each lattice point (k, l) included in the inherited quadrilateral of f ^{(m, s)} (i, j).

ただしここで、

Where

である（ここでベクトルは三次元ベクトルとし、ｚ軸は直交右手座標系において定義される）。もしＷが負であれば、その候補についてはＤ^{（ｍ，ｓ）} _{（ｋ，ｌ）}にψを掛けることによってペナルティを与え、できるかぎり選択しないようにする。

Where the vector is a three-dimensional vector and the z-axis is defined in an orthogonal right-handed coordinate system. If W is negative, the candidate is penalized by multiplying D ^{(m, s)} _{(k, l)} by ψ so that it is not selected as much as possible.

FIG. 5A and FIG. 5B show the reason for inspecting this condition. FIG. 5A shows a candidate without a penalty, and FIG. 5B shows a candidate with a penalty. When determining the mapping f ^{(m, s)} (i, j + 1) for the adjacent pixel (i, j + 1), if the z component of W is negative, there is no pixel that satisfies the bijection condition on the starting image plane. . This is because q ^{(m, s)} _{(k, l)} exceeds the boundary line of the adjacent quadrilateral.

[1.7.1] Submapping Order In implementation, when the resolution level is even, σ (0) = 0, σ (1) = 1, σ (2) = 2, σ (3) = 3, σ (4) = 0 was used, and when odd, σ (0) = 3, σ (1) = 2, σ (2) = 1, σ (3) = 0, and σ (4) = 3 were used. . This effectively shuffled the submap. Note that there are essentially four types of submappings, and s is one of 0 to 3. However, in practice, processing corresponding to s = 4 was performed. The reason will be described later.

[1.8] Interpolation calculation After the mapping between the start point image and the end point image is determined, the luminance of the corresponding pixels is interpolated. In the experiment, trilinear interpolation was used. A square p _{(i, j)} p _{(i + 1, j)} p _{(i, j + 1)} p _{(i + 1, j + 1)} in the start image plane is a quadrangle q _{f (i, j)} q _{f (i + 1, j in the} end image plane. ₎ Q _{f (i, j + 1)} Assume that q _{f (i + 1, j + 1)} is projected. For simplicity, the distance between images is 1. The pixel r (x, y, t) (0 ≦ x ≦ N−1, 0 ≦ y ≦ M−1) of the intermediate image whose distance from the starting image plane is t (0 ≦ t ≦ 1) is as follows. Is required. First, the position of the pixel r (x, y, t) (where x, y, tεR) is obtained by the following equation.

つづいてｒ（ｘ，ｙ，ｔ）における画素の輝度が次の式を用いて決定される。

Subsequently, the luminance of the pixel at r (x, y, t) is determined using the following equation.

ここでｄｘ及びｄｙはパラメータであり、０から１まで変化する。

Here, dx and dy are parameters and change from 0 to 1.

[1.9] Mapping when imposing constraint conditions We have described the determination of mapping when no constraint conditions exist. However, when a correspondence is defined in advance between specific pixels of the start point image and the end point image, the mapping can be determined using this as a constraint.

  The basic idea is that the starting point image is roughly deformed by a rough mapping in which specific pixels of the starting point image are transferred to specific pixels of the end point image, and then the mapping f is accurately calculated.

First, a specific pixel of the start point image is projected onto a specific pixel of the end point image, and a rough mapping for projecting other pixels of the start point image to an appropriate position is determined. That is, a pixel that is close to a specific pixel is a mapping that is projected near the place where the specific pixel is projected. Here, a rough mapping of the m-th level is described as F ^(m) .

The rough map F is determined as follows. First, a mapping is specified for several pixels. _{N s} pixels for the source image,

を特定するとき、以下の値を決める。

When specifying, the following values are determined.

始点画像の他の画素の変位量は、ｐ_{（ｉｈ，ｊｈ）}（ｈ＝０，…，ｎ_ｓ−１）の変位に重み付けをして求められる平均である。すなわち画素ｐ_{（ｉ，ｊ）}は、終点画像の以下の画素に射影される。

The displacement amount of the other pixels of the starting point image is an average obtained by weighting the displacement of p _{(ih, jh)} (h = 0,..., N _s −1). That is, the pixel p _{(i, j)} is projected onto the following pixels of the end point image.

ただしここで、

Where

とする。

And

Subsequently, the energy D ^{(m, s)} _{(i, j)} of the map f is changed so that the candidate map f near F ^(m) has less energy. To be precise, D ^{(m, s)} _{(i, j)} is

である。ただし、

It is. However,

であり、κ，ρ≧０とする。最後に、前述の写像の自動計算プロセスにより、ｆを完全に決定する。

And κ, ρ ≧ 0. Finally, f is completely determined by the automatic map calculation process described above.

Here, when f ^{(m, s)} (i, j) is sufficiently close to F ^(m) (i, j), that is, their distance is

以内であるとき、Ｅ_２ ^{（ｍ，ｓ）} _{（ｉ，ｊ）}が０になることに注意すべきである。そのように定義した理由は、各ｆ^{（ｍ，ｓ）}（i,j）がＦ^（ｍ）（i,j）に十分近い限り、終点画像において適切な位置に落ち着くよう、その値を自動的に決めたいためである。この理由により、正確な対応関係を詳細に特定する必要がなく、始点画像は終点画像にマッチするように自動的にマッピングされる。

Note that E ₂ ^{(m, s)} _{(i, j)} is zero when The reason for this definition is that as long as each f ^{(m, s)} (i, j) is sufficiently close to F ^(m) (i, j), its value is automatically set so that it will settle at an appropriate position in the end point image. Because we want to decide. For this reason, it is not necessary to specify an exact correspondence relationship in detail, and the start point image is automatically mapped so as to match the end point image.

[2] Specific Processing Procedure A processing flow according to each elemental technique of [1] will be described.
FIG. 6 is a flowchart showing the overall procedure of the base technology. As shown in the figure, first, processing using a multi-resolution singularity filter is performed (S1), and then the start point image and the end point image are matched (S2). However, S2 is not essential, and processing such as image recognition may be performed based on the characteristics of the image obtained in S1.

  FIG. 7 is a flowchart showing details of S1 of FIG. Here, it is assumed that the start point image and the end point image are matched in S2. Therefore, first, the starting point image is hierarchized by a singular point filter (S10), and a series of starting point hierarchical images are obtained. Subsequently, the end point images are hierarchized by the same method (S11), and a series of end point layer images are obtained. However, the order of S10 and S11 is arbitrary, and the start point hierarchical image and the end point hierarchical image can be generated in parallel.

FIG. 8 is a flowchart showing details of S10 in FIG. The size of the original starting point image is 2 ⁿ × 2 ⁿ . Since the start point hierarchical image is created in order from the finer resolution, the parameter m indicating the resolution level to be processed is set to n (S100). Subsequently, a singular point is detected from the m-th level images p ^{(m, 0)} , p ^{(m, 1)} , p ^{(m, 2)} and p ^{(m, 3)} using a singular point filter (S101), The m-1st level images p ^(m-1 , ⁰⁾ , p ^(m-1 , ¹⁾ , p ^(m-1 , ²⁾ , p ^{(m-1, 3)} are generated (S102). Since m = n here, p ^{(m, 0)} = p ^{(m, 1)} = p ^{(m, 2)} = p ^{(m, 3)} = p ⁽ⁿ⁾ , and 4 from one starting point image. A type of sub-image is generated.

FIG. 9 shows a correspondence relationship between a part of the mth level image and a part of the m−1th level image. The numerical values in the figure indicate the luminance of each pixel. In FIG ^{p (m, s)} is intended to symbolize the four images ^{p (m, 0) ~p (} m, 3), when generating the ^{images p (m-1,0), p ( m, s)} is considered to be p ^{(m, 0)} . The rules given in ^{[1.2], p (m-} 1,0) for blocks fill luminance in FIG example, 4 out of the pixels "3" contained ^{therein, p (m-1, 1 )} Is “8”, p ^(m−1,2) is “6”, p ^(m−1,3) is “10”, and this block is replaced with one acquired pixel. Therefore, the size of the sub-image at the (m−1) -th level is 2 ^m−1 × 2 ^m−1 .

  Next, m is decremented (S103 in FIG. 8), it is confirmed that m is not negative (S104), and the process returns to S101 and a sub-image with a coarse resolution is generated. As a result of this iterative process, S10 ends when m = 0, that is, when the 0th level sub-image is generated. The size of the 0th level sub-image is 1 × 1.

  FIG. 10 illustrates the start point hierarchical image generated in S10 for n = 3. Only the first starting point image is common to the four sequences, and thereafter, sub-images are generated independently according to the types of singular points. Note that the processing in FIG. 8 is common to S11 in FIG. 7, and an end point hierarchical image is also generated through the same procedure. Thus, the process by S1 in FIG. 6 is completed.

In the base technology, preparation for matching evaluation is made in order to proceed to S2 in FIG. FIG. 11 shows the procedure. As shown in the figure, first, a plurality of evaluation formulas are set (S30). The energy C ^{(m, s)} _f related to the pixel introduced in [1.3.2.1] and the energy D ^{(m, s)} _f related to the smoothness of the map introduced in [1.3.2.2] is there. Next, a comprehensive evaluation formula is established by integrating these evaluation formulas (S31). The total energy λC ^{(m, s)} _f + D ^{(m, s)} _f introduced in [1.3.2.3] is that, and if η introduced in [1.3.2.2] is used,
ΣΣ (λC ^{(m, s)} _{(i, j)} + ηE ₀ ^{(m, s)} _{(i, j)} + E ₁ ^{(m, s)} _{(i, j)} ) (Formula 52)
It becomes. However, the sum is calculated with 0, 1,..., 2 ^m −1 for i and j, respectively. The matching evaluation is now complete.

  FIG. 12 is a flowchart showing details of S2 of FIG. As described in [1], matching between the start point hierarchical image and the end point hierarchical image is performed between images having the same resolution level. In order to obtain good global matching between images, matching is calculated in order from the level with the coarser resolution. Since the start and end layer images are generated using the singularity filter, the position and brightness of the singularity are clearly preserved even at a coarse level of resolution, and the results of global matching are compared to the conventional case. It will be very good.

As shown in FIG. 12, first, the coefficient parameter η is set to 0 and the level parameter m is set to 0 (S20). Subsequently, a match is calculated between each of the four sub-images at the m-th level in the start point hierarchical image and the four sub-images at the m-th level in the end point hierarchical image, satisfying the bijection condition, and energy. 4 types of sub-mappings f ^{(m, s)} (s = 0, 1, 2, 3) are obtained (S21). The bijection condition is checked using the inherited quadrilateral described in [1.3.3]. At this time, as shown in Expressions 17 and 18, since the submapping at the m-th level is constrained to those at the (m-1) -th level, matching at a level with a coarser resolution is sequentially used. This is a vertical reference between different levels. Although m = 0 and there is no coarser level, this exceptional processing will be described later with reference to FIG.

On the other hand, horizontal reference within the same level is also performed. As shown in Equation 20 of [1.3.3], f ^{(m, 3)} is f ^{(m, 2)} , f ^{(m, 2)} is f ^{(m, 1)} , and f ^{(m, 1)} is f ^{(m, 0)} are determined to be similar to each other. The reason is that even if the types of singular points are different, it is unnatural that the submappings are completely different as long as they are originally included in the same start point image and end point image. As can be seen from Equation 20, the closer the sub-maps, the smaller the energy and the better the matching.

Since there is no submapping that can be referred to at the same level for f ^{(m, 0) to} be determined first, one coarse level is referred to as shown in Equation 19. However, in the experiment, after obtaining up to f ^{(m, 3),} the procedure of updating f ^{(m, 0)} once with this as a constraint was taken. This is equivalent to substituting s = 4 into Equation 20 and making f ^{(m, 4)} a new f ^{(m, 0)} . This is to avoid the tendency that the relation between f ^{(m, 0)} and f ^{(m, 3)} becomes too low, and this measure has improved the experimental results. In addition to this measure, the sub-map shuffle shown in [1.7.1] was also performed in the experiment. This is also intended to keep the degree of association between the submaps originally determined for each type of singularity closely. In addition, as described in [1.7], the position of the start point is changed according to the value of s in order to avoid deflection depending on the start point of processing.

FIG. 13 is a diagram showing how the submapping is determined at the 0th level. At the 0th level, since each sub-image is composed of only one pixel, all four sub-maps ^{f (0, s)} are automatically determined as unit maps. FIG. 14 is a diagram showing how the submapping is determined at the first level. At the first level, each sub-image is composed of 4 pixels. In the figure, these four pixels are indicated by solid lines. Now, when searching for a corresponding point of the point x of p ^{(1, s)} in q ^{(1, s)} , the following procedure is taken.

1. The upper left point a, the upper right point b, the lower left point c, and the lower right point d of the point x are obtained at the first level resolution.
2. The pixel to which the points a to d belong at one coarse level, that is, the 0th level is searched. In the case of FIG. 14, the points a to d belong to the pixels A to D, respectively. However, the pixels A to C are virtual pixels that do not originally exist.
3. The corresponding points A ′ to D ′ of the pixels A to D already obtained at the 0th level are plotted in q ^{(1, s)} . Pixels A ′ to C ′ are virtual pixels, and are assumed to be in the same positions as the pixels A to C, respectively.
4). The corresponding point a ′ of the point a in the pixel A is considered to be in the pixel A ′, and the point a ′ is plotted. At this time, it is assumed that the position occupied by the point a in the pixel A (in this case, the lower right) is the same as the position occupied by the point a ′ in the pixel A ′.
Corresponding points b ′ to d ′ are plotted in the same manner as in 5.4, and an inherited quadrilateral is created with the points a ′ to d ′.
6). The corresponding point x ′ of the point x is searched so that the energy is minimized in the inherited quadrilateral. The candidate for the corresponding point x ′ may be limited to, for example, a pixel whose center is included in the inherited quadrilateral. In the case of FIG. 14, all four pixels are candidates.

  This is the procedure for determining the corresponding point of point x. Similar processing is performed for all other points to determine the submapping. At the level higher than the second level, it is considered that the shape of the inherited quadrilateral gradually collapses. Therefore, as shown in FIG. 3, a situation occurs in which the intervals between the pixels A ′ to D ′ are increased.

When four sub-mappings at a certain m-th level are thus determined, m is incremented (S22 in FIG. 12), it is confirmed that m does not exceed n (S23), and the process returns to S21. Hereinafter, every time the process returns to S21, a sub-mapping with a finer resolution level is gradually obtained, and when the process finally returns to S21, the n-th level mapping f ⁽ⁿ⁾ is determined. Since this mapping is determined with respect to η = 0, it is written as f ⁽ⁿ⁾ (η = 0).

Next, η is shifted by Δη and m is cleared to zero in order to obtain a mapping for different η (S24). After confirming that the new η does not exceed the predetermined search truncation value η _max (S25), the process returns to S21, and the mapping f ⁽ⁿ⁾ (η = Δη) is obtained with respect to the current η. This process is repeated, and f ⁽ⁿ⁾ (η = iΔη) (i = 0, 1,...) Is obtained in S21. When η exceeds η _max , the process proceeds to S26, an optimum η = η _opt is determined by a method described later, and f ⁽ⁿ⁾ (η = η _opt ) is finally set as a map f ⁽ⁿ⁾ .

  FIG. 15 is a flowchart showing details of S21 of FIG. According to this flowchart, the submapping at the m-th level is determined for a certain η. When determining the submapping, the base technology determines the optimum λ for each submapping independently.

As shown in the figure, s and λ are first cleared to zero (S210). Next, a sub-mapping f ^{(m, s)} that minimizes energy is obtained for λ at that time (and implicitly for η) (S211), and this is written as f ^{(m, s)} (λ = 0). In order to obtain a mapping with respect to different λ, λ is shifted by Δλ, it is confirmed that the new λ does not exceed the predetermined search truncation value λ _max (S213), the process returns to S211 and f ^{(m , S)} (λ = iΔλ) (i = 0, 1,...) Is obtained. When λ exceeds λ _max , the process proceeds to S214, the optimum λ = λ _opt is determined, and f ^{(m, s)} (λ = λ _opt ) is finally set as a map f ^{(m, s)} (S214). .

Next, to obtain another submapping at the same level, λ is cleared to zero and s is incremented (S215). It is confirmed that s does not exceed 4 (S216), and the process returns to S211. When s = 4, f ^{(m, 0)} is updated using f ^{(m, 3)} as described above, and the submapping at that level is completed.

FIG. 16 shows the behavior of energy C ^{(m, s)} _f corresponding to f ^{(m, s)} (λ = iΔλ) (i = 0, 1,...) Obtained while changing λ for a certain m and s. FIG. As described in [1.4], as λ increases, C ^{(m, s)} _f usually decreases. However, when λ exceeds the optimum value, C ^{(m, s)} _f starts to increase. Therefore, in the base technology, λ when C ^{(m, s)} _f takes a minimum value is determined as λ _opt . Even if C ^{(m, s)} _f becomes smaller again within the range of λ> λ _opt as shown in the figure, the mapping is already broken at that point and it makes no sense, so pay attention to the first local minimum point. That's fine. λ _opt is determined independently for each sub-mapping, and finally f ⁽ⁿ⁾ is also determined.

On the other hand, FIG. 17 is a diagram showing the behavior of energy C ⁽ⁿ⁾ _f corresponding to f ⁽ⁿ⁾ (η = iΔη) (i = 0, 1,...) Obtained while changing η. Again, when η increases, C ⁽ⁿ⁾ _f usually decreases, but when η exceeds the optimum value, C ⁽ⁿ⁾ _f starts to increase. Therefore, η when C ⁽ⁿ⁾ _f takes the minimum value is determined as η _opt . FIG. 17 may be considered as an enlarged view of the vicinity of zero on the horizontal axis of FIG. If η _opt is determined, f ⁽ⁿ⁾ can be finally determined.

  As described above, according to the base technology, various advantages can be obtained. First, since it is not necessary to detect an edge, it is possible to solve the problem of the conventional technology of the edge detection type. In addition, a priori knowledge about the object included in the image is unnecessary, and automatic detection of corresponding points is realized. The singularity filter can maintain the luminance and position of the singularity even at a coarse resolution level, and is extremely advantageous for object recognition, feature extraction, and image matching. As a result, it is possible to construct an image processing system that greatly reduces manual work.

It should be noted that the following modification technique is also conceivable for this prerequisite technique.
(1) In the base technology, the parameters are automatically determined when matching between the start layer image and the end layer image. However, this method performs matching between two normal images, not between layer images. If available in general.

For example, between two images, the energy E ₀ related to the difference in luminance of the pixels and the energy E ₁ related to the positional deviation of the pixels are used as evaluation expressions, and these linear sums E _tot = αE ₀ + E ₁ are comprehensive evaluation expressions. And Focusing on the vicinity of the extreme value of this comprehensive evaluation formula, α is automatically determined. That is, a mapping that minimizes E _tot for various α is obtained. Among these mappings, α when E ₁ takes a minimum value with respect to α is determined as an optimum parameter. The mapping corresponding to that parameter is finally regarded as the optimal matching between both images.

In addition to this, there are various methods for setting the evaluation formula. For example, a value that takes a larger value as the evaluation result is better, such as 1 / E ₁ and 1 / E ₂ , may be adopted. The comprehensive evaluation formula is not necessarily a linear sum, and an n-th power sum (n = 2, 1/2, −1, −2 etc.), a polynomial, an arbitrary function, or the like may be appropriately selected.

  The parameter may be either α, two cases of η and λ as in the base technology, or more than that. If the parameter is 3 or more, change it one by one.

(2) In the base technology, after determining the mapping so that the value of the comprehensive evaluation formula is minimized, a point where C ^{(m, s)} _f ^, which is one evaluation formula constituting the comprehensive evaluation formula, is minimized is detected. Parameters were determined. However, instead of such a two-stage process, it is effective to determine parameters so that the minimum value of the comprehensive evaluation formula is minimized in some situations. In that case, for example, αE ₀ + βE ₁ may be set as a comprehensive evaluation formula, and a constraint condition of α + β = 1 may be set to treat each evaluation formula equally. This is because the essence of automatic parameter determination is that the parameter is determined so that the energy is minimized.

(3) In the base technology, four types of sub-images relating to four types of singular points are generated at each resolution level. However, of course, one, two, and three of the four types may be selectively used. For example, if there is only one bright point in the image, a corresponding effect should be obtained even if a hierarchical image is generated using only f ^{(m, 3)} related to the maximum point. In this case, since different submappings at the same level are not required, there is an effect of reducing the amount of calculation regarding s.

(4) In the base technology, when the level is advanced by one by the singularity filter, the pixel becomes 1/4. For example, a configuration in which 3 × 3 is one block and a singular point is searched for is possible. In this case, the pixel becomes 1/9 when the level advances by one.

(5) If the start point image and the end point image are in color, they are first converted to a black and white image and a mapping is calculated. The starting point color image is converted using the mapping obtained as a result. As another method, a submapping may be calculated for each component of RGB.

[Embodiment related to image interpolation]
An image interpolation technique using the above prerequisite technique will be described. According to this technique, a plurality of face images having different facial expressions are input, and a facial image in which an arbitrary facial expression is projected can be generated using this. For example, if a plurality of different facial expressions such as “joy”, “anger”, “sadness”, and “fun” are input, various facial expressions can be generated.
FIG. 18 is a diagram for explaining the outline of the technology according to the embodiment. FIG. 18A, FIG. 18B, FIG. 18C, and FIG. 18D are four key frames that are face images of the same person with different facial expressions. The key frame is a real image that has been captured and prepared in advance, and an object of the embodiment is to generate an intermediate frame shown in FIG. 18E from these key frames. The key frame in FIG. 18 (a) and the key frame in FIG. 18 (b) form a first image pair, and the key frame in FIG. 18 (c) and the key frame in FIG. 18 (d) form a second image pair. To do. The target intermediate frame cannot be generated correctly in either the first image pair or the second image pair, and both can be generated together. This is because the intermediate frame is generated by interpolating a plurality of key frames in two vertical and horizontal directions.

  By generating an intermediate frame according to the user's preference according to the embodiment, a face image with an arbitrary expression can be generated from a few key frames. The face image generated in this way is useful for attaching to an e-mail in order to convey his / her emotions to the e-mail destination, or for a photo processing tool that can adjust the expression as desired after shooting. .

  FIG. 19 is a configuration diagram of the image interpolation apparatus 10 according to the embodiment. The image interpolation apparatus 10 includes a GUI (graphical user interface) 12 that interacts with a user, an intermediate frame position acquisition unit 14 that acquires position information 28 of an intermediate frame to be generated via the GUI 12, and A key frame storage unit 16 that stores a plurality of key frames in which facial expressions are copied in advance, and a key frame necessary for generating an intermediate frame in which intermediate facial expressions are copied based on the position information 28 Are selected from the key frame storage unit 16 and the matching processor 18 performs matching calculation based on the base technology, and the corresponding point file storage unit 20 that records the corresponding point information between the key frames obtained as a result as a corresponding point file; Intermediate frame generation for generating an intermediate frame by interpolation calculation based on the corresponding point file and the position information 28 Including the 22. The apparatus 10 further includes a display unit 24 that displays the generated intermediate frame on the screen, and a communication unit 26 that transmits the intermediate frame to the outside as necessary.

  FIG. 20 shows the positional relationship between spatially distributed key frames and intermediate frames. Each key frame is arranged in a matrix at predetermined intervals, and an intermediate frame to be generated is positioned between these key frames.

  Here, nine key frames, ie, a first key frame I1 to a ninth key frame I9 are prepared. When the position of the intermediate frame to be generated is acquired as the intermediate frame Ic in the figure through the GUI 12, the key frame surrounding the intermediate frame Ic (hereinafter referred to as “target key frame”) is first key frame I1, The second key frame I2, the fourth key frame I4, and the fifth key frame I5 are specified. The first key frame I1 and the second key frame I2 are determined as the first image pair, and the fourth key frame I4 and the fifth key frame I5 are determined as the second image pair. Subsequently, the position occupied by the intermediate frame Ic in the quadrilateral formed by these four key frames is obtained geometrically. Subsequently, an intermediate frame image is generated by interpolation described later.

  In this process, the position occupied by the intermediate frame in FIG. 20 and the target key frame are specified by the intermediate frame position acquisition unit 14. The key frame of interest is notified to the matching processor 18, where matching calculation based on the base technology is performed between the first image pair and the second image pair. Each matching result is recorded in the corresponding point file storage unit 20 as a corresponding point file.

  The position information of the intermediate frame acquired by the intermediate frame position acquisition unit 14 is sent to the intermediate frame generation unit 22. The intermediate frame generation unit 22 performs interpolation calculation based on the position information and the two corresponding point files.

  FIG. 21 shows an interpolation method. Here, when the first key frame I1, the second key frame I2, the fourth key frame I4, and the fifth key frame I5 are schematically indicated by points P1, P2, P4, and P5, respectively, Assume that the position of the point Pc schematically showing the intermediate frame satisfies the following condition.

“A line segment connecting a point Q that internally divides the side connecting P1 and P2 to s: (1-s) and a line segment connecting the point R that internally divides the side connecting P4 and P5 to s: (1-s) (1 -T): Divide into t "
The intermediate frame generation unit 22 first generates an image corresponding to the point Q by interpolation based on a ratio of s: (1-s) based on the corresponding point file relating to the first image pair. Subsequently, an image corresponding to the point R is generated by interpolation based on a ratio of s: (1-s) based on the corresponding point file relating to the second image pair. Finally, these two images are generated by interpolation with a ratio of (1-t): t.
FIG. 22 shows a processing procedure of the image interpolation apparatus 10. First, the display unit 24 displays a plurality of key frames arranged in a matrix. When the user indicates an arbitrary position in the matrix with the mouse button, the position is acquired as the position of the intermediate frame (S1000).

  Subsequently, the intermediate frame position acquisition unit 14 selects the above-described four frames as the key frame of interest (S1002), and transmits this to the matching processor 18. The matching processor 18 reads the images of those key frames from the key frame storage unit 16, and performs matching calculation for the first image pair and the second image pair, respectively (S1004). The result is stored in the corresponding point file holding unit 20 as two corresponding point files.

  The intermediate frame generation unit 22 first obtains the points Q and R of FIG. 21 individually from these corresponding point files, and then obtains the intermediate frame by interpolation (S1006). Finally, the generated intermediate frame is displayed (S1008). The intermediate frame is output to the network as necessary.

  FIG. 23 exemplifies a GUI for the user to specify an arbitrary expression on the new e-mail creation screen. On this screen, a facial expression designation field 32 is displayed in addition to fields for inputting an e-mail address, title, body text, and the like. Facial marks indicating joy, anger, sadness, and enjoyment are displayed at the four corners of the facial expression designation field 32, and the user moves the mouse pointer 36 between them to set the mark 34 to an arbitrary point. Based on the positional relationship between the mark 34 and the four face marks, intermediate frames of four face images recorded in advance are generated and attached to the e-mail. The recipient can guess the mail creator's feelings based on the facial expression attached.

  The embodiment has been described above. Here, interpolation is performed based on a quadrilateral, but this may be performed based on a triangle. In addition, the corresponding point file is generated each time, but it may be generated by calculating between key frames in advance. Naturally, in that case, the generation of the intermediate frame can be realized at a higher speed, and the attachment to the e-mail can also be processed at a higher speed.

  In FIG. 23, the facial expression designation field 32 is configured in such a way as to require the user to designate a two-dimensional position. For example, this is a form in which each parameter of joy, anger, sadness, and fun is designated numerically. Alternatively, the numerical value may be finely adjusted with a lever or scroll on the screen. It is also possible to prepare face images of a plurality of facial expressions to which other emotions such as surprise and normal are further added and specify the degree thereof. The generated specific face image may be set as an image attached by default.

  In addition to attaching a face image to an e-mail, for example, this technique can also be used for photo processing software. In this software, a face image with an arbitrary expression can be created based on a plurality of face images input by a user, and the plurality of face images to be input do not necessarily have the same person as a subject. It may be a non-human animal. In this case, face images obtained by morphing various faces can be easily generated at an arbitrary blend rate.

  This technique may be applied to an ID photo camera. In this case, the subject is photographed four times and the digital image is displayed in a matrix on the screen. The subject specifies an arbitrary point between the four images, and an intermediate frame that is interpolated according to the position is finally printed. If the photographer consciously creates a different facial expression in front of the camera, it is easy to adjust to the desired facial expression after shooting. In addition, when the eye blinks or the line of sight is not fixed in the direction of the camera lens, this can be easily adjusted later.

FIG. 1 (b) is an image obtained by applying an averaging filter to the faces of two persons, and FIGS. 1 (c) and 1 (d) are assumptions regarding the faces of the two persons. image ^{p (5, 0)} obtained by the technique, the image shown in FIG. 1 (e) and and 1 (f) show the subimages, ^p sought base technology with respect to the face of Futari person ^(5,1), FIG. 1 (g ) And FIG. 1 (h) are images of p ^(5,2) required by the base technology regarding the faces of the two persons, and FIGS. 1 (i) and 1 (j) are base technologies regarding the faces of the two persons. ⁵ is a halftone image photograph in which images of p ^{(5, 3)} obtained by the above are respectively displayed on a display. FIG. 2 (R) is a diagram showing the original quadrilateral, and FIG. 2 (A), FIG. 2 (B), FIG. 2 (C), FIG. 2 (D), and FIG. FIG. It is a figure which shows the relationship between a starting point image and an end point image, and the relationship between the m-th level and the m-1st level using an inheritance quadrilateral. It is a diagram showing the relationship between parameters η and energy C _f. FIG. 5A and FIG. 5B are diagrams illustrating a state in which whether or not a mapping related to a certain point satisfies the bijection condition is calculated from outer product calculation. It is a flowchart which shows the whole procedure of a premise technique. It is a flowchart which shows the detail of S1 of FIG. It is a flowchart which shows the detail of S10 of FIG. It is a figure which shows the correspondence of a part of image of a m-th level, and a part of image of a m-1st level. It is a figure which shows the starting point hierarchy image produced | generated by the base technology. It is a figure which shows the procedure of the preparation of matching evaluation before progressing to S2 of FIG. It is a flowchart which shows the detail of S2 of FIG. It is a figure which shows a mode that a submapping is determined in the 0th level. It is a figure which shows a mode that a submapping is determined in a 1st level. It is a flowchart which shows the detail of S21 of FIG. It is a figure which shows the behavior of energy C ^{(m, s)} _f corresponding to f ^{(m, s)} (λ = iΔλ) obtained while changing λ for a certain f ^{(m, s)} . It is a figure which shows the behavior of energy C ⁽ⁿ⁾ _f corresponding to f ⁽ⁿ⁾ (η = iΔη) (i = 0, 1,...) obtained while changing η. FIGS. 18A to 18E are diagrams schematically showing four key frames and an intermediate frame to be generated in the embodiment. It is a block diagram of the image interpolation apparatus which concerns on embodiment. It is a figure which shows notionally the positional relationship of the intermediate | middle frame which should be produced | generated by embodiment, and the key frame used as it. It is a figure which shows the method of the interpolation process implemented with the image interpolation apparatus of embodiment. It is a flowchart which shows the process sequence of the image interpolation apparatus of embodiment. It is a figure which illustrates GUI for a user to designate arbitrary facial expressions in the new creation screen of an email.

Explanation of symbols

10 Image Interpolation Device 12 GUI
14 Intermediate frame position acquisition unit 16 Key frame storage unit 18 Matching processor 20 Corresponding point file holding unit 22 Intermediate frame generation unit 24 Display unit 26 Communication unit

Claims (15)

Obtaining a first image pair composed of two key frames each including a face captured with an arbitrary expression as a subject, and first corresponding point information between the two key frames;
Obtaining a second image pair consisting of two key frames each including a face captured with an arbitrary expression as a subject, and second corresponding point information between the two key frames;
A positional relationship between a first axis that is temporally or spatially defined between two key frames of the first image pair and a second axis that is temporally or spatially defined between two key frames of the second image pair; Using the one corresponding point information and the second corresponding point information to generate, by interpolation, an intermediate frame in which a face with an intermediate expression should be projected;
An image interpolation method characterized by comprising: Arranging the plurality of acquired key frames in a matrix at predetermined intervals and displaying them on a screen;
Allowing the user to specify any point on the screen;
Further including
The method according to claim 1, wherein the interpolation is performed based on a positional relationship between the designated point and a plurality of key frames.   The method according to claim 1, wherein the two key frames of the first image pair and the two key frames of the second image pair are face images that are copied with different facial expressions of the same person. Performing a matching calculation on a first image pair composed of two key frames each including a face photographed in an arbitrary expression as a subject, and detecting first corresponding point information between the two key frames;
Performing a matching calculation on a second image pair composed of two key frames each including a face photographed with an arbitrary expression as a subject, and detecting second corresponding point information between the two key frames;
A positional relationship between a first axis determined temporally or spatially between two key frames of the first image pair and a second axis determined temporally or spatially between the two key frames of the second image pair; An image interpolation method, wherein an intermediate frame in which a face with an intermediate expression is to be projected is generated by interpolation using one corresponding point information and second corresponding point information. A step of arranging a plurality of key frames each including a face captured with an arbitrary expression in a subject at a predetermined interval in a matrix and displaying on a screen;
Allowing the user to specify any point on the screen;
Generating an intermediate frame by interpolation based on a positional relationship between the designated point and a plurality of key frames, in which a face having an intermediate expression is to be projected;
An image interpolation method characterized by comprising: A unit for storing a plurality of key frames each including a face photographed in an arbitrary expression as a subject;
A unit for obtaining temporal or spatial positional information of an intermediate frame in which an intermediate facial expression is to be projected in relation to a key frame;
A first image pair each consisting of two key frames, corresponding point information determined for each second image pair, and a unit for generating an intermediate frame by interpolation processing based on the position information;
A first axis that is temporally or spatially defined between the two key frames of the first image pair and a second axis that is temporally or spatially defined between the two key frames of the second image pair. An image interpolating apparatus characterized in that the image pairs are selected so as not to be on a straight line. A unit for arranging a plurality of key frames in a matrix at predetermined intervals and displaying them on a screen;
The apparatus according to claim 6, further comprising a user interface for inputting a designation regarding a temporal or spatial position of the intermediate frame from the outside.   The device according to claim 6, wherein the two key frames of the first image pair and the two key frames of the second image pair are face images captured by different expressions of the same person. A unit that displays a plurality of key frames each containing a face captured with an arbitrary expression in a matrix at predetermined intervals and displayed on a screen;
A unit that acquires position information of an arbitrary point specified by the user on the screen;
A unit that generates, by interpolation, an intermediate frame on which a face having an intermediate expression is to be projected based on a positional relationship between the designated point and a plurality of key frames;
An image interpolating apparatus comprising: Obtaining a first image pair composed of two key frames each including a face captured with an arbitrary expression as a subject, and first corresponding point information between the two key frames;
Obtaining a second image pair consisting of two key frames each including a face captured with an arbitrary expression as a subject, and second corresponding point information between the two key frames;
A positional relationship between a first axis that is temporally or spatially defined between two key frames of the first image pair and a second axis that is temporally or spatially defined between two key frames of the second image pair; Using the one corresponding point information and the second corresponding point information to generate, by interpolation, an intermediate frame in which a face with an intermediate expression should be projected;
A computer program for causing a computer to execute. A step of arranging a plurality of key frames each including a face captured with an arbitrary expression in a subject at a predetermined interval in a matrix and displaying on a screen;
Allowing the user to specify any point on the screen;
Generating an intermediate frame by interpolation based on a positional relationship between the designated point and a plurality of key frames, in which a face having an intermediate expression is to be projected;
A computer program for causing a computer to execute. Displaying a plurality of images corresponding to various facial expressions to the user;
Obtaining instructions from the user regarding mixing of the images;
According to the instructions, generating a new image corresponding to a facial expression that did not originally exist;
Including
The image interpolation method, wherein the instruction is acquired in a form including a blending ratio of the plurality of images at the time of mixing.   The method according to claim 12, wherein the blending ratio is determined from a relationship between a display position of the images on the screen on which the plurality of images are displayed and an action position at which the user inputs an instruction on the screen. A function to display a plurality of images corresponding to various facial expressions to the user;
A function to obtain instructions from the user regarding the mixing of these images;
According to the instructions, a function to generate a new image corresponding to a facial expression that did not exist at first,
With
The image editor, wherein the instruction is acquired in a form including a blending ratio of the plurality of images at the time of mixing.   An image interpolation method characterized by generating a new image corresponding to a facial expression that did not originally exist by performing interpolation processing on at least three images corresponding to various facial expressions.

Images