JP2005018195A - Image processing apparatus and image processing program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an image processing apparatus capable of compensating distortion even if tilt photographing is conducted for an image from any direction. <P>SOLUTION: A quadrangle ABCD, which is distorted from an original rectangle by the tilt photographing, is transformed to a rectangle by a perspective conversion. A minimal rectangle EFGH, which is parallel with edges of the image and circumscribes the quadrangle ABCD, is created and a perpendicular line is dropped from each apex of the quadrangle ABCD to each edge of the rectangle EFGH, then segments connecting legs of the perpendicular lines JK, IL, OP, QR are obtained. A rectangle EMST is created by magnifying the rectangle EFGH to a lateral direction for proportion of length of the vertical segment IL/JK(≥1), and magnifying it to a vertical direction for the proportion of the length of the lateral segment QR/OP(≥1), then a parameter of the perspective conversion is set so that the apexes of the quadrangle ABCD correspond to the apexes of the rectangle EMST. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to an image processing apparatus and an image processing program for correcting distortion of a tilted image.
[0002]
[Prior art]
Photographing and recording characters and figures on white boards and sheets has long been done, but in recent years, with the spread of digital cameras and personal computers, images of white boards taken with digital cameras have been taken into personal computers. Replaying and displaying on the Internet has come to be performed on a daily basis. However, an image without distortion can be obtained by shooting from the direction facing the shooting target. However, when tilt shooting is performed on the shooting target from an oblique direction, the shot image is usually distorted. The problem is that the characters in the image are difficult to read and the figure is deformed.
[0003]
Special shooting lenses that do not cause distortion in the image even when tilted shooting have been put to practical use in the past, but in many cases, distortion is corrected during playback without using such special shooting lenses. I have to. In the correction of distortion due to tilting, perspective transformation according to equations (1) and (2) is employed. Here, (x, y) is the coordinates of the point P of the image before correction, and (x ′, y ′) is the coordinates of the point P ′ of the corrected image corresponding to the point P.
x ′ = (m1 · x + m2 · y + m3) / (m7 · x + m8 · y + 1) (1)
y ′ = (m4 · x + m5 · y + m6) / (m7 · x + m8 · y + 1) (2)
[0004]
In order to perform coordinate conversion by the equations (1) and (2), it is necessary to determine eight parameters m1 to m8. These parameters m1 to m8 can be obtained from the tilt of the camera in the vertical direction and the horizontal direction from the direction facing the object to be imaged, and the distance between the camera and the object to be imaged. However, acquiring such information at the time of shooting is complicated and is not usually performed. Therefore, Japanese Patent Laid-Open No. 2001-84365 proposes to obtain parameters m1 to m8 from a photographed image itself. In this publication, when a portion that should be a rectangle becomes a trapezoid due to distortion, parameters m1 to m8 for making the trapezoid a rectangle based on a straight line passing through the midpoints of the two sides of the trapezoid that are not parallel to each other. Asking for.
[0005]
[Patent Document 1] Japanese Patent Application Laid-Open No. 2001-84365
[Problems to be solved by the invention]
However, the method described in the above publication is applicable when the image is taken from the oblique direction in the vertical direction and when the image is taken from the oblique direction in the horizontal direction, but is applied when the image is taken obliquely in both the vertical direction and the horizontal direction. Can not do it. For this reason, there is a restriction on the position of the camera with respect to the photographing target.
[0007]
The present invention has been made in view of such problems, and an object thereof is to provide an image processing apparatus and an image processing program capable of correcting distortion even if an image is taken from any direction. .
[0008]
[Means for Solving the Problems]
In order to achieve the above object, according to the present invention, an image processing apparatus that corrects distortion of a rectangular image having distortion due to tilt shooting is specified with a quadrangle indicating a partial region of the image, and the four sides of the specified quadrangle Of each of the first side and the second side forming the opposite sides that are closer to the side parallel to the horizontal side than the vertical side of the image. The first value is divided and the third side and the fourth side forming opposite sides that are closer to the vertical side than the horizontal side of the image among the four sides of the specified quadrangle. Find the length in the vertical direction and divide the long side by the short side to get the second value. From the sum of the horizontal lengths of the first side and the second side, overlap the sides in the horizontal direction. The value obtained by multiplying the value obtained by subtracting the length of the portion by the second value is the sum of the length of the side in the horizontal direction and the length in the vertical direction of the third side and the fourth side. Generates a rectangle whose vertical length is the value obtained by multiplying the length of the vertical overlap of those sides by the first value, and generates four vertices of the specified rectangle. The distortion of the image is corrected by perspective transformation that matches the four vertices of the rectangle.
[0009]
In order to achieve the above object, according to the present invention, an image processing apparatus that corrects distortion of a rectangular image having distortion caused by tilt shooting is specified with a quadrangle indicating a partial area of the image, and the apexes are arranged. A, B, C, and D are set in this order, and the smallest rectangle that has a side parallel to the side of the image and circumscribes the rectangle ABCD is generated. The vertex of the rectangle is the vertex A and the vertex of the rectangle ABCD. E, F, G, H in order of arrangement so that side GH touches at least one of B and side GH touches at least one of vertex C and vertex D of quadrilateral ABCD. Let I be a perpendicular from the vertex B to the side FG and let the foot be J, drop a perpendicular from the vertex C to the side FG and let the foot be K, drop a perpendicular from the vertex D to the side HE and let the foot be L , From vertex A to edge EF Lower the line to make the foot O, drop the perpendicular from the vertex B to the side EF and make the foot P, drop the perpendicular from the vertex C to the side GH and make the foot Q, and make the perpendicular from the vertex D to the side GH Lower the leg to R and expand the rectangle EFGH in the direction from the vertex E to the vertex F by the ratio of the longer length of the line segment IL and line segment JK to the shorter one, and from the vertex E to the vertex In a direction toward H, a rectangle EMST is created by expanding the ratio of the longer one of the line segment OP and line segment QR to the shorter one, and the vertices A, B, C, and D of the rectangle ABCD are formed into the rectangle EMST. It is assumed that image distortion is corrected by perspective transformation that matches the vertices E, M, S, and T respectively.
[0010]
These image processing apparatuses perform correction so that a rectangular region having an arbitrary shape designated by the user becomes a rectangle parallel to the side of the image. By enlarging the horizontal size of the quadrangle by the ratio of the length of opposite sides in the vertical direction (≧ 1), and expanding the size of the vertical direction by the ratio of the length of the opposite sides in the horizontal direction (≧ 1), A rectangle that can be appropriately corrected is easily obtained. The user may specify a part of the image that is originally a rectangle, for example, a quadrangle having apexes at the four corners of a white plate or sheet image.
[0011]
Here, when the specified rectangular area becomes larger than the whole image before correction after correction, the corrected image may be reduced at the same rate in two directions perpendicular to each other. In this way, it is possible to reliably fit the designated corrected area within the range in which the image before correction is displayed.
[0012]
Prior to correction, a designated rectangular area may be displayed together with the image. It is easy for the user to determine whether or not the designated rectangular area is appropriate.
[0013]
The processing performed by each of the image processing apparatuses can be described as a program executed by a computer.
[0014]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments of the present invention will be described with reference to the drawings. FIG. 1 shows a personal computer 1 which is an example of an image processing apparatus. The personal computer includes a main body incorporating a CPU, a hard disk, and the like, a display unit provided on the main body, and a keyboard and mouse (not shown). The optical disc 2 can be mounted on the main body. An image processing program in which processing performed on images by the personal computer 1 is recorded on the optical disc 2, and the personal computer 1 copies the program to a built-in hard disk for use. The process performed by the personal computer 1 on the image includes a process of correcting distortion of the tilted image.
[0015]
FIG. 2 shows how a white board is photographed with a digital camera. 3A and 3B are images taken when the digital camera 11 is photographed from the direction A facing the white plate 12 and from the direction B oblique to the white plate 12 in the lateral direction. B) respectively. The squares in FIGS. 3A and 3B represent the image of the edge of the white plate 12, and when taken from the opposite direction, as shown in FIG. 3A, the edge of the rectangular white plate 12 has no distortion. It becomes a rectangular image. Characters, figures and the like drawn on the white board 12 are also images without distortion.
[0016]
On the other hand, when the image is taken from an oblique direction in the horizontal direction, as shown in (B), the edge of the rectangular white plate 12 is distorted to form a trapezoidal image, and characters drawn on the white plate 12 are also distorted. Become. When the white plate 12 is photographed not only in the horizontal direction but also in the vertical direction from an oblique direction, the edge image of the white plate 12 is often a quadrilateral with different lengths on all sides.
[0017]
The personal computer 1 designates a rectangular area of an arbitrary shape on an image having distortion due to tilt shooting, and performs correction for converting the square into a rectangle parallel to the side of the image whose side is a rectangle. The image to be corrected is transmitted from the digital camera 11 to the personal computer 1 via a detachable recording medium or cable, and the rectangular area is designated by a user operation using a mouse or the like.
[0018]
Conversion for correction is performed according to the above-described equations (1) and (2). These equations include eight parameters m1 to m8. For example, the coordinates (x, y) of the four vertices A, B, C, and D of the square of the image having the distortion before correction shown in FIG. By substituting the coordinates (x ′, y ′) of the four vertices A ′, B ′, C ′, D ′ of the corrected image rectangle corresponding to these into the equations (1), (2), Parameters m1 to m8 are easily obtained. However, unless the rectangles A′B′C′D ′ are appropriately determined, the distortion cannot be corrected satisfactorily.
[0019]
In the present invention, in order to define the rectangle A′B′C′D ′, the following is performed. Of the two pairs of opposite sides of the specified quadrangle ABCD, the length in the horizontal direction (the x coordinate difference) of the opposite side (side AB and side CD in the example of FIG. 4) that is more parallel to the horizontal direction (x direction). And the ratio RH of the longer side to the shorter side is obtained. Further, the length (y coordinate) in the vertical direction of the remaining opposite sides (of the two opposite sides of the quadrangle ABCD, the opposite side that is nearly parallel to the vertical direction (y direction), side DA and side BC in the example of FIG. 4). The difference RV is calculated, and the longer ratio RV to the shorter one is determined. Then, the horizontal size of the rectangle ABCD is multiplied by the ratio RV in the vertical direction to obtain the length of the side in the horizontal direction of the rectangle A′B′C′D ′, and the vertical size of the rectangle ABCD is obtained. Multiply by the ratio RH in the horizontal direction to make this the length of the sides in the vertical direction of the rectangle A′B′C′D ′.
[0020]
With such a simple process, parameters m1 to m8 that can satisfactorily correct distortion caused by tilt shooting can be obtained. Hereinafter, this method will be described more specifically with reference to FIG.
[0021]
First, a minimum rectangle EFGH that is parallel to the side of the image and circumscribes a specified rectangular ABCD (the vertices are arranged in this order) is created (FIG. 5A). The minimum bounding rectangle EFGH can be easily obtained from the maximum and minimum values of the x and y coordinates of the four vertices of the rectangle ABCD. The vertices of the rectangle EFGH are E, F, G, H in order so that the side EF touches at least one of the vertices A and B of the quadrangle ABCD and the side GH touches at least one of the vertices C and D of the quadrangle ABCD. And
[0022]
Next, a vertical line is dropped from the vertex A of the rectangle ABCD to the side HE of the rectangle EFGH, the leg is set to I, a vertical line is dropped from the vertex B to the side FG, the leg is set to J, and a vertical line is dropped from the vertex C to the side FG. The foot is set as K, and a perpendicular is dropped from the vertex D to the side HE to set the foot as L (FIG. 5B). In this example, since the vertex A of the rectangle ABCD is in contact with the side EF of the rectangle EFGH, the point I coincides with the vertex E of the rectangle EFGH. In addition, since the vertex D of the rectangle ABCD is in contact with both the side GH and the side HE of the rectangle EFGH (is in contact with the vertex H), the point L coincides with the vertex D and the vertex H.
[0023]
Next, the lengths of the line segment IL and the line segment JK are compared to determine the ratio R1 of the longer length to the shorter one (IL / JK in this example). Then, the rectangle EFGH is enlarged R1 times in the direction of the vertex F with respect to the vertex E, thereby creating a rectangle EMNH (FIG. 5C).
[0024]
Furthermore, a perpendicular line is dropped from the vertex A of the rectangle ABCD to the side EF of the rectangle EFGH, the foot is set to O, a vertical line is dropped from the vertex B to the side EF, the foot is set to P, and a vertical line is dropped from the vertex C to the side GH. The leg is defined as Q, a perpendicular is dropped from the vertex D to the side GH, and the leg is defined as R (FIG. 5D). In this example, since the vertex A of the rectangle ABCD is in contact with the side EF of the rectangle EFGH, the point O is coincident with the vertex A of the rectangle ABCD, and the vertex C of the rectangle ABCD is in contact with the side FG of the rectangle EFGH. Therefore, the point Q coincides with the vertex G of the rectangle EFGH. Further, since the vertex D of the rectangle ABCD is in contact with both the side GH and the side HE of the rectangle EFGH (is in contact with the vertex H), the point R coincides with the vertex D and the vertex H.
[0025]
Next, the lengths of the line segment OP and the line segment QR are compared to determine the ratio R2 of the longer length to the shorter one (QR / OP in this example). Then, the rectangle EMNH is enlarged R2 times in the vertex H direction with reference to the vertex E, thereby creating a rectangle EMST (FIG. 5E).
[0026]
This rectangle EMST is the rectangle A′B′C′D ′ of FIG. 4, and the vertexes A, B, C, D of the rectangle ABCD are associated with the vertices E, M, S, T of the rectangle EMST, respectively. The parameters m1 to m8 are obtained by substituting the coordinates into the equations (1) and (2). Here, the enlargement of the rectangle EFGH is performed first in the horizontal direction (x direction) and later in the vertical direction (y direction), but the order may be reversed. Alternatively, the rectangle EMNH may be created by directly enlarging the rectangle EFGH in the horizontal direction and the vertical direction by obtaining the ratios R1 and R2 of the lengths of the line segments without creating the rectangle EMNH in the middle.
[0027]
In the example shown here, the side length of the rectangle ABCD has a relationship of AB <CD and BC <DA. However, the above method is applied to any rectangle having a different side length relationship. be able to.
[0028]
The flow of distortion correction processing in the personal computer 1 is shown in the flowchart of FIG. First, an image to be corrected having distortion is read (step # 1), and the entire image is displayed on the display unit (# 2). An example of this display is shown in FIG. Here, in addition to the read image 21, a button 22 for instructing whether or not to perform distortion correction processing, a button 23 for instructing whether or not to perform background removal processing, and execution of processing are executed. An instruction button 24 is displayed. At this stage, the user operates the buttons 22 and 23 with the mouse, and further operates the button 24 to instruct execution of processing.
[0029]
Next, a predetermined rectangle indicating the area of the image is displayed so as to overlap the image (# 3). An example of this display is shown in FIG. The predetermined rectangle 32 is a rectangle located at the center of the image. In FIG. 8, reference numeral 31 denotes a rectangular image to be photographed (for example, an image of a white plate edge). After displaying the quadrangle 32, designation of a rectangular area is accepted (# 4). The user designates a region by moving the four vertices of the displayed rectangle 32 using the mouse. In this example, the vertex of the quadrangle 32 is positioned on the vertex of the image 31. A quadrangle 33 representing the designated area is shown in FIG. It should be noted that the outside of the default rectangle 32 or the rectangle 33 after the shape change is displayed with lower brightness than the inside so that the user can clearly see the designated area.
[0030]
After accepting the area designation, it is determined whether or not an instruction to correct distortion is given by operating the button 22 in FIG. 7 (# 5). When the instruction is given, the parameters m1 to m8 in the equations (1) and (2) are determined by the above-described method, and the distortion correction is performed on the inside of the rectangle 33 in the image 21 (# 6). ). After the end of the correction process and when no correction instruction is given in the determination of step # 5, it is determined whether or not an instruction to perform the background removal process is given by operating the button 23 in FIG. # 7).
[0031]
If this instruction has been given, a background removal process is performed to increase the luminance of pixels whose luminance is greater than or equal to a predetermined value (# 8). By this processing, the base portion on which nothing is drawn is observed in white in the image, and the drawn characters, figures, and the like become clearer. The ground removal process is disclosed in, for example, Japanese Patent Application Laid-Open No. 2002-281369.
[0032]
After completion of the background removal process and when the instruction is not given in the determination in step # 7, the corrected image (the part corresponding to the area of the rectangle 33) is displayed (# 9), and the process is performed. finish. A display example of the corrected image is shown in FIG. The images in FIGS. 8 and 9 have distortions, and therefore the sizes of the characters are different. However, the corrected images have the distortion removed and the size of the characters becomes uniform.
[0033]
In the method of the present invention for enlarging a specified quadrangle, the corrected image (the portion obtained by enlarging the quadrangle into a rectangle) is larger than the entire image before correction, and the entire image is displayed on the display unit. May not be possible. In that case, the corrected image may be reduced so as to be smaller than the image before the correction. At the time of the reduction, it is preferable that the reduction ratio is the same in the vertical direction and the horizontal direction so as not to impair that the aspect ratio of the image is appropriate by correcting the distortion.
[0034]
In this example, only the designated rectangular area is corrected. However, the entire image may be corrected. This is because characters, figures, and the like may be drawn outside the rectangular area designated by the user. Such a situation occurs, for example, in the following case. Some white plates have ruled lines in the vertical and horizontal directions, and such ruled lines form a rectangle, so that the white plate can be used as a rectangular region after correction in the same manner as the edge of the white plate. The user shoots only the portion of the white board with the ruled lines on which characters, figures, etc. are drawn so that it reaches the other end from one end of the image, and creates a relatively small rectangular area along the ruled line. When specified, characters, figures, etc. will be located outside that area.
[0035]
When the entire image is corrected, the entire corrected image may be displayed. Although the entire image after correction does not become a rectangle, it is displayed in a reduced size so that it can be observed, and the user can specify a rectangular area for that image, and only the specified rectangular area is enlarged. And redisplay it. Also in this case, it is preferable that the reduction ratio and the enlargement ratio are equal in the vertical direction and the horizontal direction.
[0036]
In the present embodiment, the image captured by the digital camera 11 is corrected by the personal computer 1. However, the digital camera 11 itself can correct the image. Although an example in which the image processing program is provided by the optical disc 2 has been described here, the image processing program may be provided via the Internet.
[0037]
【The invention's effect】
According to the image processing apparatus and the image processing program of the present invention, distortion of a tilted image can be easily corrected based on only the image and irrespective of the tilt direction.
[0038]
When the specified rectangular area becomes larger than the entire image before correction after correction, if the image after correction is reduced at the same rate in two directions perpendicular to each other, the image before correction is displayed. The specified corrected area can be reliably contained within the range.
[0039]
If the designated rectangular area is displayed together with the image before correction, it is easy for the user to know whether or not the designated rectangular area is appropriate.
[Brief description of the drawings]
FIG. 1 is a diagram schematically showing a personal computer which is an embodiment of an image processing apparatus of the present invention.
FIG. 2 is a diagram showing a state in which a white board is photographed by a digital camera.
FIG. 3 is a view showing an image taken as shown in FIG. 2;
FIG. 4 is a diagram illustrating a correspondence relationship between an image before correction and an image after correction.
FIG. 5 is a diagram showing a process for obtaining parameters necessary for distortion correction.
FIG. 6 is a diagram showing an overall flow of distortion correction processing;
FIG. 7 is a diagram showing a display example at an initial stage of distortion correction processing;
FIG. 8 is a diagram showing an example of a default rectangular area to be displayed prior to area designation.
FIG. 9 is a view showing a rectangular area designated by a user.
FIG. 10 is a diagram illustrating an example of an image after distortion correction.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 1 Personal computer 2 Optical disk 11 Digital camera 12 White board 21 Image 22 Edge correction button 23 Ground-off button 24 Execution button 31 White board image 32 Default area 33 Specified area

Claims (6)

In an image processing apparatus that corrects distortion of a rectangular image having distortion due to tilt shooting,
Given a rectangle that represents a partial area of the image,
Finding the horizontal lengths of the first and second sides of the four sides of the specified quadrangle, which are opposite to each other and closer to the horizontal side than the vertical side of the image, Divide the longer one by the shorter one to get the first value,
Finding the vertical lengths of the third and fourth sides of the four sides of the specified quadrangle, which are opposite to each other and closer to the vertical side than the horizontal side of the image, Divide the longer one by the shorter one to get the second value,
The length of the side in the horizontal direction is obtained by multiplying the sum of the lengths in the horizontal direction of the first side and the second side by the value obtained by subtracting the length of the overlapping portion in the horizontal direction of those sides and the second value. The vertical side is a value obtained by multiplying the sum of the vertical lengths of the third side and the fourth side by the length obtained by subtracting the length of the vertical overlapping portion of those sides and the first value. Generate a rectangle with the length of
An image processing apparatus that corrects image distortion by perspective transformation that matches four vertices of a specified rectangle with four vertices of a generated rectangle. In an image processing apparatus that corrects distortion of a rectangular image having distortion due to tilt shooting,
Given a quadrangle that indicates a partial area of the image, the vertices are A, B, C, and D in order,
A smallest rectangle having sides parallel to the sides of the image and circumscribing the rectangle ABCD is generated, and the vertex of the rectangle is touched by at least one of the vertex A and the vertex B of the rectangle ABCD, and the side GH is E, F, G, H in order of arrangement so as to contact at least one of the vertex C and the vertex D of the rectangle ABCD,
Draw a perpendicular from the vertex A to the side HE and let that foot be I,
Draw a perpendicular from the vertex B to the side FG and let that foot be J,
Draw a perpendicular from the vertex C to the side FG and let that foot be K,
Draw a perpendicular from the vertex D to the side HE and let that foot be L,
Draw a perpendicular line from the vertex A to the side EF and set the foot to O.
Draw a perpendicular from vertex B to side EF and let that foot be P,
Draw a perpendicular from the vertex C to the side GH and let that foot be Q,
Draw a perpendicular from the vertex D to the side GH and let that foot be R,
The rectangle EFGH is enlarged in the direction from the vertex E to the vertex F by the ratio of the longer length of the line segment IL and the line segment JK to the shorter one, and the line segment in the direction from the vertex E to the vertex H. A rectangle EMST is created by enlarging by the ratio of the longer length of the OP and the line segment QR to the shorter one,
An image processing apparatus that corrects image distortion by perspective transformation in which vertices A, B, C, and D of a quadrangle ABCD coincide with vertices E, M, S, and T of a rectangle EMST, respectively. When the specified rectangular area is larger than the entire image before correction after correction, the corrected image is at the same rate in two directions perpendicular to each other so as to be less than the size of the entire image before correction. The image processing apparatus according to claim 1, wherein the image processing apparatus is reduced. The image processing apparatus according to claim 1, wherein a specified rectangular area is displayed together with an image before correction. In an image processing program in which processing for correcting distortion of a rectangular image having distortion due to tilt shooting is described,
A process of accepting specification of a rectangle indicating a partial area of the image;
Finding the horizontal lengths of the first and second sides of the four sides of the specified quadrangle, which are opposite to each other and closer to the horizontal side than the vertical side of the image, A process of dividing the long side by the short side to obtain the first value;
Finding the vertical lengths of the third and fourth sides of the four sides of the specified quadrangle, which are opposite to each other and closer to the vertical side than the horizontal side of the image, A process of dividing the longer one by the shorter one to obtain the second value;
The length of the side in the horizontal direction is obtained by multiplying the sum of the lengths in the horizontal direction of the first side and the second side by the value obtained by subtracting the length of the overlapping portion in the horizontal direction of those sides and the second value. The vertical side is a value obtained by multiplying the sum of the vertical lengths of the third side and the fourth side by the length obtained by subtracting the length of the vertical overlapping portion of those sides and the first value. Processing to generate a rectangle with the length of
An image processing program characterized in that a process for correcting image distortion is described by perspective transformation for matching four vertices of a specified rectangle with four vertices of a generated rectangle. In an image processing program in which processing for correcting distortion of a rectangular image having distortion due to tilt shooting is described,
A process of accepting designation of a quadrangle indicating a partial area of an image and setting the vertices to A, B, C, and D in the order of arrangement;
A smallest rectangle having a side parallel to the side of the image and circumscribing the rectangle ABCD is generated, and the vertex of the rectangle is touched by at least one of the vertex A and the vertex B of the rectangle ABCD, and the side GH is A process of setting E, F, G, and H in the arrangement order so as to contact at least one of the vertex C and the vertex D of the rectangle ABCD;
Draw a perpendicular from the vertex A to the side HE and let that foot be I,
Draw a perpendicular from the vertex B to the side FG and let that foot be J,
Draw a perpendicular from the vertex C to the side FG and let that foot be K,
Draw a perpendicular from the vertex D to the side HE and let that foot be L,
Draw a perpendicular line from the vertex A to the side EF and set the foot to O.
Draw a perpendicular from vertex B to side EF and let that foot be P,
Draw a perpendicular from the vertex C to the side GH and let that foot be Q,
A process of dropping a perpendicular from the vertex D to the side GH and setting the foot to R;
The rectangle EFGH is enlarged in the direction from the vertex E to the vertex F by the ratio of the longer length of the line segment IL and the line segment JK to the shorter one, and the line segment in the direction from the vertex E to the vertex H. A process of enlarging by a ratio of the longer length of the OP and the line segment QR to the shorter one to create a rectangle EMST;
An image processing program characterized in that a process for correcting image distortion is described by perspective transformation in which the vertices A, B, C, and D of the rectangle ABCD are made to coincide with the vertices E, M, S, and T of the rectangle EMST, respectively. .

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