JP2008252856A - Method of correcting image, correction program, and apparatus of correcting image distortion - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a technique capable of performing skew correction even in a case where characters in a document image are not arranged linearly or even in a case where a linear portion is not present in a character, and a technique also applicable to correction of an image subjected to deformation such as shading transform or affine transform. <P>SOLUTION: A geometrical estimation technique combining invariant and variant is used to estimate a deformation amount and on the basis of the estimation, an image is corrected. In an embodiment, a change in the variant (e.g., area of circumscribed rectangle of character) is measured while rotating various character fonts in advance, and this is stored as a case together with the invariant (e.g., areas of black pixels and white pixels in a character convex closure). The case is then called by the rotation invariant calculated from connection components (most of which correspond to single characters) in an image desired to be corrected, and a rotary angle of a character is obtained from rotation variant calculated similarly. When a simple inclination estimation experiment is done using 44 pieces of samples of document image, precision is obtained that error is less than or equal to 1 degree for 22 pieces of samples and error is less than or equal to 2 degrees for 42 pieces of samples. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention generally relates to an image correction method, a correction program, and an image distortion correction apparatus. More particularly, the present invention relates to a method, a program, and an apparatus for correcting a geometric deformation received by an image.

In character recognition for document images, estimation and compensation of geometric deformation (geometric deformation) is one of important problems. Here, the “document image” is a kind of image and is a document recorded as an image. Some of them may include images other than characters such as photographs and illustrations. For example, with regard to characters in a document image acquired by a scanner, rotational deformation due to the inclination (skew) of the paper has been an important problem. As will be described later, there are a great many research examples of this skew correction.
On the other hand, in the case of a document image acquired by a camera, the geometric deformation received by characters in the image becomes more diverse and complicated (see, for example, Non-Patent Document 1). For example, projective transformation distortion due to the camera and the paper not facing each other, and non-linear distortion due to the paper itself not being flat may occur. These distortion correction methods are called dewarping and are currently being actively studied along with the rise of camera-based character recognition.

  In the process using a digital camera, the image deteriorates due to non-uniform illumination and focus shift that cannot occur with a scanner, and projection distortion that occurs when an object is photographed from an oblique direction. difficult. Nevertheless, the reason for using a digital camera instead of a scanner is its portability and simplicity. For example, since it takes time and labor to install a scanner, it is not suitable for applications where the scanner is easily moved or carried around. Also, it cannot be used for large objects that cannot be moved, such as posters and billboards. On the other hand, with a digital camera, you can easily shoot when you think of it, and it has the potential to develop into a new form of use that has never existed before.

  There are many research examples on document image tilt correction methods. Many of them use the general features of document images. For example, a typical example is a method based on the peripheral distribution obtained while changing the rotation angle. On the other hand, several methods for estimating the rotation angle of the entire document image by estimating the inclination angle for each local region (for example, connected components) and integrating the inclination angle over the entire image have been proposed. They are outlined below.

  First, in Non-Patent Document 2, a local region of a certain size circle is extracted from an image, and a change in pixel value of a document on a straight line drawn in the circle is measured. A straight line is drawn by changing the angle, and the angle direction of the straight line where the change is the largest is taken as the rotation angle estimation result of the local region. Also, as an integration method, the angle of the straight line with the largest change is set as the rotation angle of the entire document.

  Next, in Non-Patent Document 3, feature points are first detected from connected components in a certain local region. For each feature point, a straight line representing the approximate direction of rotation is obtained by comparing line segments between the three nearest feature points, and a final number is obtained by least square approximation using a certain number of points within a minute distance. A straight line representing a local rotation angle is obtained. This operation is performed for each feature point, the result is voted, and the rotation angle as a whole is obtained.

  Further, in Non-Patent Document 4, first, for a certain connected component, connected components satisfying a certain neighborhood condition are combined to form an expanded connected component. Next, a straight line is drawn between the two pixels that are the farthest points, and the angle is set as the local rotation angle. Here, the neighborhood condition is such that, for example, the straightness of the character line is taken into consideration. If there is no connected component that satisfies the condition, the local rotation angle cannot be obtained. The above processing is performed for each connected component, and the median of the plurality of local rotation angles obtained is set as the entire rotation angle.

  Further, since correction of projective distortion of a document image is a basic problem in document image processing using a camera, various studies have already been performed. They can be broadly divided into (1) a method using a document frame, (2) a method using a character line in a document, and (3) a method using stereo vision.

  The method (1) is based on the premise that the document frame is rectangular and can be clearly obtained from the photographed document image. If the rectangle is affected by the projective distortion, the parallelism of the opposite side, which should be parallel, is lost, so that it becomes a general rectangle in the acquired image. Here, if conversion that returns to a rectangle using information that the rectangle was originally a rectangle is obtained, the document image that has undergone the projection distortion can be restored to a directly opposed image (see, for example, Non-Patent Document 5). ). It is also mounted on a commercially available digital camera (such as Ricoh Caplio (registered trademark) R6).

Method (2) assumes parallelism of character lines. For example, Non-Patent Document 5 proposes a method for estimating the inclination from the vanishing point. Non-Patent Document 5 describes both the method (1) and the method (2). In this method, first, a character line in a document image is extracted to obtain a vanishing point in the horizontal direction of the document. Next, assuming that both ends of the character line are almost aligned, three straight lines of the right end, the center, and the left end of the character line are estimated, and the vanishing point in the vertical direction of the document is also obtained. Using the two vanishing points obtained in this way, the document image that is directly facing is restored.
(3) is a method for restoring a three-dimensional shape using a plurality of cameras (for example, see Non-Patent Document 6) or moving images (for example, see Non-Patent Document 7).

Koichi Kise, Shinichiro Omachi, Seiichi Uchida, Masakazu Iwamura, "Recognition and Understanding of Characters and Documents Using Digital Cameras" IEICE Journal, vol.89, no.9, pp.36-841, Sep. 2006. Y.Ishitani, "Document Skew Detection Based on Local Region Complexity," Proc. Int. Conf. Doc. Anal. Recog., Pp.49-52, 1993. X.Jiang, H.Bunke, and D.Widmer-Kljajo, "Skew Detection of Document Images by Focused Nearest-Neighbor Clustering," Proc. Int. Conf. Doc. Anal. Recog., Pp.629-632, 1999. Y.Lu and C.L.Tan, "Improved Nearest Neighbor Based Approach to Accurate Document Skew Estimation," Proc. Int. Conf. Doc. Anal. Recog., Pp.503-507, 2003. P. Clark and M. Mirmehdi, "Recognising text in real scenes," Int'l Journal of Document Analysis and Recognition, vol.4, pp.243-257, 2002. CH Lampert, T. Braun, A. Ulges, D. Keysers and TM Breuel, "Oblivious document capture and real-time retrieval", Proc. First Int'l. Workshop on Camera-Based Document Analysis and Recognition, pp. 79- 86, Aug. 2005. Akihiko Ikeda, Tomokazu Sato, Kiyoshi Ikeda, Noriyuki Kanbara, Noboru Nakajima, Naokazu Yokoya, "Super-resolution video mosaic for paper, estimated by camera parameters," IEICE (D), vol.J88-D, no .8, pp.1490-1498, Aug. 2005.

  All of the above-described skew correction methods assume local linearity of the document. That is, it is an assumption that, among the components constituting the document image, some connected components in the vicinity form a straight character line, or a character has a straight line portion. However, there are cases where such assumptions do not hold. That is, the characters in the document image may not be arranged in a straight line. Or it is a case where a linear part does not exist in a character. Therefore, there is a demand for a technique that can correct skew without using such assumptions.

  In addition to skew correction of document images, a more universal method that can be applied to correction of geometric deformation with a higher degree of freedom, that is, correction of images that have undergone geometric deformation such as projective transformation or affine transformation. Is desired. As described above, document image processing using a digital camera may produce an excellent application, but its realization is not easy. The reason is that many existing document image processing techniques target document images acquired by a scanner. That is, in order to apply an existing technique to a document image acquired by a digital camera, it is necessary to convert and correct the document image acquired by the digital camera and obtain an image as if it was acquired by a scanner. Of the deterioration of document images caused by using a digital camera, a method for correcting projection distortion is desired. That is, there is a demand for a technique capable of obtaining a document image facing directly as obtained by a scanner from a document image taken obliquely by a digital camera.

The method (1) described above uses a reasonable assumption that many document frames are rectangular, but requires the entire document image including the frame to be photographed.
Further, the method (2) has a problem in that the application range is limited because a strong assumption is imposed on the layout of the document. This is because it cannot be applied to a page with a special layout, and even if the layout is general, it is not easy to estimate both ends of a character line on a page containing many figures and mathematical expressions in a document.

The above methods (1) and (2) cannot be applied to images whose layout is complicated (character lines are not parallel) and whose frame does not include a document frame (for example, FIG. 16).
The method (3) is not intended for an image photographed using a single still camera, and differs from the present invention in the number and type of devices used.

  The present invention has been made in consideration of the above-described circumstances, and provides a distortion correction method that can be applied to correction of an image subjected to geometric deformation belonging to projective transformation, affine transformation, similarity transformation, and the like. .

  The present invention relates to a method for correcting an image subjected to geometric deformation by inputting the image subjected to geometric deformation, the step of dividing the input image into local patterns which are local patterns, For the pattern, a calculation step for calculating an invariant whose value is substantially constant according to the degree of deformation and a variable whose value changes according to the degree of deformation based on a predetermined procedure, and each based on the calculated invariant A step of classifying a local pattern into one of a plurality of categories, an estimation step of estimating the degree of deformation received by the local pattern based on a variable calculated for each local pattern of each category, and an image based on the estimation result And an image correction method, wherein each step is performed by a computer.

  Also, from a different point of view, the present invention is a program for correcting an image subjected to geometric deformation as an input, and correcting the deformation received by the image. And a calculation process for calculating, based on a predetermined procedure, an invariant whose value is substantially constant according to the degree of deformation and a variable whose value changes according to the degree of deformation for each local pattern A process for classifying each local pattern into one of a plurality of categories based on the invariant, and an estimation process for estimating the degree of deformation received by the local pattern based on the variable calculated for each local pattern in each category And an image correction program that causes a computer to execute processing for correcting an image based on the estimation result.

  Furthermore, from a different point of view, the present invention is an apparatus that receives an image subjected to geometric deformation as an input and corrects the deformation received by the image, and divides the input image into local patterns that are local patterns. A division unit that calculates, for each local pattern, a calculation unit that calculates an invariant whose value is substantially constant according to the degree of deformation and a variable whose value changes according to the degree of deformation based on a predetermined procedure. A classification unit that classifies each local pattern into one of a plurality of categories based on the invariant, and an estimation unit that estimates the degree of deformation received by the local pattern based on the variable calculated for each local pattern in each category. And a correction unit that corrects the image based on the estimation result.

  In other words, the feature of the present invention in the first aspect is that only the “variable” and “invariant” for a specific geometric deformation is used to estimate the degree of geometric deformation (deformation amount) that the object has received. There is in point to do. Taking a skew or rotation as an example of a specific geometric deformation, a rotation angle is estimated by combining a feature amount whose value changes with rotation and a feature amount that does not change. Therefore, the present invention takes a completely different approach from the conventional skew correction method that uses the inclination of the character line and the inclination of the vertical and horizontal strokes of each character as a clue.

  Further, the feature of the present invention in the second aspect is that, unlike the first aspect, the amount of deformation is estimated based on an example. This feature will be described below assuming a simple formula. Now, if the category of each character pattern in the document is known, the standard pattern of that category is superimposed on the pattern while rotating, and the rotation angle with the largest overlap is the estimated rotation angle of that character. Let's go. In the case of this simple method, it can be said that the rotation angle is estimated by taking all the standard patterns rotated at various angles as examples and comparing the character patterns in the document with each example. However, this simple method has a first problem that the number of cases becomes enormous when considering the range of rotation angle and enlargement / reduction, which is not practical. In addition, the category of each character pattern in the document is unknown in the first place, so the second problem of how to select cases remains. Therefore, for the first problem, a scalar amount called a variable is used as an example to improve the efficiency of deformation amount estimation. For the second problem, the above invariant is used so that the case can be referred to even if the category is unknown.

The document image correction method according to the present invention includes a step of classifying each local pattern into one of a plurality of categories based on the calculated invariant, and a local pattern based on the variable calculated for each local pattern of each category. An estimation step for estimating the degree of deformation received, and a step for correcting the image based on the estimation result. Therefore, the category is determined using the invariant of the local pattern, and the category and the variable of the local pattern are determined. The degree of geometric deformation can be estimated using and and the image can be corrected based on the estimation result. Therefore, the present invention can be applied not only to skew correction of a document image but also to correction of an image subjected to geometric deformation having a higher degree of freedom, that is, an image subjected to geometric deformation belonging to projective transformation or affine transformation.
In addition, if the skew correction of the document image is performed using the correction method of the present invention, the rotation angle can be accurately determined even when the assumption that has been generally used in the past is not satisfied that the characters have a linear partial shape and alignment. It becomes possible to correct. That is, even when characters as local patterns in a document image are not arranged in a straight line, or even when characters with many curves such as hiragana are dominant, the rotation angle can be accurately estimated.

  Further, the document image correction program according to the present invention includes a process for classifying each local pattern into one of a plurality of categories based on the calculated invariant, and a variable calculated for each local pattern in each category. Since the computer executes an estimation process for estimating the degree of deformation received by the local pattern and a process for correcting the image based on the estimation result, the category is determined using the invariant of the local pattern, and the category and The degree of geometric deformation can be estimated using the local pattern variables, and the image can be corrected based on the estimation result. Therefore, the present invention can be applied not only to skew correction of a document image but also to correction of an image subjected to geometric deformation having a higher degree of freedom, that is, an image subjected to geometric deformation belonging to projective transformation or affine transformation.

Hereinafter, preferred embodiments of the present invention will be described.
In the correction method and the correction program according to the present invention, the geometric deformation may be projective transformation, affine transformation, or similarity transformation.

  The image may be a document image, and at least a part of the local pattern may be a character pattern.

  Further, the geometric deformation is rotation, the variable is a value that changes by rotating the local pattern, and the invariant may be a substantially constant value even if the local pattern is rotated.

  The geometric deformation may be projective transformation, the variable may be a value that varies with depth, and the invariant may be a substantially constant value with respect to a change in depth.

Further, the variable may be a rectangular area circumscribing the local pattern.
Alternatively, the variable may be the area of the black pixel portion of the local pattern.

Still further, the invariant may be an area within the convex hull of the local pattern.
Here, the convex hull refers to a convex polygon having a minimum area among convex polygons including a certain pattern (here, a local pattern). A convex polygon means a polygon in which the inner angles of the tops are all less than 180 degrees.

  The local pattern may be a pattern divided as a connected component in the image or a set of the patterns.

Each category has q _{c as} the invariant for that category and q _{x as} the invariant for each local pattern.
(Where ε is a predetermined constant)
It may consist of a local pattern that satisfies this relationship.

  Furthermore, the estimation step tentatively estimates the degree of deformation for each local pattern by comparing a variable calculated from each local pattern with a reference value stored in advance corresponding to each category. Each result may be statistically processed to estimate the degree of deformation.

  Further, the reference value may be a variable in which the standard pattern of each category is deformed step by step to measure a variable, and the deformation amount of each step and the measured variable are stored in association with each other.

The estimation step temporarily estimates the degree of deformation for each category based on the relationship between the position of each local pattern and the variable of the local pattern, and statistically processes each temporarily estimated result to determine the degree of deformation. May be estimated.
Specifically, for example, the area of the connected component is used as the “variable”, and the area ratio is used as the “invariant”. These values are basic quantities that can be calculated from any document and can be calculated easily, so that the rectangular frame of the document is completely visible as in other methods, and the characters in the document Does not impose strong restrictions on the layout such as being aligned on a straight line. Therefore, it can be applied to a wide range of objects, including documents with a unique layout shown in FIG.

  The input image is a document image, the geometric deformation is projective transformation, the variable is the area of the black pixel portion of the local pattern, and the invariant is the area within the convex hull of the local pattern, In the estimation step, provisional estimation of the inclination of the paper surface of the document image may be performed based on the relationship between the area of the black pixel portion of each local pattern and its position on the paper surface.

  The various preferred embodiments shown here can also be combined together.

Hereinafter, the present invention will be described in more detail with reference to the drawings. In addition, the following description is an illustration in all the points, Comprising: It should not be interpreted as limiting this invention.
<< Embodiment 1 >>
In this embodiment, first, the procedure will be described by taking as an example the case of applying the technique of the present invention to skew correction of a document image. A quantitative and qualitative description of the correction result will be described later in Experimental Example 1.

  However, the technical idea of the present invention is not limited to this, and can be applied in principle to correction of an image subjected to geometric deformation with a higher degree of freedom such as projective transformation or affine transformation. Further, the correction target is not limited to the document image, and any image including a predetermined pattern can be applied in principle. General geometric deformation and expansion to a correction target will be described after describing skew correction of a document image.

1. Gradient estimation using a combination of variables and invariants This section describes a method for estimating geometric deformation using a combination of variables and invariants. As described above, rotation will be described as an example of geometric deformation. Further, the correction target is also limited to document images. If the skew correction of the document image is performed using the correction method of the present invention, the rotation angle can be accurately corrected even when the generally used assumption that characters have a linear partial shape and alignment is not satisfied. It becomes possible. That is, even when characters as local patterns in a document image are not arranged in a straight line, or even when characters with many curves such as hiragana are dominant, the rotation angle can be accurately estimated.

1-1. Principle of tilt estimation First, prepare standard patterns for character categories that may exist in the document image. As described above, if all the rotated images of this standard pattern are registered as examples, all of them are compared with each character (connected component) in the input document image, and the angle of the rotated standard pattern image most matched From this, the rotation angle of the document image can be estimated. This simple method of powering is very clear but clearly inefficient.

  Therefore, the present invention performs efficient tilt estimation by using a rotation variable as an example. Cases are collected as a preparation stage for estimation. When the collection of cases is finished, the inclination of the input document image is estimated using the result. For ease of understanding, it is assumed in this description that the category of a certain character in the input document image is known as c. (This assumption is unnecessary by the method described later.)

1-1-1. Collection of cases (learning steps)
The variable p is measured while rotating the standard pattern of each category c little by little. This is stored as a relation p = _pc (θ) between the rotation angle θ and the variable p. It is a kind of learning step and is also a collection stage of cases. The category set is “A” to “Z” and “a” to “z” in the case of an English document image.

1-1-2. Inclination estimation (estimation step)
A variable p _x is obtained for a (tilted) character pattern x in the input document image. If the category is c, θ satisfying p _x = p _c (θ) is a candidate for the rotation angle of the input document image. This θ can be obtained by creating a reverse lookup table for the one-dimensional function p _c (θ), which requires a small amount of calculation with O (1).
In this way, using the rotation variable makes it possible to estimate the inclination very easily. In the following, the estimation method for category c, the details of the estimation steps, and the variables and invariants actually used are described.

1-2. Estimation of category c by invariant In the previous section, it was assumed that category c of each character was known. However, if the category c can be known before the tilt correction, the situation will not require tilt correction in the first place. For this reason, it is uncertain that it is necessary to determine a category for referring to the case.
Therefore, it is considered to estimate the category c of each character (connected component) robustly (stably and reliably) with respect to rotational deformation using the rotation invariant q calculated from the image information. Specifically, the rotation invariant q _c is obtained for the standard pattern of each category c. Thus, when estimating the category of the input character x, the rotation invariant q _x is obtained from the character, and _{c where} q _x = q _c is obtained. Since q _x does not change with respect to the rotation of the document image, in principle, correct c is obtained.

  In practice, however, it is difficult to narrow down the character category solely based on the rotation invariant q. The degree of difficulty depends on the invariants used, the number of categories, the noise of the document image, etc., but in short, it is character recognition based on a single feature amount, and it is impossible to expect strict category estimation. For this reason, actually using the decimal ε (epsilon),

A plurality of c satisfying the condition is used as a category candidate.

1-3. Details of the estimation step As can be seen from the use of the word “candidate” in the above estimation steps, it is difficult to uniquely determine θ using only one character. This is due to the following reason.

The first is that p and θ do not have a one-to-one correspondence, and a plurality of θ often corresponds to the same variable p. Therefore, multiple rotation angle candidates are given for one character.
Second, if the variable p does not change much even when the rotation angle θ is changed (when the function p _c (θ) becomes flat), θ reacts sharply to the measurement error of the variable p, and the estimated value θ The reliability becomes low.
Third, as described above, there are a plurality of estimated categories c. Eventually, with respect to the plurality of c, there is no other way than driving the estimation step in the previous section, and eventually a plurality of rotation angle candidates are given.

  Therefore, the angle estimated from a plurality of characters in the document image is voted, and the one with the highest voting result is used as the estimation result. That is, the voting process is applied as one of statistical methods to obtain an estimation result. If there are multiple characters of different categories in the document image, candidates will be given by different cases, and even if many wrong candidates are mixed, it is unlikely that they will be concentrated on one wrong point. It is expected.

The processing of the above estimation step will be specifically described with reference to FIG. FIG. 1 is an explanatory diagram showing how the rotation angle of a document image is estimated.
Step 1: First, a variable p _x and an invariant q _x are calculated for the character pattern x in the input document image.
Step 2: Based on the calculated q _x
Select a category.
Step 3: Vote for angles, θ ₁ , θ ₂ , and θ _3, where p _x = p _c (θ). In the case of FIG. 1, there are two θ ₂ , so vote twice. Such processing is performed for all connected components in the document image, and the one with the largest number of votes is set as the rotation angle of the document.

When voting based on case p _c (theta), as in the case of invariants, friendly error of p _x,
Vote for all θ in the range that satisfies FIG. 2 is a graph showing a voting state with respect to the rotation angle θ satisfying the relationship of the above equation. The point to be noted here is that the size of the voting range varies depending on the slope of the variable function p _c (θ).
If the rotation angle (tilt) of the image can be estimated by the above steps, the target document image is corrected according to the estimation result. That is, the image is rotated so that the inclination becomes zero.

1-4. Specific Examples of Variables and Invariants In this invention, arbitrary variables and invariants with respect to rotation may be used, but in this invention, the simplest one is used. Specifically, as the variable p, a value that changes by rotating one connected component in the document image, specifically, an area of a circumscribed rectangle (FIG. 3A) is used. Further, as the invariant q, a value that does not change even when rotated, specifically, the area in the convex hull (FIG. 3B) is used. FIG. 3 is an explanatory diagram illustrating the area of the circumscribed rectangle / area of the convex hull of the character that is the variable / invariant in this embodiment, taking the character “A” as an example. Here, by taking the ratio between these areas and the area of the black pixels, these variables and invariants are made independent of the size of the connected component in the image. That is, both p and q are set as scale invariants.

  In this specification, the term “black pixel” and “white pixel” are used for the black pixel on the assumption that the background is white, that is, the background is white and the local pattern is black. However, if the local pattern and the “ground” can be identified, their colors are not limited to black and white. For example, in a red pattern, a red pixel may be a “black pixel” in this specification. When the ground is yellow, the yellow pixel may be a “white pixel” in this specification.

The rotational variable p and the invariant q can be expressed again by the following equations.
The variable p described above changes periodically as shown in FIG. FIG. 4 is a graph showing the value of the variable p in the range of the rotation angle from −180 ° to 180 ° for the category “y” in this embodiment. Therefore, only one cycle, in this case, −45 ° to 45 ° can be used, and the rotation angle that can be estimated according to this embodiment is limited to the same range.

<< Embodiment 2 >>
In this embodiment, the procedure will be described by taking as an example a case where the projection distortion of a document image is corrected to affine distortion. A quantitative and qualitative description of the correction result will be described later in Experimental Example 2.
For the purpose of describing this embodiment, the relationship between the three-dimensional coordinates and the two-dimensional coordinates in computer vision is first described, and then details of this embodiment are described.

2.1. Camera coordinate system and image coordinate system
Consider how a 2D image can be obtained when an object in 3D space is photographed with a camera. FIG. 11 is an explanatory diagram showing a coordinate system using a pinhole camera as a model and a coordinate system in which the pinhole camera is rearranged (a coordinate system commonly used in the technical field of computer vision).
Usually, a pinhole camera as shown in FIG. 11 (a) is used as a camera model. Point C is a pinhole, and all the light coming from the object 11 passes through the pinhole and forms an image on the image plane I. Point C is called the focal point. The distance f between the image plane I and the focal point C is referred to as the focal length, the straight line passing through the focal point C and perpendicular to the image plane is referred to as the optical axis, and the intersection of the optical axis and the image plane is defined as the image center c. In this model, two parallel lines are not necessarily converted to parallel lines. Such conversion is called projective transformation, and distortion caused by projective transformation is called projective distortion. Of the projective transformations, those that are parallel lines when the parallel lines are transformed are called affine transformations, and the distortions that have undergone affine transformations are called affine distortions.

In the field of computer vision technology, image planes are generally rearranged and used as shown in Fig. 11 (b) (for example, Xugang, Saburo Tsubaki, "3D Vision", Kyoritsu Publishing, 1998, and Koichiro Deguchi , “Image and Space”, Shosodo, 1991). A coordinate system having the image center c on the image plane as the origin and having an x-axis and a y-axis as shown in FIG. 11B is called an image coordinate system. A three-dimensional coordinate system having the focal point C as the origin, the optical axis as the Z axis, and the X and Y axes in the directions corresponding to the x and y axes of the image coordinate system is referred to as a camera coordinate system. When a point (X, Y, Z) ^T in the camera coordinate system is projected onto the image plane, the corresponding point (X, Y) ^T in the image plane coordinate system is

It is obtained by

2.2. Area and Depth of Black Pixel Focusing on each character in the document image, the size changes depending on the position even for the same character type. For example, consider a case where only a specific character such as a in the alphabet is extracted from an image. At this time, the area of the black pixel of the character is larger near the camera and smaller near the camera due to projection distortion. Since the depth information of the document can be obtained from the change in the area, in this embodiment, the document image is corrected based on this.

The relationship between the depth and the area of the black pixel of the character is obtained. Assume that when the same type of characters on the paper surface 13 are selected, the Z coordinates of their centers are Z ₁ and Z ₂ , respectively. To simplify the problem, consider the relationship between depth and character length using the schematic diagram in FIG. FIG. 12 is an explanatory diagram for explaining the projection and approximation of characters when the inclined paper surface 13 is viewed from the camera. In FIG. 12, assuming that the original length of the extracted character is L, Z ₁ , ≠ Z _{2 at} this time, so the projection lengths l ₁ and l ₂ of the character obtained from the image are different. In order to easily obtain each length, approximation as shown in FIG. 12 (b) is performed. That is, a plane parallel to the image plane is placed at the center of each, and an orthogonal projection of the character is obtained. If the angle between the paper surface 13 and the image plane is α and the length of the orthogonal projection is L ′,

It is. Therefore, considering only the x-coordinate of equation (1),

Is obtained.

  Next, the same applies to the area of these characters. If each area is S and the area of orthographic projection is S ',

It becomes. At this time, the area s _j of the mapping to the image plane is

It is.

From equation (5), it can be seen that the area on the image plane is inversely proportional to the square of the depth with respect to the original area. Therefore, when attention is paid to the area of a black pixel of a certain character type, the depth Z _j of the j-th character is represented by the area s _j of the black pixel,

It becomes. Further, since the focal length f and the angle α between the paper surface 13 and the image plane are determined at the time of photographing, they are constants.
Next, the inclination of the paper surface 13 in the camera coordinate system is considered from the depth of each character. The coordinate (X _j , Y _j , Z _j ) ^T of the _jth character from equation (1) is

It is. Here, if each coordinate is expressed in a coordinate system replaced with Z ′ that is Z multiplied by 1 / f,

Thus, the unknown constant f can be eliminated in terms of shape. Since the characters in the image are essentially on the same plane, the three-dimensional coordinates of each character are calculated using Equation (7) and applied to the plane represented by Z '= aX + bY + c. The slope can be estimated. Details are described in 2.4.

2.3. Clustering by area ratio The method of estimating the depth from the area described in item 2.2 can be used only when there is only one type of character in the document. However, since a plurality of character types are mixed in an actual document, it is necessary to divide the characters for each type in advance. Character recognition can be considered as a method for discriminating character types, but processing is difficult when subject to projective distortion. Here, it is only necessary to classify the character type, and it is not necessary to label the character as in character recognition.

  Therefore, in this embodiment, a classification using an area ratio, which is an amount that does not change even when subjected to affine transformation (affine invariant), is considered. That is, when two regions are obtained from a character, an invariant is obtained from the area ratio of the two regions, and the character type is classified using this. Affine invariants are not invariant to projective transformations, but projective transformations can be approximated to affine transformations in local regions, so the area ratio of a small area such as a character region can be treated like a projection invariant. .

There are two conditions that the area ratio must satisfy to determine the character type.
(1) The area where the area ratio (area) is calculated must be the same even if it undergoes projective transformation.
(2) The area ratio must be able to distinguish the character type sufficiently.

  Regarding the item (1), since the area ratio is an invariant, the same value can be calculated (approximately) from the same region. However, since the same value cannot be calculated if the area for calculating the area is different, an area invariant method for projective transformation is required. This embodiment utilizes the fact that the convex hull of each region is invariant to linear transformation.

  Regarding the item (2), different character types may accidentally have the same area ratio. In that case, confusion of character types occurs, and the inclination of the page cannot be estimated correctly. Therefore, a plurality of area ratios are used to improve the area ratio discrimination performance. This is because the probability that a plurality of area ratios are close by chance is smaller than the probability that one area ratio calculated from different character types is close by chance. Since the types of area that can be calculated from one character are limited, in this embodiment, the nearest two characters are combined and the area calculated from the two characters is used. FIG. 13 and FIG. 14 are explanatory diagrams illustrating an example of obtaining a variable and an invariant from two selected characters. As shown in FIG. 13, when two characters are selected (in this case, “t” and “h”), the five types of regions shown in FIGS. 14 (a) to (e) are determined from the black pixel region and the convex hull region of the character. Is obtained. By combining these, a plurality of area ratios can be created. The obtained m area ratios are used as m-dimensional invariant vectors.

  Let us consider dividing a set of characters taken out of a document (hereinafter referred to as a cluster or category) into a subset of characters having a close area ratio. In this embodiment, the k-means method is used for clustering. Each cluster obtained by clustering is expected to contain the same set of character types. Subsequent processing is performed every two characters.

  Here, regarding the clustering, restrictions on the character size of this embodiment will be described. The relationship between the area and depth described in item 2.2 above assumes that the original character size is the same. However, in clustering using the area ratio, characters having the same character shape but different in size cannot be distinguished. Therefore, if characters of different sizes exist in the cluster, it is impossible to distinguish whether the difference in character size is due to a change in depth or due to a difference in the original size. It becomes a disturbance factor. However, as with normal documents, if most characters are the same size and only a part such as the heading is a large character, it can be rejected by the noise removal processing described later, so there is no problem. Conceivable.

2.4. Fitting to a plane When clustering is performed as described above, it is possible to consider the fitting to the plane described in item 2.2 above in each cluster. In order to estimate the inclination of the page with high accuracy, it is desirable that the same character type is dispersed in the document, but such a situation cannot be expected. Therefore, consider integrating the information on the inclination of the paper estimated for each cluster (character type). At that time, the problem is the area S of the black pixel. In the description of the above item 2.2, it is assumed that S is known, but it is actually unknown and differs for each character. Therefore, the ratio of the black pixel area for each cluster is estimated at the same time so that the inclinations of the respective planes are equal. The details will be described below. In the following description, cluster numbers i are added to S, (X _j , Y _j , Z _j ) ^T , Z ′ _j in the above item 2.2, and S _i , (X _ij , Y _ij , Z _ij ) ^T and Z ' _ij respectively. The same applies to the equations (6) to (8).
First, Equation (8) uses Equation (6),

It can be expressed as. This expression means that the coordinates (X _ij , Y _ij , Z ′ _ij ) of each character can be calculated using x _ij , y _ij , s _ij obtained from the image. However, since the S _i representing the original area of the characters in the formula (9), the plane of inclination α is unknown,

And the error of the depth of each character relative to the plane

It is defined as And the sum of errors for all characters

[K _i ] that minimizes and parameters a, b, and c of the plane are obtained. Here, [K _i ] has an arbitrary multiple, and each parameter is not uniquely determined. Therefore, in this embodiment, [K _i ], a, and b are obtained by fixing c = 1.
However, it is necessary to consider the influence of noise (outliers) when fitting to a plane. Causes of noise include image processing failure when extracting characters from the image, misclassification in clustering, and there are cases where characters of the same character type and multiple sizes exist as described in 2.3. Conceivable. In order to cope with these noises, two types of noise removal are performed in this embodiment.

The two types of noise removal are (A) removing outliers in the cluster and (B) removing the cluster itself. For (A), the distance ε _ij from the plane to each character is calculated for each cluster, and characters whose distance is greater than or equal to the threshold value t ₁ are removed. For (B), a cluster having a small number of elements (t ₂ or less) is removed. This is because there is a high possibility that an erroneous plane is estimated from such a cluster.

2.5. Rotating the paper Finally, rotate the paper in the image so that it faces the front. Since this is equivalent to moving the viewpoint to the front of the page, it is considered to obtain a normal vector of the inclined page and move the viewpoint on the extension. The rotation expression uses a roll / pitch / yaw type rotation transformation in which an arbitrary rotation is represented by three stages of rotation φ around the Z axis, rotation θ around the Y axis, and rotation psi around the X axis. A rotation matrix R using roll, pitch, and yaw is expressed by the following equation.

When the paper surface is expressed as Z ′ = aX + bY + 1, since Z ′ = Z / f, Z = afX + bfY + f. Its normal vector is (afbf (-f)) ^T. Therefore, rotation conversion may be performed using R so that the x coordinate and the y coordinate are zero. In consideration of not rotating around the Z axis, the rotation angle of R is

It becomes. Equation (13) shows that the unknown parameter f is required for angle estimation. However, since f is not estimated at this stage, f = 1 is provisionally set. In this case, after the projection distortion correction, there is a possibility that an affine distortion in which a figure that is originally a rectangle becomes a parallelogram may remain.
Hereinafter, a two-dimensional image after rotation is obtained. Camera coordinate system point (X _ij , Y _ij , Z _ij ) A point obtained by rotating ^T

If you

It becomes. Furthermore, by projecting this onto the image plane, the coordinates of the two-dimensional image by rotation

Can be obtained.

  The target for correction differs between the first embodiment and the second embodiment. However, not only that, it also differs greatly in whether learning is necessary in advance. In the first embodiment, the correspondence between the rotation angle and the variable (area of the circumscribed rectangle of the character) is registered in advance for each character type, so that correction can be performed with high accuracy even if the difference from the learning result is small. However, a learning procedure and a storage unit for storing it are necessary. Also, the assumption is that all characters in the document are facing the same direction (not rotated). On the other hand, Embodiment 2 can correct | amend without using the assumption with respect to a prior learning process and a layout at all. Therefore, it can be applied to various fonts of various layouts (even to the kind of marks that are not characters). Further, a storage unit for storing the learning result is not necessary. Furthermore, the present invention can be applied to a document composed of fonts that are not targeted for learning.

≪Estimating more general geometric deformation≫
The correction to rotation and the correction from projection distortion to affine distortion have been described above as examples, but this can also be applied to estimation of other geometric deformations and correction based thereon. In other words, the degree of various geometric deformations can be estimated by combining the geometric deformation variable and the invariant to be corrected. For example, if there is an invariant for affine transformation (which is of course invariant to translation, scale transformation, and rotation) and a quantity that is invariant to similarity transformation (translation, scale transformation, and rotation), combine these two quantities. Therefore, the shear component of the affine transformation can be estimated.

≪Experimental example 1≫
In Experimental Example 1 below, an experimental example corresponding to Embodiment 1 will be described.
3-1. The target of the experimental sample skew estimation is five types of document images D1, D2, D3, D4 and D5 created by LaTeX, which is known as a text-based typesetting system. The images of these documents are shown in FIG. Mostly composed of the same font as the example, but some documents contain mathematical expressions. There is no corresponding case for italic fonts and mathematical symbols in these mathematical expressions, which can cause erroneous estimation. Each test document image was rotated at ± 30 °, ± 20 °, ± 10 °, ± 5 °, ± 2 °, and 0 ° to generate 44 test images. FIG. 6 is an example. These test images were voted one connected component (in most cases, a single character) from the upper left to the lower right.

Example of measuring variable and invariant in increments of 0.1 ° from -45 ° to 45 ° for 52 characters of “A” to “Z” and “a” to “z” in a single font (Times-Roman) Created. FIG. 7 shows examples of variables and invariants actually measured. Since the invariant measured for each category has an error, the invariant q _c stored as an example is averaged.

3-2. Result of tilt correction according to this invention
Table 1 summarizes the results of estimating the tilt for 44 test images. The unit in parentheses in Table 1 is%. It was possible to estimate 95% of the test images with an error of 2.0 ° or less.

  As an example of successful tilt estimation, the estimation result obtained by rotating the test image D1 by -2.0 ° is shown in D1 (-2 °) of FIG. The estimated angle in Fig. 8 (a) is -1.4 °, which can be estimated with sufficient accuracy.

In addition, the vertical axis in FIG. 8B represents the number of characters used for estimation, and voting proceeds in the direction from top to bottom. That is, the number of characters used for estimation increases. It can be confirmed that the estimation accuracy improves as the number of characters used for estimation increases. However, there is a slight vibration near the correct angle. This is because, as shown in FIG. 8 (a), almost the same number of votes are performed near the correct angle. As mentioned in item 1.3, to account for errors in the p _x,
Voting to satisfy θ. Therefore, even always the same value as found by p _x, comes out ambiguity amount corresponding estimated angle of the width of 2 [epsilon] _p. As a result, a plurality of peaks are seen near the correct angle.

  Table 2 shows the estimation error (in degrees) of the tilt for each test image. The average slope estimation error was 1.4 °. Even in the case of images including characters that have no examples such as test images D3 and D4, if most of the connected components have examples, they can be correctly estimated by voting. Further, the rotation angle of a test image in which characters such as D5 are not arranged on a straight line is difficult to estimate by the conventional method, but can be estimated correctly by the present invention.

  The error between the test image D3 tilt of 20 ° and the D5 tilt of -5 ° was 2.0 ° or more. These estimation results are shown as D3 (20 °) and D4 (-5 °) in Fig. 8. The former voted for a completely different angle, and the latter oscillated near the correct angle. This has a common cause that current invariants refer to multiple cases. Details are shown below.

In item 1-2, using decimal ε,

We explained using multiple c satisfying the above as candidate categories. However, this may lead to incorrect cases being referenced and they may vote for the wrong angle more than the correct angle. Take "e" which appears most frequently in a document as an example. Table 3 shows the category “e” and its neighboring categories and their invariants. When x = "e" is given as an input, according to Table 3, “u” and “n” are referred to as examples in addition to “e”. In addition, due to invariant measurement errors, it may be within the voting range up to "s". As a result, many votes were taken at the wrong angle.
Based on the above causes, we consider two samples with large errors. The voting state at the input x = "e" when the test image D3 has an inclination of 20 ° is as shown in FIG. The variable of the letter “e” rotated by 20 ° is p _x in the figure. The p _x angle to be voted in accordance with the one in the shaded area, the black portions are voted two to overlap is variable. As a result, the vote will be almost twice from -11 ° to -12 °, rather than around 20 °. As a result, it is thought that many people voted for the wrong angle rather than the correct angle.

When the test image D4 has an inclination of -5 °, “e” was voted correctly, but “t”, which has a large proportion of the document in D4, voted at the wrong angle as before. FIG. 10 shows a graph of the relationship between the variable and angle of categories “b”, “f”, and “t” in the vicinity of “t” and its invariant. p _x represents a variable at -5 ° of the input x = "t". The shaded area in the figure is voted one by one, and the black part is voted two or three because two or three variable graphs overlap each other. As a result, they voted 2 to 3 times around the correct angle, and oscillated near the correct angle.

«Experimental example 2»
Next, an experiment was performed to verify the effectiveness of the second embodiment. For the experimental data, images taken with Canon EOS 5D and having a size of 4,368 x 2,912 were used. The quantitative evaluation of the experimental results will be performed in the future. In this embodiment, the experimental results were evaluated visually. The method of the second embodiment does not require a document frame, but in this experiment, an image with a frame was selected so that the effect of the method can be easily understood.
In considering the combination of invariants, the larger character area of the two pixels is called “character large” and the smaller character area is called “small character”. The five invariant combinations used are:

It is. If the invariant vector has 5 dimensions, use all 5 types, and if it has 3 dimensions, use only i. To iii.
FIG. 15 is an explanatory view showing an experimental result of correction of projection distortion according to the present invention. FIG. 15 shows target images 1 to 3, parameters used for correcting those images, and correction results of images 1 to 3.

The parameters for clustering and noise removal were adjusted to optimize the clustering result. “Before correction” in FIG. 15 is the original image. FIG. 16 shows details of the original image of “image 2” in FIG. “Image 2” is a sample for demonstrating that the method of the present invention can be applied even to a layout in which characters in a document are not arranged on a straight line.
With respect to the correction result, first, the result when the unknown focal length is set to f = 1 is shown as “after correction (f = 1)” in FIG. Ideally, the right angle of the document corner is not restored, but the parallel lines should be restored. As a result of the experiment, the parallel lines in image 1 were almost restored, but some errors remained in images 2 and 3. The main cause is that an outlier has an effect upon plane fitting, and an error has occurred in parameter estimation.

  Next, the result of manually searching for the focal length f and determining a substantially optimal value is shown as “after correction (f is an optimal value)” in FIG. Ideally, the rectangle of the document frame should be restored. However, for the same reason as when f = 1, in this case as well, the rectangle of image 1 was almost restored, but errors remained in images 2 and 3.

  As described above, Embodiment 1 and Experimental Example 1 describe a method of estimating a deformation amount by using only “variables” and “invariants” for a specific geometric deformation, and correcting based on the estimation result. did. Taking a skew or rotation as an example of a specific geometric deformation, the rotation angle is estimated by combining a feature amount that changes with rotation and a feature amount that does not change. As a result, the rotation angle can be estimated even if the characters in the document image are not arranged in a straight line. In addition, the amount of deformation was estimated based on the case. Instead of using the standard pattern as an example as it is, the relationship between the variable and the rotation angle is obtained from the standard pattern and registered as an example, enabling efficient estimation of the amount of deformation. Furthermore, by using the invariants described above, we devised a way to refer to cases even if the category is unknown.

Further, in the second embodiment and the experimental example 2, the aspect in which the projection distortion of the document image is corrected by combining “variable” and “invariant” with respect to the inclination of the paper surface is shown. By using the area as “variable” and the area ratio as “invariant” for each connected component in the document image, the relative depth information of each connected component can be estimated. Then, the inclination angle of the paper surface is estimated by integrating the information on the entire paper surface. In the second embodiment, only the relative information of the connected components is used, and no strong restrictions are applied to the shooting method and layout, so that it is possible to correct projection distortion of various document images.
In Experimental Example 2, the potential to restore an originally rectangular object to a parallelogram (projection distortion to about affine distortion) was confirmed, but the original rectangle was not restored. This is due to the fact that uncertainties of a constant multiple remain in the estimated depth information and an error has occurred in the fitting of the plane. The former can be solved by using “variables” and “invariants” different from those used in the second embodiment, and the latter can be solved by introducing robust estimation and improving the accuracy of noise removal. Seem. Note that the robust estimation here is a term in this technical field, and when the sample used for parameter estimation is mixed with a sample whose characteristics are different from others (so-called “outliers”), the effect is as much as possible. An estimation method that is excluded.

≪Device block configuration≫
FIG. 17 is a block diagram showing a functional configuration of the image distortion correction apparatus of the present invention. As shown in FIG. 17, the apparatus of the present invention includes a dividing unit 21, a calculating unit 23, a classifying unit 25, an estimating unit 27, and a correcting unit 29. One aspect of hardware that implements this apparatus is a personal computer in which the correction program of the present invention is installed. The function of each block is realized by the CPU of the personal computer executing the correction program. That is, the function of the dividing unit 21 is realized by the CPU executing a process of dividing the input image into local patterns that are local patterns. For each local pattern, the CPU executes a process of calculating, based on a predetermined procedure, an invariant whose value is substantially constant according to the degree of deformation and a variable whose value changes according to the degree of deformation. 23 functions are realized. Further, the function of the classification unit 25 is realized by the CPU executing a process of classifying each local pattern into one of a plurality of categories based on the calculated invariant. Furthermore, the function of the estimation unit 27 is realized by the CPU executing a process of estimating the degree of deformation received by the local pattern based on the variable calculated for each local pattern of each category. Furthermore, the function of the correction unit 29 is realized by the CPU executing a process of correcting an image based on the estimation result.

  In addition to the embodiments described above, there can be various modifications of the present invention. These modifications should not be construed as not belonging to the scope of the present invention. The present invention should include the meaning equivalent to the scope of the claims and all modifications within the scope.

In this embodiment, it is explanatory drawing which shows a mode that the rotation angle of a document image is estimated. In this embodiment, it is a graph which shows the mode of voting with respect to rotation angle (theta) which satisfy | fills a predetermined relationship. It is explanatory drawing which shows the area of the circumscribing rectangle of the character which is the variable / invariant / area of the convex hull in this embodiment taking the character “A” as an example. 6 is a graph showing a value of a variable p in a range of a rotation angle from −180 ° to 180 ° for the category “y” in this embodiment. In this embodiment, it is explanatory drawing which shows the document image used for experiment. In this embodiment, it is explanatory drawing which shows the example of the document image rotated as an example of an experiment. In this embodiment, it is a graph which shows the value with respect to the rotation angle of the variable and the invariant calculated | required in the experiment example. In this embodiment, the voting result of the experimental example and the transition of the estimation result based on the number of characters used are plotted on the vertical axis, and the rotation angle is plotted on the horizontal axis. In this embodiment, it is a graph which shows the relationship between the variable of category "e", "n", and "s", and a rotation angle. In this embodiment, it is a graph which shows the relationship between the variable of category "b", "f", "p", and "t", and a rotation angle. It is explanatory drawing which shows the coordinate system which makes a pinhole camera a model, and the coordinate system which rearranged it. It is explanatory drawing for demonstrating the projection and approximation of a character when the inclined paper surface is seen from a camera. In this embodiment, it is the 1st explanatory view showing the example which obtains a variable and an invariant from two chosen characters. In this embodiment, it is a 2nd explanatory view which shows the example which obtains a variable and an invariant from two selected characters. It is explanatory drawing which shows the experimental result of correction | amendment of the projection distortion which concerns on this invention. FIG. 16 is an explanatory diagram showing details of “Image 2” in FIG. It is a block diagram which shows the functional structure of the image distortion correction apparatus of this invention.

Explanation of symbols

DESCRIPTION OF SYMBOLS 11 Object, imaging | photography object 13 Paper surface 21 Division | segmentation part 23 Calculation part 25 Classification | category part 27 Estimation part 29 Correction | amendment part
C focus
D1, D2, D3, D4, D5 Document images
I Image plane
f Focal length

Claims (16)

A method for inputting an image subjected to geometric deformation and correcting the deformation received by the image,
Dividing the input image into local patterns which are local patterns;
For each local pattern, a calculation step for calculating an invariant whose value is substantially constant according to the degree of deformation and a variable whose value changes according to the degree of deformation based on a predetermined procedure;
Classifying each local pattern into one of a plurality of categories based on the calculated invariants;
An estimation step for estimating the degree of deformation that the local pattern has undergone based on the variables calculated for each local pattern of each category;
Correcting the image based on the estimation result,
A method of correcting an image, wherein a computer executes each step.   The method according to claim 1, wherein the geometric deformation is a projective transformation, an affine transformation, or a similarity transformation.   The method according to claim 1, wherein the image is a document image, and at least a part of the local pattern is a character pattern. The geometric deformation is rotation;
A variable is a value that changes by rotating a local pattern,
The method according to claim 1, wherein the invariant is a substantially constant value even when the local pattern is rotated. The geometric deformation is a projective transformation;
A variable is a value that changes with depth,
The method according to claim 1, wherein the invariant is a substantially constant value with respect to a change in depth.   The method according to claim 1, wherein the variable is a rectangular area circumscribing the local pattern.   The method according to claim 1, wherein the variable is an area of a black pixel portion of a local pattern.   The method according to claim 1, wherein the invariant is an area within a convex hull of a local pattern.   The method according to claim 1, wherein the local pattern is a pattern divided as a connected component in an image or a set of the patterns. For each category, let q _{c be} the invariant for that category and q _{x be} the invariant for each local pattern.
(Where ε is a predetermined constant)
The method according to claim 1, comprising a local pattern satisfying the relationship:   The estimation step compares a variable calculated from each local pattern with a reference value stored in advance corresponding to each category, temporarily estimates the degree of deformation for each local pattern, and calculates each temporarily estimated result. The method according to claim 1, wherein the degree of deformation is estimated statistically.   The method according to claim 11, wherein the reference value is obtained by measuring a variable by stepwise deforming a standard pattern of each category, and storing the amount of deformation of each step and the measured variable in association with each other.   The estimation step temporarily estimates the degree of deformation for each category based on the relationship between the position of each local pattern and the variable of the local pattern, and statistically processes each temporarily estimated result to estimate the degree of deformation. The method according to any one of claims 1 to 10. The input image is a document image,
The geometric deformation is a projective transformation;
The variable is the area of the black pixel portion of the local pattern,
The invariant is the area within the convex hull of the local pattern,
6. The method according to claim 5, wherein the estimating step performs temporary estimation of the inclination of the paper surface of the document image based on the relationship between the area of the black pixel portion of each local pattern and the position on the paper surface. A program for correcting a deformation received by an image subjected to geometric deformation,
Processing to divide the input image into local patterns that are local patterns;
For each local pattern, a calculation process for calculating an invariant whose value is substantially constant according to the degree of deformation and a variable whose value changes according to the degree of deformation based on a predetermined procedure;
A process of classifying each local pattern into one of a plurality of categories based on the calculated invariant,
An estimation process for estimating the degree of deformation that the local pattern has undergone based on the variables calculated for each local pattern of each category;
An image correction program causing a computer to execute a process of correcting an image based on an estimation result. An apparatus that receives an image subjected to geometric deformation as an input and corrects the deformation received by the image,
A dividing unit that divides the input image into local patterns that are local patterns;
For each local pattern, a calculation unit that calculates an invariant whose value is substantially constant according to the degree of deformation and a variable whose value changes according to the degree of deformation based on a predetermined procedure;
A classification unit for classifying each local pattern into one of a plurality of categories based on the calculated invariant,
An estimation unit that estimates the degree of deformation that the local pattern has undergone based on the variables calculated for each local pattern of each category;
An image distortion correction apparatus comprising: a correction unit that corrects an image based on an estimation result.