KR101967284B1 - Apparatus and method for aligning multi image - Google Patents

Abstract

Disclosed is a method for aligning multiple images comprising the following steps: selecting three first images among a plurality of images; extracting a triple tie point of the selected three first images; selecting the number of appropriate points corresponding to an estimated position and an estimated posture in the extracted triple tie point based on each estimated position and estimated posture of the three first images; and determining the estimated position and estimated posture of the three first images as a final position and a final posture of the three first images based on the number of appropriate points.

Description

Multi-image alignment device and method {APPARATUS AND METHOD FOR ALIGNING MULTI IMAGE}

The present invention relates to the field of image processing. More specifically, the present invention relates to an apparatus and method for aligning various images taken by a camera.

BACKGROUND ART [0002] Techniques for photographing the surface of the earth and roads by mounting a camera on a moving object such as an unmanned aerial vehicle or a car, and acquiring three-dimensional spatial information or performing three-dimensional analysis of the surrounding environment by using the photographed images are widely used.

In order to extract precise 3D information from images, a process of first calculating a position and a posture of the captured image is required, and this process is called an image alignment process. In order to automatically align images, feature points are extracted from each image using feature extractors such as scale-invariant feature transform (SIFT) and speeded up robust features (SURF), and the same feature points in multiple images through feature point matching Follow the process to find out.

At this time, the same feature point extracted from several images is called a tie point. The same feature point extracted from two images is called a double tie point, and the same feature point extracted from three images is called a triple tie point. Similarly, four tie points, five tie points, and the like can be defined.

However, due to factors such as inaccuracy of feature point matching and quality of photographed images, an error exists in the tie point obtained in the feature point matching process, so that the points that are not actually the same feature point are included in the tie point. Due to such a tie point error, a problem arises that the position and attitude of the image are not calculated correctly in the image alignment process, and that the accuracy of 3D spatial information extracted from the images is greatly reduced. For this reason, in the case of multiple images consisting of several images, error-free tie point extraction is the most important factor in the image alignment process.

An apparatus and method for aligning multiple images according to an embodiment of the present invention are directed to removing an inappropriate tie point (or error tie point) from multiple images.

In addition, the multi-image alignment device and method according to an embodiment of the present invention to align the multiple images in the correct position and posture as a technical problem.

In the multi-image alignment method according to an embodiment of the present invention,

Selecting three first images from among the plurality of images; Extracting triple tie points from the selected three first images; Calculating a number of fitting points corresponding to the estimated position and the estimated position among the extracted triple tie points based on the estimated positions and the estimated attitude of each of the three first images; And determining the estimated positions and the estimated poses of the three first images as the final positions and the final poses of the three first images based on the number of the fitting points.

The calculating of the number of fitting points may include: randomly selecting a part of the extracted triple tie points; And deriving an estimated position and an estimated pose of each of the first three images by applying the image coordinates of the selected partial triple points to a relative expression relational expression.

The calculating of the number of fitting points may include assigning each of the remaining triple tie points included in two first images of the three first images arranged according to the estimated position and the estimated attitude to the other first image. And determining the fit point based on the distance between the projection points when the projection is performed and the triple tie points included in the other first image.

The multi-image sorting method may include selecting a second image of the plurality of images; Extracting a second triple tie point between two first images and the second image; Calculating a number of fitting points from the extracted second triple tie points based on a final position and a final position of each of the two first images and an estimated position and the estimated position of the second image; And determining the estimated position and the estimated position of the second image as the final position and the final position of the second image based on the calculated number of fitting points.

The determining of the final position and the final posture of the second image may include randomly selecting a portion of the second triple tie points; And deriving an estimated position and an estimated pose of the second image by applying the image coordinates of the selected partial second triple point to a relative expression relational expression.

The determining of the final position and the final posture of the second image may include: three including the two first images arranged according to the final position and the final pose and a second image arranged according to the estimated position and the estimated pose. The distance between the projection points when each of the second triple tie points included in two of the images is projected onto another image and the second triple tie points included in the other image. Based on the above, may determine the fit point.

The determining of the final position and the final posture of the second image may include setting three-dimensional coordinates of each of the second triple tie points included in the two first images as reference points; Randomly selecting some of the set reference points; The second image by applying the three-dimensional coordinates of the randomly selected partial reference points and the image coordinates of the second triple tie points of the second image corresponding to the randomly selected partial reference points to an absolute expression relational expression; And determining an estimated position and estimated pose of the.

The determining of the final position and the final pose of the second image may include projecting each of the reference points onto the second image according to the estimated position and the estimated pose of the second image; And determining the fit point in consideration of the distance between the projection points projected on the second image and the second tie points of the second image. And determining the estimated position and the estimated pose of the second image when the determined number of the fitting points is the largest as the final position and the final pose.

According to another embodiment of the present invention,

At least one processor; And a memory electrically connected to the processor, wherein when the processor is executed, the memory selects a first image of three images and extracts triple tie points from the selected three first images. Based on the estimated positions and the estimated poses of each of the three first images, the number of fitting points corresponding to the estimated positions and the estimated positions among the extracted triple tie points is calculated, and the number of the fitting points is calculated. In consideration of this, instructions for determining the estimated positions and the estimated poses of the three first images as the final positions and the final poses of the three first images may be included.

An apparatus and method for aligning multiple images according to an embodiment of the present invention may remove an unsuitable tie point from multiple images.

In addition, the apparatus and method for aligning multiple images according to an embodiment of the present invention may align multiple images in a precise position and posture.

However, the effects that the multi-image alignment device and method according to an embodiment of the present invention can achieve are not limited to those mentioned above, and other effects not mentioned are described in the following description. It will be clearly understood by those skilled in the art.

BRIEF DESCRIPTION OF THE DRAWINGS In order to better understand the drawings referred to herein, a brief description of each drawing is provided.
FIG. 1A is a diagram illustrating three images including a fit tie point and a non-fit tie point.
FIG. 1B is a diagram illustrating image coordinates of tie points shown in FIG. 1A.
2 is a block diagram illustrating a configuration of a multi-image alignment device according to an embodiment of the present invention.
3 is a flowchart illustrating a method of aligning multiple images according to an embodiment of the present invention.
FIG. 4 is a diagram illustrating three first images illustrated for explaining a multiple image alignment method according to an embodiment of the present invention.
5 is an exemplary diagram illustrating first images aligned according to an estimated position and an estimated pose.
6 is an exemplary diagram illustrating first images aligned according to a final position and a final pose.
7 is a flowchart illustrating a method of aligning multiple images according to an embodiment of the present invention.
FIG. 8A is a diagram illustrating three images including a fit tie point excluding an unsuitable tie point.
FIG. 8B is a diagram showing image coordinates of the fit tie points shown in FIG. 8A.

The present invention may be variously modified and have various embodiments, and specific embodiments are illustrated in the drawings and described in detail with reference to the accompanying drawings. However, this is not intended to limit the present invention to specific embodiments, it should be understood that the present invention includes all modifications, equivalents, and substitutes included in the spirit and scope of the present invention.

In describing the present invention, when it is determined that the detailed description of the related known technology may unnecessarily obscure the subject matter of the present invention, the detailed description thereof will be omitted. In addition, the numbers (eg, first, second, etc.) used in the description process of the present specification are merely identification symbols for distinguishing one component from another component.

In addition, in the present specification, when one component is referred to as "connected" or "connected" with another component, the one component may be directly connected or directly connected to the other component, but in particular It is to be understood that, unless there is an opposite substrate, it may be connected or connected via another component in the middle.

In addition, in the present specification, the components represented by '~ unit (unit)', 'module', etc., two or more components are combined into one component or two or more components for each functionalized function May be differentiated into In addition, each component to be described below may additionally perform some or all of the functions of other components in addition to the main functions of which they are responsible, and some of the main functions of each of the components may be different. Of course, it may be carried out exclusively by the component.

Hereinafter, embodiments according to the spirit of the present invention will be described in detail.

FIG. 1A is a diagram showing three images 10a, 10b, and 10c including a fit tie point and a non-fit tie point, and FIG. 1B is a diagram showing image coordinates of the tie points shown in FIG. 1A.

As described above, when the camera is mounted on the moving object to capture an image, each of the images includes a portion shared with each other and a portion not shared with each other. Therefore, in order to determine the position and posture of each of the images 10a, 10b, and 10c, it is preliminary to extract tie points commonly included in the images 10a, 10b and 10c.

As shown in FIG. 1A, the tie points extracted from the three images 10a, 10b, and 10c correspond to the same point in the real world. However, referring to FIG. 1B, the image coordinates of the tie points may be different for each of the three images. It can be seen that there is. Since image coordinates are values extracted according to an image coordinate system (that is, a local coordinate system) set for each image, there is a high possibility that they differ from each other. In FIG. 1B, the first column is the ID of the tie point, the second and third columns are the column coordinates and the row coordinates of the first image 10a, respectively, and the fourth and fifth columns are the column coordinates and the row coordinates of the second image 10b, respectively. The sixth and seventh columns correspond to the column coordinates and the row coordinates of the third image 10c, respectively.

Among the tie points extracted according to the traditional method, non-conforming tie points (or error tie points, error points) extracted as tie points may be included even though they are not actually identical feature points.

When determining the position and posture of the images based on the inappropriate tie point, the accuracy is inevitably reduced. Therefore, selecting only the suitable tie point (or the suitable point) except the non-compliant tie point to determine the position and posture of the images. It is important.

2 is a block diagram illustrating a configuration of a multi-image alignment device 200 according to an embodiment of the present invention.

Referring to FIG. 2, the multiple image alignment device 200 according to an embodiment of the present invention may include a memory 210 and at least one processor 220. The memory 210 and the at least one processor 220 may be electrically connected to each other.

The processor 220 may control the overall operation of the multiple image alignment device 200. The processor 220 may perform an operation of aligning each of the multiple images.

For example, the processor 220 executes instructions stored in the memory 210 to determine the final position and the final posture of three first images of the plurality of images, and the remaining second according to the determined final position and the final posture. The final position and final pose of the images may be determined.

The memory 210 stores various instructions for the operation of the processor 220.

For example, when the at least one processor 220 is executed, the memory 210 selects a first image of three images, extracts triple tie points from the selected three first images, and Based on the estimated positions and the estimated poses of each of the three first images, the number of fitting points corresponding to the estimated positions and the estimated positions among the extracted triple tie points is calculated, and the number of the estimated fit points is considered. In this case, instructions for determining the estimated position and the estimated position as the final position and the final position of the three first images may be stored.

Also, the memory 210 selects a second image of one of the plurality of images when the at least one processor 220 is executed, and stores a second triplet between two first images and the second image. Extracting a tie point, and based on the final position and the final posture of each of the two first images, and the estimated position and the estimated position of the second image, the number of fit points from the extracted second triple tie points In this case, instructions for determining the estimated position and the estimated position of the second image as the final position and the final position of the second image in consideration of the number of the fitting points may be stored.

Although not shown in FIG. 2, the multi-image alignment device 200 according to an exemplary embodiment of the present invention may further include an output unit configured to output information about a final position and a final posture of various images determined by the processor 220. Can be. The output unit may include various output devices such as a monitor and a printer, and the administrator may check the final position and the final posture of various images through the contents output from the output unit, and obtain three-dimensional information therefrom.

Hereinafter, an operation of the multi-image alignment device 200 according to an embodiment of the present invention will be described in detail with reference to FIG. 3.

3 is a flowchart illustrating a method of aligning multiple images according to an embodiment of the present invention.

In operation S310, the multiple image alignment apparatus 200 obtains three first images from among the plurality of images. The multi-image arranging apparatus 200 may receive a plurality of images from a camera or an external server through a network, or may receive a plurality of images from an administrator.

The multi-image arranging apparatus 200 may select three first images including the most double tie points when two sheets of the plurality of images are combined. For example, when a picture, b picture, c picture, d picture and the like exist as a plurality of pictures, the most 2 in the combination of a picture and b picture, a picture and c picture, and b picture and c picture If the tie point is extracted, the a image, the b image, and the c image can be selected as three first images. This may be viewed as a process of selecting three images having the largest area shared among the plurality of images.

According to an exemplary embodiment, the multi-image arranging apparatus 200 may select three first images arbitrarily from among a plurality of images.

In operation S320, the multi-image alignment apparatus 200 extracts triple tie points from three first images. The multi-image alignment apparatus 200 may compare the feature points included in each first image with each other and extract feature points commonly included in the three first images as triple tie points. The multi-image alignment apparatus 200 may extract the triple tie points by comparing feature values of each of the feature points included in the three first images.

In operation S330, the multi-image alignment apparatus 200 determines an estimated position and an estimated posture of each of the three first images based on a randomly selected triple tie point. In operation S340, the multi-image alignment apparatus 200 may determine the remaining positions. The number of fitting points corresponding to the estimated position and the estimated attitude among the three tie points is calculated.

Specifically, in steps S330 and S340, the multi-image arranging apparatus 200 randomly selects some of the triple tie points, and sets the image coordinates of each of the randomly selected triple tie points to the relative expression relation. The estimated position and the estimated pose of each of the three first images may be derived. Estimating the position and posture of each image by applying the image coordinates of each of the three tie points to the relative expression relation is obviously used in the field of photogrammetry, and thus detailed description thereof will be omitted.

4 and 5, three first images 400a, 400b, and 400c may include triple tie points 410 shown as circles, of which triple tie points 410 are included. According to the image coordinates of the randomly selected triple tie points 410, an estimated position and an estimated pose of each first image 400a, 400b, and 400c in the global coordinate system 500 may be derived. The estimated position may include the x-axis distance, the y-axis distance, and the z-axis distance of each of the first images 400a, 400b, and 400c based on the origin O of the global coordinate system 500. The posture may include rotation angles of the first images 400a, 400b, and 400c having the x, y, and z axes as the rotation axis of the global coordinate system 500.

The triple tie points extracted from the three first images 400a, 400b, and 400c should correspond to the same point in the real world, but as shown in FIG. 5, the first image according to the estimated position and the estimated posture. When the three 400a, 400b, and 400c are aligned, all triple tie points may not overlap, and triple tie points that do not overlap each other are likely to correspond to error tie points (hereinafter, referred to as error points).

The multi-image arranging apparatus 200 arranges each of the first images according to the estimated position and the estimated posture, and then triples tie points included in two first images of the three first images (specifically, The three-dimensional coordinates of each of the triple tie points except for the triple tie point selected at random are projected onto the other first image. The three-dimensional coordinates refer to the coordinates of the triple tie point in the global coordinate system.

When the triple tie point is projected onto the other first image, the multi-image alignment device 200 calculates a conversion relation between the global coordinate system 500 and the image coordinate system of the first image to which the triple tie point is projected. It is available. For example, image coordinates in the first image to which the triple tie point is projected may be obtained by applying the global coordinates of the triple tie point to the transformation relation.

In addition, the multi-image alignment apparatus 200 considers the distance between the projection point projected on any one first image and the corresponding triple tie point included in any one first image, and thus, each of the triple tie points. You can judge the match. For example, when the global coordinate of the triple tie point 'A' is projected on any one first image, the triple tie point 'A' projected on the first image and 'A' included in the first image 'If the' A 'triple tie point can be determined in consideration of the distance between the triple tie points, and when the global coordinates of the' B 'triple tie point are projected on any one first image, In accordance with the distance between the 'B' triple tie point projected on the first image and the 'B' triple tie point included in the first image, it may be determined whether the 'B' triple tie point matches.

Specifically, when the distance between the projection point and the triple tie point corresponding thereto exceeds a predetermined reference value, the multi-image alignment apparatus 200 may determine that the corresponding triple tie point is an error point. If the distance between the triple tie points is less than or equal to a predetermined reference value, it may be determined that the triple tie points are suitable points.

As such, the multi-image alignment apparatus 200 determines an estimated position and an estimated pose of each of the first images based on a randomly selected triple tie point among the triple tie points, and then selects each of the remaining triple tie points. By projecting onto one first image, it is possible to calculate how many fit points are among the triple tie points.

Referring back to FIG. 3, the multi-image arranging apparatus 200 calculates the number of fitting points by repeating steps S330 and S340 a predetermined number of times, and at step S350, for example, a robust estimation called RANSAC (Random Sample Consensus) According to the technique, the estimated position and the estimated pose when the number of fitting points is the largest may be determined as the final positions and the final poses of the three first images.

FIG. 6 is an exemplary diagram showing the first images 400a, 400b, 400c arranged according to the final position and the final posture, in which all the error points are removed from the first images 400a, 400b, 400c. It can be seen that the tie points are overlapped with each other in the global coordinate system 500.

7 is a flowchart illustrating a method of aligning multiple images according to an embodiment of the present invention.

When the final position and the final posture of the three first images of the plurality of images are determined, in operation S710, the multi-image arranging apparatus 200 selects any one second image except for the first images among the plurality of images. do.

In operation S720, the multiple image alignment apparatus 200 extracts a second triple tie point from two first images and a second image. The multi-image arranging apparatus 200 may arbitrarily select two first images, and the first two images including the most double tie points when the two images are included, including the second image among the three first images. You can also select.

In operation S730, the multi-image alignment apparatus 200 determines an estimated position and an estimated pose of the second image.

As an example of a method of determining the estimated position and the estimated pose of the second image, the multi-image arranging apparatus 200 randomly selects a portion of two first triplets and a second triple tie point of the second image, The estimated position and the estimated pose of the second image may be determined based on the relative coordinate relational expression of the image coordinates of the selected second triple tie point.

As another example, the multi-image alignment apparatus 200 may include three-dimensional coordinates of each of the second triple tie points included in the two first images, specifically, of each second triple tie point in the global coordinate system. Set coordinates to reference points. The multi-image arranging apparatus 200 randomly selects some of the set reference points, and the 3D coordinates of the randomly selected some reference points and the second corresponding to the randomly selected some reference points. The image coordinates of the second triple tie points of the image may be applied to the absolute expression relation to determine the estimated position and the estimated pose of the second image. Estimation of the position and posture of an image using an absolute expression relation is obviously used in the field of photogrammetry, and thus a detailed description thereof will be omitted.

Referring to FIG. 7 again, in operation S740, when the multi-image alignment apparatus 200 arranges the second image according to the estimated position and the estimated position, the estimated position and the estimated position among the second triple tie points of the second image. Calculate the number of fit points corresponding to.

For example, when the estimated position and the estimated pose of the second image are determined according to the relative expression relation in operation S730, the second 3 included in two images among two images including two first images and a second image. Each of the middle points (eg, the remaining tie points except for a randomly selected second triple tie point) is included in each of the projection points and the other image when the other image is projected. Based on the distance between each of the second triple tie points, a fit point may be determined among the second triple tie points, and the number of fit points may be calculated. It can be seen that this is similar to the method described in step S340 of FIG.

As another example, when the estimated position and the estimated pose of the second image are determined according to the absolute expression relation in operation S730, the multi-image alignment apparatus 200 may exclude the reference points (eg, except the randomly selected reference points). Each of the reference points is projected onto the second image according to the estimated position and the estimated attitude of the second image. In addition, the multi-image alignment apparatus 200 considers the distance between each of the projection points projected on the second image and each of the second triple tie points of the second image. The fit point may be determined, and the number of fit points corresponding to the estimated position and the estimated pose of the second image may be calculated.

The multiple image aligning apparatus 200 calculates the number of fitting points by repeating steps S730 and S740 a predetermined number of times, and in step S750, for example, the fitting points according to a robust estimation technique called RANSAC (Random Sample Consensus) The estimated position and the estimated position of the second image when the number of times is the greatest are determined as the final position and the final position of the second image.

Then, the multi-image alignment device 200 sequentially determines the final position and the final posture one by one according to the method shown in FIG. 7 for each of the remaining images of the plurality of images, thereby aligning all the images according to the correct position and posture. You can do it.

Meanwhile, with reference to FIG. 7, it has been described that two first images are used to determine the final position and the final posture of the second image. In some embodiments, all three first images may be used. In this case, a quad tie point commonly included in three first and second images may be used. Specifically, after extracting the four tie points, the estimated position and the estimated pose of the second image are determined, and the final position and the final position of the second image are determined according to the number of fit points corresponding to the estimated position and the estimated pose among the four tie points. Final posture can be determined.

FIG. 8A is a diagram showing three images 80a, 80b, and 80c including a fit tie point excluding a nonconforming tie point, and FIG. 8b is a diagram showing image coordinates of the fit tie points shown in FIG. 8a. .

Referring to FIG. 8B, triple tie points having ID 1, ID 2, etc. among the triple tie points are determined as error points and deleted from the three images 80a, 80b and 80c shown in FIG. 8A. You can check it.

Meanwhile, the above-described embodiments of the present invention can be written as a program that can be executed in a computer, and the written program can be stored in a medium.

The medium may be to continue to store a computer executable program, or to temporarily store for execution or download. In addition, the medium may be a variety of recording means or storage means in the form of a single or several hardware combined, not limited to a medium directly connected to any computer system, it may be distributed on the network. Examples of the medium include magnetic media such as hard disks, floppy disks and magnetic tape, optical recording media such as CD-ROMs and DVDs, magneto-optical media such as floptical disks, And ROM, RAM, flash memory, and the like, configured to store program instructions. In addition, examples of another medium may include a recording medium or a storage medium managed by an app store that distributes an application or a site or server that supplies or distributes various software.

As mentioned above, although the technical idea of the present invention has been described in detail with reference to a preferred embodiment, the technical idea of the present invention is not limited to the above embodiments, and having ordinary skill in the art within the scope of the technical idea of the present invention. Many modifications and variations are possible.

200: multiple image alignment device
210: memory
220: processor

Claims (10)

Selecting three first images from among the plurality of images;
Extracting triple tie points from the selected three first images;
Calculating a number of fitting points corresponding to the estimated position and the estimated position among the extracted triple tie points based on the estimated positions and the estimated attitude of each of the three first images; And
Determining the estimated positions and the estimated poses of the three first images as the final positions and the final poses of the three first images based on the number of the fitting points;
Calculating the number of fit points,
Selecting some of the extracted triple tie points; And
And applying the image coordinates of the selected triple tie points to a relative expression relation to derive an estimated position and an estimated pose of each of the three first images. How to arrange images.
The method of claim 1,
In the step of calculating the number of fit points,
And selecting a part of the extracted triple tie points randomly selecting a part of the extracted triple tie points.
The method of claim 1,
Calculating the number of fit points,
Projection points and the other one when each of the remaining three tie points included in the two first images of the three first images arranged according to the estimated position and the estimated attitude is projected on the other first image And determining the fit point based on the distance between the triple tie points included in the first image of the image.
The method of claim 1,
The multi-image sorting method,
Selecting a second image of the plurality of images;
Extracting a second triple tie point between two first images and the second image; And
Calculating a number of fitting points among the extracted second triple tie points based on the final position and the final position of each of the two first images and the estimated position and the estimated position of the second image; And
And determining the estimated position and the estimated pose of the second image as the final position and the final pose of the second image based on the calculated number of fitted points.
The method of claim 4, wherein
Determining the final position and the final posture of the second image,
Randomly selecting a portion of the second triple tie points; And
And applying the image coordinates of the selected second triple tie points to a relative expression relation to derive an estimated position and an estimated pose of the second image.
The method of claim 5,
Determining the final position and the final posture of the second image,
Each of the second triple tie points included in two of the three images including the two first images arranged according to the final position and the final pose and the second image arranged according to the estimated position and the estimated pose. And determining the fit point based on the distance between the projection points when the image is projected on the other image and the second triple tie points included in the other image. Multi image sorting method.
The method of claim 4, wherein
Determining the final position and the final posture of the second image,
Setting three-dimensional coordinates of each of the second triple tie points included in the two first images as reference points;
Randomly selecting some of the set reference points;
The second image by applying the three-dimensional coordinates of the randomly selected partial reference points and the image coordinates of the second triple tie points of the second image corresponding to the randomly selected partial reference points to an absolute expression relational expression; And determining an estimated position and an estimated pose of the image.
The method of claim 7, wherein
Determining the final position and the final posture of the second image,
Projecting each of the reference points onto the second image according to the estimated position and the estimated attitude of the second image; And
Determining the fit point in consideration of the distance between the projection points projected on the second image and the second tie points of the second image; And
And determining the estimated position and the estimated pose of the second image when the determined number of the fitted points are the largest as the final position and the final pose.
A program stored on a medium in combination with hardware to execute the multiple image alignment method of any one of claims 1 to 8.
In the multiple image alignment device,
At least one processor; And
A memory electrically connected to the processor;
The memory, when the processor is running,
Select first three images of the plurality of images,
Extracting triple tie points from the selected three first images,
Based on the estimated positions and estimated postures of each of the three first images, calculating the number of fitting points corresponding to the estimated positions and the estimated postures among the extracted triple tie points,
The calculation of the number of fit points is
Selecting a part of the extracted triple tie points and applying image coordinates of the selected triple tie points to a relative expression relation to derive an estimated position and an estimated pose of each of the three first images. ,
And instructions for determining the estimated positions and the estimated poses of the three first images as the final positions and the final poses of the three first images in consideration of the number of the fitting points.

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