JP2000076439A - Picture deforming method and its device - Google Patents

Abstract

PROBLEM TO BE SOLVED: To speedily simulate how an original picture is deformed by mapping defined for deforming a picture. SOLUTION: A polygon generator 4 generates plural plygons corresponding to the original picture. A texture coordinate assigning device 5 assigns a texture coordinate for mapping the original picture to each of these generated polygons. A polygon deforming device 6 deforms each polygon by executing coordinate transformation with respect to all the vertexes of the polygons based on the defined map. Then, a texture mapping device 7 deforms the original picture by adhering a corresponding picture pattern of the original picture by texture mapping based on the original picture, a texture coordinate, etc., assigned by the device 5 with respect to each deformed polygon to display it. This device 7 consists of a dedicated hardware.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an image transformation method and apparatus for performing high-speed image transformation processing.

[0002]

2. Description of the Related Art As one of image designing methods, there is known a method of using an appropriate image as an original image and deforming the original image. As a method of deforming an image used in such a case, a method in which irregular deformation is performed is more desirable than a method in which regular deformation is performed, because the method is rich in variations.

The applicant has previously proposed an image deformation method capable of performing irregular deformation on an image, and the method will be briefly described below. This method includes a method using a rectangular coordinate system and a method using a polar coordinate system. That is, in order to perform image deformation, a mapping for coordinate transformation is defined for all pixels of the image to be deformed, and (x,
The pixel at the position y) is moved to another position (x ', y'). There are a method of defining the mapping in a rectangular coordinate system and a method of defining the mapping in a polar coordinate system.

[Image Deformation Method Using Orthogonal Coordinate System] First, an original image and two two-dimensional scalar fields A and B are prepared (step S1 in FIG. 4). As the two-dimensional scalar fields A and B, any two-dimensional scalar fields may be used, but here, a two-dimensional fractal field is used. A fractal field is a field in which scalar values are defined in space in a self-similar manner and is a continuous field with natural fluctuations.Therefore, if a fractal field is used as a two-dimensional scalar field, the natural This is because irregular deformation with fluctuation can be performed. In order to generate a two-dimensional fractal field, for example, a method widely known as a midpoint displacement method may be used.

Next, an orthogonal coordinate system is set for the original image and the two-dimensional fractal fields A and B (step S2 in FIG. 4). Here, the original image and the two-dimensional fractal fields A and B
May be the same, but may be different. Original image and two-dimensional fractal fields A and B
Are different, the coordinate system may be normalized so that the positions of the pixels in each image have a one-to-one correspondence. Here, it is assumed that the coordinate system is normalized. That is, the size of each image is [0, 1] in both the x and y directions.
].

Next, a mapping is defined (step S in FIG. 4).
3). That is, in order to deform the original image, a mapping that moves the pixel at the position (x, y) of the original image to the position (x ′, y ′) is necessary. Then, by applying the defined mapping to all the pixels of the original image, the original image can be deformed.

Now, assuming that the pixel at the position (x, y) in the original image is to be moved to the position (x ', y') after the transformation, the mapping is defined by the following equation, for example. Can be.

X ′ = x + k _A F _A (x, y) (1) y ′ = y + k _B F _B (x, y) (2) where k _A and k _B are in the x and y directions. This is a coefficient representing the magnitude of the displacement, and can be set arbitrarily. The functions F _A (x, y) and F _B (x, y) represent scalar values at the position (x, y) of the two-dimensional fractal fields A and B, respectively.

According to the equations (1) and (2), (x,
The magnitude of the displacement in the x direction of the pixel at the position y) is proportional to the scalar value of the two-dimensional fractal field A at the position (x, y), and the magnitude of the displacement in the y direction is the two-dimensional fractal field B Is proportional to the scalar value at the position (x, y). When the size of each image is normalized as in this case, F _A (x, y) and F _B (x, y)
Is preferably normalized to the range [-1, + 1].

Next, a deformation process is performed on the original image (step S4 in FIG. 4). That is, focusing on the pixel at the position (x, y) of the original image, the destination position (x ', y') of the pixel is obtained by mapping using the above equations (1) and (2).
The pixel value at the position (x, y) of the original image is written at the position (x ', y') in a memory space different from the previously prepared original image. Deformation can be performed by performing this processing on all pixels of the original image.

When the original image is deformed in step S4, an image obtained as a result of the deformation (hereinafter, referred to as a deformed image) has a pixel whose pixel value is not defined (hereinafter, such a pixel is referred to as a deformed image). May be referred to as a blank pixel). That is, in practice, the number of pixels is finite,
The coordinate values indicating the positions of the pixels are discrete discrete values, whereas the moving amounts k _A F _A (x, y) in the x direction and the moving amounts k in the y direction of the pixels are determined by the mapping. _B F
_{Since B} (x, y) is usually a continuous quantity, quantization is performed when obtaining the destination position (x ′, y ′), and therefore, a plurality of pixels of the original image are quantized. The destination may overlap the same position on the deformed image. For example,
Now, assuming that each of the original image and the deformed image is composed of a 10 × 10 pixel array, each of the 100 pixels constituting the pixel array of the original image is based on the mapping defined in the deformation. When the position of the movement destination obtained as a result of the mapping is quantized, a plurality of pixels of the original image may be integrated at the same position in the deformed image.

[0012] Conversely, this means that a blank pixel whose pixel value is not defined occurs on the deformed image.
For example, a total of 100 pixels that existed on the original image
Assuming that the pixels are integrated into a total of 70 pixels by the movement, 30 pixels on the deformed image become empty pixels.

Therefore, when deforming the original image in step S4, it is necessary to perform processing on empty pixels. As the processing of the empty pixel, for example, if a definition such as “set the pixel value to 0 for an empty pixel” is made in advance, the empty pixel portion is expressed in black. Further, a process of assigning some background image to the area of the empty pixel may be performed.

Further, it is possible to deform the original image so as not to cause a blank pixel on the deformed image. The technique can be performed by using the mapping in reverse. For example, now deformation of (1), assuming that is defined by the equation _{(2), x = x'-k A F} A (x ', y') ... (3) y = y'-k B F _B (x ′, y ′)... (4) Here, (x, y) is a pixel position on the original image, and (x ′, y ′) is a pixel position on the deformed image. That is, first, the position on the deformed image (x ', y') in focused, two-dimensional fractal field A at that position, B scalar value _{F A (x ', y'} ), F B (x ',
y ′), the amount of movement k _A F _A (x ′, y ′) in the x direction and y
Direction of movement amount _{k B F B (x ',} y') sought, (1) and
The position (x, y) on the original image corresponding to the position (x ', y') on the deformed image is obtained by the inverse operation of equation (2), and the position (x, y) on the original image is calculated. The pixel value is set as the pixel value at the position (x ', y') on the deformed image. With such a method, it is possible to avoid generation of empty pixels in the deformed image.

When a certain pixel p on the original image is moved by mapping, the position after the movement may protrude out of the range of the deformed image. Assuming that areas of the same size (virtual deformed images) are arranged adjacent to each other, an out-of-plane correction process may be performed to correct the moved position within the range of the deformed image. For example, as a result of mapping the pixel p of the original image, if the pixel protrudes out of the range of the deformed image as shown by p 'in FIG. 5, the same as the deformed image as shown by the broken line in the figure outside the range of the deformed image Assuming that virtual deformed images of the size are arranged adjacently,
The position is corrected to the position of the position p ″ in the deformed image which is the same as the position of p ′ in the virtual deformed image. FIG. 5 shows an example in which the deformed image extends laterally. The same correction is applied to the case of protruding in the vertical direction.

As described above, according to this deformation method, an irregular deformation having natural fluctuation can be applied to the original image. And the mode of the deformation is
It can be controlled by the values of the coefficients k _A and k _B shown in (1) and (2) and what kind of two-dimensional fractal fields A and B are used.

[Image Deformation Method Using Polar Coordinate System] In this method, a polar coordinate system is used to define a mapping for determining a destination of a pixel in an original image. The processing flow is shown in FIG.
It seems as shown. First, an original image and two two-dimensional scalar fields A and B are prepared (step S11). This step S11 is the same as step S1 in FIG. Next, a polar coordinate system is set for the original image and the two-dimensional fractal fields A and B (step S12). Here, it is also assumed that the coordinate system is normalized.

Next, a mapping is defined (step S1).
3). This mapping can be defined, for example, as in the following equations (5) to (8). _{r = k r F A (x} , y) ... (5) θ = k q F B (x, y) ... (6) x '= x + rcosθ ... (7) y' = y + rsinθ ... (8) wherein, x , Y are the x-coordinate and y-coordinate of the pixels of the original image in the orthogonal coordinate expression, respectively, and x ′, y ′ are the x-coordinate and y-coordinate of the transformed image after the pixels of the original image have been moved by mapping Where k _r is a coefficient representing the magnitude of the r component of the displacement in polar coordinates, and k _q is θ of the displacement in polar coordinates.
_A coefficient representing the magnitude of the component, and the function F _A (x, y),
F _B (x, y) represents a scalar value at the position (x, y) of the two-dimensional fractal fields A and B, respectively. In addition,
It is assumed that the range of the above two functions F _A (x, y) and F _B (x, y) is normalized to the range of [−1, +1].

According to such a mapping, the coefficients k _r and / or
Alternatively, by appropriately determining the value of the coefficient k _q , it is possible to control the magnitude of the deformation or the degree of the local deformation as desired.

Further, the value of θ determined by the above equation (6) is not used as it is as the direction component of the displacement, but an angle θ ′ deviated to a specific angle with respect to the input angle θ is output. by introducing the function _{f a θ '= f a (} θ) = f a (k q F B (x, y)) ... (9) and extends, the theta' value of the above (7), ( 8) By substituting into the equation to determine the destination position (x ', y'),
The direction of the deformation can be controlled so as to be deviated to a desired angle direction. FIG. 7 shows an example. In FIG. 7, the horizontal axis θ is the value of θ determined by the above equation (6), and the vertical axis θ ′ is the value obtained by the above equation (9). In FIG. 7, an angle θ ′ having a bias in the π direction and the 2π (= 0) direction is obtained as shown by a solid line with respect to θ uniformly distributed as shown by a broken line. Therefore, 'give, the theta' theta using a function f _a with input-output characteristic indicated by the solid line in FIG. 7 the value of the above (7), the position of the destination are substituted into equation (8) (x ', Y'), the deformation in the left-right direction (θ '= 0, π, 2π) is emphasized in the deformed image.

As described above, when the coordinate system is expressed in polar coordinates, the mapping may be defined in consideration of the above-mentioned items.

Next, a deformation process is performed on the original image (step S14). The processing of the empty pixel and the protruding processing are the same as described above. In particular, in order not to cause a blank pixel on the deformed image during the process of the variation, for _{example, r = k r F A (} x ', y') ... (10) θ = k q F B ( x ′, y ′) (11) x = x′−r cos θ (12) The original image may be deformed using the mapping y = y′−rsin θ (13). here,
(X, y) is a pixel position on the original image, and (x ', y') is a pixel position on the deformed image. As a result, the position (x, y) on the original image corresponding to the position (x ', y') on the deformed image can be obtained in the same manner as described above. What is necessary is just to write the pixel value at the position (x ', y') on the deformed image.

As described above, even with this deformation method, it is possible to apply an irregular deformation with natural fluctuations to the original image. And the mode of the deformation is
It can be controlled by various parameters described above and what two-dimensional fractal fields A and B are used.

[0024]

However, in the above-described image deformation method, since it is necessary to perform the deformation process on all the pixels of the original image according to the defined mapping, it takes a long time to perform the deformation process. There is a problem. Of course, when presenting a designed image or creating an image for a printing plate, it is necessary to apply a transformation process to all pixels of the original image to obtain a completely transformed image as described above. However, in the design process, the designer changes the two-dimensional scalar field to be used, or variously changes the coefficient or parameter value as described above, and determines what kind of image can be obtained. There is a case where it is desired to try, and in such a case, even if the obtained deformed image is not strict, it is desired that the image deforming process be performed at high speed.

SUMMARY OF THE INVENTION It is an object of the present invention to provide an image deforming method and an image deforming method capable of performing high-speed image deformation processing.

[0026]

According to a first aspect of the present invention, there is provided an image transformation method comprising: generating a plurality of polygons corresponding to an original image; By assigning texture coordinates for mapping the original image to each of the polygons, defining a mapping for performing coordinate transformation, and performing coordinate transformation on all vertices of the generated polygon by the mapping, The deformed polygon is deformed, and the original image is deformed by pasting a corresponding pattern of the original image by texture mapping based on the assigned texture coordinates on each of the deformed polygons.

According to a second aspect of the present invention, there is provided an image transformation apparatus comprising: a polygon generating means for generating a plurality of polygons corresponding to an original image; Texture coordinate allocating means for allocating texture coordinates for mapping an original image; setting means for defining a mapping for performing coordinate transformation; and texture coordinates generated by the polygon generating means, and further generated by the texture coordinate allocating means. For each vertex of the polygon to which is assigned, a coordinate transformation is performed by the mapping defined by the setting means, and a polygon deformation means for deforming each polygon, and for each polygon deformed by the polygon deformation means, To the original image, the texture coordinates assigned by the texture coordinate assigning means, etc. Zui it, characterized in that it comprises a texture mapping means for performing deformation of the original image by pasting a corresponding pattern of an original image by texture mapping. Here, the texture mapping means includes:
As described in the third aspect, if it is constituted by dedicated hardware for performing the texture mapping, the texture mapping can be performed at high speed.

[0028]

Embodiments of the present invention will be described below with reference to the drawings. FIG. 1 is a diagram showing an embodiment of an image transformation device according to the present invention, wherein 1 is an original image input device, 2 is a two-dimensional scalar field input device, 3 is a mapping / parameter setting device, and 4 is a polygon. A generating device, a texture coordinate assigning device, a polygon deforming device, a texture mapping device, and a display device.

First, the outline of each device shown in FIG. 1 will be described. The original image input device 1 is a device for inputting an image to be deformed. The two-dimensional scalar field input device 2 is for inputting two two-dimensional scalar fields A and B used when the polygon deforming device 6 deforms a polygon. Here, a two-dimensional fractal field is used as the two-dimensional scalar field.

The mapping / parameter setting device 3 defines a mapping used when the polygon is deformed by the polygon deforming device 6, and sets a coefficient used when defining the mapping. For example, the mapping
In the case of defining by the equations (1) and (2), or the equations (3) and (4), the values of the coefficients k _A and k _B are set. When the mapping is defined by the above equations (5) to (8) or (10) to (13), the values of the coefficients k _r and k _q and the function f _a shown in the equation (9) (Θ) is set.

The polygon generating device 4 includes the original image input device 1
This is a device that divides a rectangle having the same size as the original image input from, into polygons. The shape of the polygon and the number of divisions are set in advance.

The texture coordinate allocating device 5 takes in the polygon generated by the polygon generating device 4 and the original image input from the original image input device 1, and allocates texture coordinates for mapping the original image to each polygon. Device. At this time, if the size of the rectangular area in which the polygon generating device 4 generates the polygon is the same as the original image, a one-to-one correspondence is established, so that texture coordinates may be assigned to each polygon as it is. If the size of a rectangular area for generating a polygon is different from that of the original image, the rectangle and the original image may be normalized, and texture coordinates may be assigned to each polygon.

The polygon deforming device 6 is a device for deforming a polygon. Specifically, the two fractal fields A and B input from the two-dimensional scalar field input device 2 are mapped to a map / map.
Using the mapping and parameters set by the parameter setting device 3, coordinate conversion is performed on all vertices of the polygon.

The texture mapping device 7 includes an original image input from the original image input device 1, texture coordinates assigned to each polygon by the texture coordinate assigning device 5, and coordinates of each vertex subjected to coordinate transformation by the polygon deforming device 6. This is to perform texture mapping based on the value. As the texture mapping device 7, dedicated hardware for performing texture mapping is used in order to speed up the processing. Such hardware is currently widely marketed, and its algorithm and hardware configuration are well known, so detailed description will be omitted. Note that texture mapping usually means mapping a two-dimensional image (texture) to the surface of a three-dimensional object, but here, a technique for mapping a two-dimensional texture to another two-dimensional polygon is used. Is used.

The display device 8 displays an image mapped by the texture mapping device 7.
It is composed of display means such as a color CRT.

The image transformation apparatus as described above can be constituted by a personal computer or the like, except for the texture mapping apparatus 7. If the hardware of the texture mapping device 7 can be set in the expansion slot of the personal computer, this image deforming device includes one unit including the texture mapping device 7.
It can be composed of one personal computer system.

Next, a case where an image is deformed by the image deforming apparatus shown in FIG. 1 will be described together with an image deforming method. First, an operator inputs an original image from the original image input device 1, inputs two two-dimensional women's rooms A and B from the two-dimensional scalar field input device 2, and further defines a mapping by the mapping / parameter setting device 3. , And parameters are set.

When an image of a desired pattern is stored in a storage medium such as a floppy disk, the input of the original image may be performed by setting the storage medium in the original image input device 1 and capturing the image. If the image is a printed matter, the image may be read and input by a color scanner. If the data of the desired image is in a database, the image data may be captured by the original image input device 1 via a network. The same can be applied to input of a two-dimensional fractal field. When the two-dimensional scalar field input device 2 has a function of generating a two-dimensional fractal field, the two-dimensional scalar field input device 2 may generate two two-dimensional fractal fields.

Further, the definition of the mapping may be defined using an orthogonal coordinate system, or may be defined using a polar coordinate system. When using the rectangular coordinate system, the above equation (1) or (2) or the equation (3) or (4) may be used. When using the polar coordinate system, the above equation (5) is used. To (8) or (10) to (1
It can be defined as in equation 3).

When an original image is input, the polygon generating device 4 takes in the input original image, creates a rectangular area having the same size as the original image, and divides the created rectangular area into a plurality of polygons. . Actually, the rectangular area is finely divided by a large number of small polygons. However, in order to facilitate understanding, here, as shown in FIG. 2, the rectangular area is divided into nine 3 × 3 square polygons. It shall be. Therefore, in this case, as shown in FIG. 2, P ₁ ~
Polygon P ₉ is generated, so that it is 16 vertices of Q ₁ to Q _16. Then, the polygon generation device 4 passes the generated polygon data to the texture coordinate assignment device 5.

The texture coordinate assigning device 5 takes in the polygon data received from the polygon generating device 4 and the original image received from the original image input device 1, and assigns texture coordinates to each polygon. Then, the texture coordinates assigned to each polygon are determined by the polygon deforming device 6,
The texture is passed to the texture mapping device 7.

The polygon deforming device 6 generates the two fractal fields A and B input from the two-dimensional scalar field input device 2, the mapping and parameters set by the mapping / parameter setting device 3, and the polygon generating device 4. polygon vertex coordinates, and captures the texture coordinates assigned to each polygon received from the texture coordinates assignment device 5 performs only coordinate transformation with respect to 16 vertices of Q ₁ to Q ₁₆ of the polygon of Figure 2. This coordinate conversion is performed as described in the section of the related art described above. Then, the polygon transformation device 6 passes the new coordinates of the vertices obtained by the coordinate transformation to the texture mapping device 7.

The texture mapping device 7 includes the original image input from the image input device 1, the texture coordinates assigned to each polygon by the texture coordinate assigning device 5,
Based on the coordinates of all the vertices of the polygon, the coordinates of which are converted by the polygon deforming device 6, the polygon is projected and texture mapping is performed to create a deformed image.

For example, the vertices Q _{1 to} Q _{16 of} each polygon shown in FIG.
Are moved as shown by Q ₁ ′ to Q ₁₆ ′ in FIG.
The polygons P _{1 to} P ₉ in FIG. 2 are transformed like P ₁ ′ to P ₉ ′ in FIG. 3, but the texture mapping device 7 uses the polygons P _i (i = 1,. , 9) are replaced with the polygons P _i ′ of FIG.
(I = 1,…, 9) Paste while keeping the texture coordinates. Through such processing, a deformed image is created and displayed on the display device 8.

The operator observes the deformed image displayed on the display device 8 to confirm how the original image is substantially deformed by the input two-dimensional fractal field, the defined mapping, and the set parameters. can do.

As can be seen from FIG. 3, the deformed image displayed on the display device 8 is generally not a clear rectangle such as a square or a rectangle. Of course, as described above, since it is actually divided into many small polygons,
Although it does not become extremely distorted as shown in (1), it is general that it still does not become a proper rectangle. However, what we are trying to do with this image transformation device is to quickly simulate how the original image is roughly transformed by the input two-dimensional fractal field, defined mapping, and set parameters. Therefore, the deformed image does not have to be a clean rectangle such as a square or a rectangle.

As described above, the operator simulates how the original image is generally deformed by changing the two-dimensional fractal field, changing the mapping, or changing the parameters. Can be
The above processing can be repeated until a desired deformed image is obtained. Moreover, since dedicated hardware is used as the texture mapping device 7, the texture mapping can be performed at a high speed, and the operator can perform the above processing interactively with the image deforming device. When the operator finds a two-dimensional fractal field, a mapping, and a parameter that can perform a desired deformation on the original image, the operator can use the two-dimensional fractal field, the mapping,
For the original image by batch processing using parameters,
What is necessary is just to perform the image deformation processing described in the section of the related art described above, whereby a completed deformed image can be obtained.

As described above, according to this image transformation device,
Since the coordinate transformation by mapping only needs to be performed on the vertices of the polygon, the time required for coordinate transformation by mapping is greatly reduced compared to the case where coordinate transformation is performed on all pixels of the original image as before. Since texture mapping is performed using dedicated hardware, the texture mapping can be performed at high speed. Therefore, it is possible to interactively and quickly simulate how the original image is to be deformed, so that the working efficiency can be greatly improved as compared with the related art.

As described above, one embodiment of the present invention has been described. However, it is apparent to those skilled in the art that the present invention is not limited to the above-described embodiment, and that various modifications are possible.

[Brief description of the drawings]

FIG. 1 is a diagram showing an embodiment of an image deformation device according to the present invention.

FIG. 2 is a diagram for explaining generation of a polygon by the polygon generation device 4;

FIG. 3 is a diagram illustrating an example of polygon deformation by a polygon deformation device 6;

FIG. 4 is a flowchart showing a flow of an image deformation process by a mapping defined using an orthogonal coordinate system.

FIG. 5 is a diagram for explaining a protrusion correction process in step S4 of FIG. 4;

FIG. 6 is a flowchart illustrating a flow of an image deformation process based on a mapping defined using a polar coordinate system.

FIG. 7 is a diagram illustrating an example of a graph of a function with respect to θ for biasing the direction of deformation to a desired angle direction when a mapping is defined by a polar coordinate expression.

[Explanation of symbols]

1. Original image input device 2. Two-dimensional scalar field input device 3.
... mapping / parameter setting device, 4 ... polygon generation device,
5: Texture coordinate assigning device, 6: Polygon deformation device, 7: Texture mapping device, 8: Display device.

Claims (3)

[Claims] A plurality of polygons are generated in correspondence with an original image, texture coordinates for mapping the original image are assigned to each of the generated polygons, and a mapping for performing coordinate conversion is defined. The generated polygon is deformed by performing coordinate transformation on all vertices of the generated polygon by mapping, and the original image is transformed by texture mapping based on the assigned texture coordinates for each of the deformed polygons. An image deformation method, wherein an original image is deformed by pasting a corresponding picture. 2. A polygon generating means for generating a plurality of polygons corresponding to an original image, and texture coordinate assignment for assigning texture coordinates for mapping the original image to each polygon generated by said polygon generating means. Means, setting means for defining a mapping for performing coordinate conversion, and setting for each vertex of the polygon generated by the polygon generating means and further assigned texture coordinates by the texture coordinate allocating means. Polygon transformation means for transforming each polygon by performing coordinate transformation according to the mapping defined by the means, and for each polygon transformed by the polygon transformation means, an original image and texture coordinates assigned by the texture coordinate assignment means. Of the original image by texture mapping An image transformation device comprising: a texture mapping unit for transforming an original image by pasting a corresponding picture. 3. The image transformation apparatus according to claim 2, wherein said texture mapping means is constituted by dedicated hardware for performing texture mapping.