JP2000151971A - Picture processor - Google Patents

Abstract

PROBLEM TO BE SOLVED: To highly precisely correct a distorted picture by assuming a quadrangle surrounding an original picture and correcting/outputting the picture distortion with coordinates of the eight reference points of the four apexes and four midpoints of sides and shape functions corresponding to the eight points. SOLUTION: A photographing object image 1 is taken on a solid-state coupling element CCD array 3 through a lens 2 and it is picture-processed by a picture processing processor 4. A right-angle coordinate system being a reference is made to correspond to the CCD array 3 and respective picture elements on a picture are made correspond to coordinate values on a reference orthogonal coordinate system. The picture of eight reference points are recognized by a binarization processing, and their coordinates are obtained. The whole picture is scanned and an operation is executed from the coordinates of the respective picture elements and the coordinates of the eight reference points and the corrected coordinates are decided. When the correction of all the picture elements is completed by the picture processing processor 4, a picture 5 is outputted after correction. Thus, correction in spite of the character of a distortion is highly precisely executed whether the distortion of the picture is geometric or not.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention corrects a terrain image photographed by remote sensing or a general image read by an image scanner when the terrain image is distorted for some irregular reason. The present invention relates to an improvement of an image processing apparatus having a function of restoring an image.

[0002]

2. Description of the Related Art A technique for correcting a distortion of a plane figure is required in various industrial fields, but a basic technique is to correct a geometric distortion by coordinate transformation. When it is estimated that the distortion is caused by enlargement, reduction, translation, or rotation, the Helmert transformation formula is used. When the deformation includes a skew distortion (shear distortion), an affine transformation formula is used.

In addition, a pseudo-affine transformation formula, a quadratic conformal transformation formula, a secondary projection transformation formula, and the like are used depending on the nature of distortion. If the distortion is not geometric, a higher order polynomial is used.

[0004] For these conventional techniques, see Obayashi; Remote sensing for practitioners;
Published by Techno System; p83, Takagi, Shimoda; Image Analysis Handbook; (1991) Published by The University of Tokyo Press; p42
3

[0005]

The correction of the distortion by the above-mentioned known geometric transformation formula can be applied by a corresponding transformation formula if the nature of the distortion is known. However, for example, when an image printed on a thick book is copied by a copier, the distortion of the image after copying, which is caused by the fact that the image cannot be pressed on a flat surface, is not geometric in nature. There are many. In such a case, it is not possible to determine which conversion formula is to be applied to correct the correction with high accuracy. On the other hand, the method of using a higher-order polynomial as a conversion equation largely depends on how to select a reference point only by minimizing a correction error at a plurality of appropriately selected reference points.

[0006]

When a distorted image is compared with an image before being distorted, an arbitrary rectangular area (quadrilateral area) of the image before being distorted is replaced with a distorted quadrilateral area of the image after being distorted. Correspondingly, a quadrilateral region can be chosen in which the image distortion is characterized by the shape of the distorted quadrilateral sides.

[0007] A function called a shape function is known as a relationship that associates the coordinates of the midpoint of each vertex and side of such a quadrilateral area with the coordinates of an arbitrary point in the quadrilateral area. The present invention is characterized in that this shape function is used as means for solving the above problem.

[0008] The shape function is defined as P ₁ (−1, −1), P ₂ (1, −1) when a square having a side length of 2 is assumed on the ξ, η orthogonal coordinate system shown in FIG. , P ₃ (1,
1), P ₄ (−1, 1), P ₅ (0, −1), P ₆ (1,
0), P ₇ (0,1), P ₈ (-1,0), so that the value is 1 at one point and the value is 0 at the other seven points. Special eight functions Fi (ξ, η), (i = 1, 8). Such functions cannot be derived theoretically, but are found by accident by trial and error. Equations (1) to (8) show the shape function for each point.

[0009]

F ₁ (ξ, η) = (1−ξ) (1−η) (− 1−ξ−η) (1)

[0010]

F ₂ (ξ, η) = (1 + ξ) (1−η) (− 1 + ξ−η) (2)

[0011]

F ₃ (ξ, η) = (1 + ξ) (1 + η) (− 1 + ξ + η) (3)

[0012]

F ₄ (ξ, η) = (1−ξ) (1 + η) (− 1−ξ + η) (4)

[0013]

F ₅ (ξ, η) = (1−ξ ² ) (1−η) (5)

[0014]

F ₆ (ξ, η) = (1 + ξ) (1−η ² ) (6)

[0015]

F ₇ (ξ, η) = (1−ξ ² ) (1 + η) (7)

[0016]

F ₈ (ξ, η) = (1 − () (1−η ² ) (8) Using the above shape function, it is drawn on the u and v coordinates as shown in FIG. , Any point R inside the distorted quadrilateral
The coordinates of (u, v) can be approximately obtained. The coordinates of the vertex of the quadrilateral and the midpoint of the side are ui, vi (i = 1,
8), u and v are known to be obtained by the following equations.

[0017]

(Equation 9)

[0018]

(Equation 10)

The present invention converts the u, v coordinates of an arbitrary point inside the distorted quadrilateral into the coordinates of the corresponding points of the undistorted quadrilateral by using the properties of the shape function in reverse. An object of the present invention is to provide an image processing apparatus having a function of correcting a distorted image. The procedure will be specifically described.

When the equations (9) and (10) are solved for ξ and η, the following equations are obtained.

[0021]

Equation 11] G (ξ, η) = A 1 ξ + A 2 η + A 3 ξη + A 4 ξ 2 + A 5 η 2 + A 6 ξ 2 η + A 7 ξη 2 + A 8 -4u = 0 ... (11)

[0022]

Equation 12] H (ξ, η) = B 1 ξ + B 2 η + B 3 ξη + B 4 ξ 2 + B 5 η 2 + B 6 ξ 2 η + B 7 ξη 2 + B 8 -4v = 0 ... (12) Here,

[0023]

A ₁ = 2 (u ₆ −u ₈ ) (13)

[0024]

A ₂ = −2 (u ₅ −u ₇ ) (14)

[0025]

A ₃ = u ₁ −u ₂ + u ₃ −u ₄ (15)

[0026]

A ₄ = u ₁ + u ₂ + u ₃ + u ₄ -2 (u ₅ + u ₇ ) (16)

[0027]

Equation 17] _{A 5 = u 1 + u 2} + u 3 + u 4 -2 (u 6 + u 8) ... (17)

[0028]

A ₆ = −u ₁ −u ₂ + u ₃ + u ₄ +2 (u ₅ −u ₇ ) (18)

[0029]

A ₇ = −u ₁ + u ₂ + u ₃ −u ₄ −2 (u ₅ −u ₈ ) (19)

[0030]

A ₈ = − (u ₁ + u ₂ + u ₃ + u ₄ ) +2 (u ₅ + u ₆ + u ₇ + u ₈ ) (20)

[0031]

B ₁ = 2 (v ₆ −v ₈ ) (21)

[0032]

B ₂ = −2 (v ₅ −v ₇ ) (22)

[0033]

B ₃ = v ₁ −v ₂ + v ₃ −v ₄ (23)

[0034]

B ₄ = v ₁ + v ₂ + v ₃ + v ₄ -2 (v ₅ + v ₇ ) (24)

[0035]

Equation 25] _{B 5 = v 1 + v 2} + v 3 + v 4 -2 (v 6 + v 8) ... (25)

[0036]

B ₆ = −v ₁ −v ₂ + v ₃ + v ₄ +2 (v ₅ −v ₇ ) (26)

[0037]

Equation 27] _{B 7 = -v 1 + v 2} + v 3 -v 4 -2 (v 5 -v 8) ... (27)

[0038]

B ₈ = − (v ₁ + v ₂ + v ₃ + v ₄ ) +2 (v ₅ + v ₆ + v ₇ + v ₈ ) (28) Ai, Bi (i = 1, 8) are represented by ui, vi. If the coordinates of the vertex of the distorted quadrilateral and the midpoint of the side are determined by the coefficient, it becomes a constant. U and v are constants if the coordinates of the point R inside the quadrilateral are determined. Therefore, equations (11) and (12) are ξ, η
It is a simultaneous equation regarding.

This equation includes bilinear, biquadratic and bicubic unknowns and cannot be solved algebraically. However, it is possible to solve by using an approximate solution method of a nonlinear equation. For example, by using the Newton-Rapson method, a solution very close to the true solution can be obtained by several repetition operations.

According to the above procedure, the points ui, vi (i = 1, 2) on the distorted coordinates (u, v) corresponding to the vertices of the quadrilateral on the original coordinates (x, y) and the midpoints of the sides. 8), from the coordinates (u, v) of an arbitrary point R inside the area surrounded by ui, vi (i = 1, 8), the value of (ξ, η) corresponding to that point is calculated. You can ask. Since the value of (ξ, η) corresponds to a square having a height and width of ± 1, if the vertical and horizontal scale (or enlargement ratio) is determined from the vertical and horizontal dimensions of the original quadrilateral, the corresponding point (x , Y) can be determined approximately.

The actual accuracy with which the image distortion is corrected by the above-described means will be described with reference to an actual example. FIG.
Is a circle with a radius of 50, the solid line is the original image without distortion, and the dashed line is the image after distortion. FIG. 4 shows the result of applying the above means to the distorted image.

In FIG. 4, the solid line represents the original image before distortion, and the eight points on the circumference correspond to the eight points on the dotted circle in FIG.
The point is obtained by correcting the above-mentioned means.
As shown in FIG. 4, the corrected point almost completely matches the original image, and it can be seen that the above means is extremely effective as a method for correcting a distorted image.

[0043]

According to the means described in the preceding paragraph, a quadrilateral region surrounding the original image is assumed, and eight points on the distorted image corresponding to the vertices and the midpoint of the side are determined. Just by specifying, the distorted image can be corrected with high accuracy.

FIG. 5 shows an example of an image processing apparatus incorporating this means as software. An object to be imaged 1 is imaged as an image on a solid-state coupling device (CCD) array 3 via a lens 2. In the case of FIG. 5, there are eight reference points in the object to be photographed in advance, and their positions (coordinates) are known.

The image data is sent to the image processor 4 for processing. A rectangular coordinate system serving as a reference is associated with the CCD array 3, and each pixel (pixel) on the image is associated with a coordinate value on the reference coordinate system. The images of the eight reference points are recognized by the binarization processing, and the coordinates are obtained.

The entire image is scanned and the coordinates R of each pixel are
Equations (11) and (1) are obtained from (u, v) and the coordinates of the eight reference points.
The corrected coordinates (x, y) are determined using 2). When the correction of all the pixels is completed, the corrected image 5 is output.

When the terrain is photographed from an airplane or an artificial satellite, eight points on a quadrilateral of which latitude and longitude are known can be determined. Can be modified well.

In FIG. 5, a lens is used for the image capturing section, but the same applies to an image scanner such as an image reading section of a copying machine. In this case, it is assumed that the reference point is written on the read original.

[0049]

According to the present invention, there is an effect that the image can be corrected with high accuracy regardless of the nature of the distortion whether the distortion of the image is geometric or not.

[Brief description of the drawings]

FIG. 1 is a diagram illustrating a square shape function according to the present invention.

FIG. 2 is a schematic view of a quadrilateral distorted image of the present invention.

FIG. 3 is an original image to which the correction of the present invention is applied.

FIG. 4 is an image illustrating a corrected result of the present invention.

FIG. 5 is a block diagram showing an embodiment of the present invention.

[Explanation of symbols]

DESCRIPTION OF SYMBOLS 1 ... Target image, 2 ... Lens, 3 ... Solid coupling element array, 4 ... Image processor, 5 ... Modified image.

 ──────────────────────────────────────────────────続 き Continued on the front page F term (reference) 5B057 AA14 BA02 BA23 CA06 CA12 CA16 CB06 CB12 CB16 CC01 CD12 CH01 CH08 DA17 DB02 DB08 DC05 5C076 AA40 BA06

Claims (1)

[Claims] An image processing apparatus for inputting an image distorted for some reason, correcting the distortion by processing the image, and outputting the corrected image. Eight reference points corresponding to the points are given, and the distortion of the image is corrected and output using the coordinates of the eight reference points on the input image and the shape function corresponding to the eight points. An image processing apparatus comprising: