JPH03175583A - Deforming method for two-dimensional bit map picture - Google Patents

Abstract

PURPOSE:To easily obtain a three-dimensional picture looking like a cylindrical form by combining the processing, which continuously changes the picture element density of a uniform-density square two-dimensional bit map original picture in horizontal and vertical directions, and the processing which changes the rough form of the whole of this picture. CONSTITUTION:The picture element density of the rectangular two-dimensional bit map original picture in the horizontal direction is converted, and that in the vertical direction is converted, and the size of this picture is converted by independent longitudinal and transverse variable magnifications, and the size in the vertical direction is changed in the horizontal direction by positional difference, and the whole of the picture is shifted in the vertical direction along a curve, and the picture width in the horizontal direction is changed to form the picture into a trapezoid, thereby deforming the picture into a cylindrical form. Thus, the three-dimensional picture looking like a cylindrical form is easily obtained, and a plane picture can be stuck to the picture having the cylindrical form projected in a two-dimensional plane by the easy operation.

Description

DETAILED DESCRIPTION OF THE INVENTION (Field of Industrial Application) The present invention relates to an image transformation method for changing the shape of a two-dimensional bitmap image.

(Prior Art) When creating a new image from a plurality of original images, image compositing work is performed. In order to paste multiple images together without looking unnatural, it is necessary to transform the image to be pasted to match the shape of the target images to be pasted together. There is a demand for deformation so that a two-dimensional image can be pasted onto a three-dimensional object appearing in a bitmap image without any unnaturalness. There are many different shapes that can be considered as three-dimensional objects, but among them, there are those who want to transform them so that they can be pasted onto basic shapes such as perspective, cylinders, and spheres. There are many demands.

Here, we will take up the cylindrical shape among various three-dimensional shapes.

Now, there is a special effect device used in broadcasting stations and the like that transforms a two-dimensional bitmap planar image into a three-dimensional shape. In this device, a two-dimensional planar image is arranged three-dimensionally in a three-dimensional space, in this case in a cylindrical shape, and then the image is transformed by performing a perspective transformation operation.

According to this deformation method, since the image is deformed using three-dimensional information, a cylindrical image with an accurate shape can be obtained.

In order to make the shape of the original image to be pasted match the size and shape of the circle @ image in the two-dimensional bitmap image using this method, the following operation is performed. In other words, a cylindrical image developed in three-dimensional space can be moved and
Enlarge/reduce/rotate the image to adjust its orientation and size when viewed from the viewpoint so that it has the same shape as the image to be transformed. However, since this work involves handling three-dimensional images, there is a problem in that it is very difficult to operate to match the shape of a three-dimensional object image in a two-dimensional plane, and the work efficiency is poor.

(Problems to be Solved by the Invention) The present invention was proposed in order to solve the problems related to the workability of image deformation processing described above. The purpose of this project is to provide a method for transforming the image so that it can be pasted on the screen with a simple operation.

(Means for solving ff!ffl) The present invention provides processing for converting the pixel density in the horizontal direction, processing for converting the pixel density in the vertical direction, and processing for converting the pixel density in the vertical direction for a rectangular two-dimensional bitmap original image. There is a process to convert the size by vertical and horizontal independent scaling, a process to change the vertical size by changing the horizontal position, a process to shift the entire image vertically along a curve, and a process to change the horizontal size. This is a method of transforming a two-dimensional bitmap image in which the image is transformed into a cylindrical shape by combining the process of changing the image width and making it into a trapezoid.

(Function) As shown in FIG. 1, the present invention converts the pixel density in the horizontal direction and the pixel density in the vertical direction for a rectangular two-dimensional bitmap original image. °shi([
Convert the size of the image by vertical and horizontal independent scaling [
(Uko), change the vertical size according to the difference in horizontal position [Engine]), shift the entire image vertically along the curve ([Oko]), and change the horizontal image width to create a trapezoid. ([force]) to transform the image into a cylindrical shape.

According to the present invention, by combining a process of continuously changing the pixel density in the horizontal and vertical directions and a process of changing the outline of the entire image on a rectangular two-dimensional bitmap original image of equal density, A three-dimensional image that looks like a cylinder (including a cone) can be easily obtained. Therefore, it becomes possible to paste a planar image onto an image of the internal shape shown in a two-dimensional plane with a simple operation.

(Example) An example of the present invention will be described with reference to the drawings. Second
The figure shows an example of images before and after deformation processing, and the second rgJ(a)
is an original image which is a rectangle before deformation, and FIG. 2(b) is an image of an inner groove shape to be pasted. This second figure (
The shape of the image b) is the shape to be finally transformed. To make the discussion easier to understand, we will only deal with the right half of the cylindrical image. In Figure 2, 21, 22,
23°24 are the four corner vertices P, Pz, Ps, P4 of the original image
25.2B, 27.28 are each vertex P1 of the original image
．． P8. P1. The four corner vertices Q, Q2. of the transformed image corresponding to P, Q2. Q3. Q. The method of performing the transformation as shown in FIG. 2 and its calculation method will now be explained.

If we pay attention to the image to be deformed in FIG. 2(b), we can see that the point Q1 of 25 is closest to the viewpoint, and the size of the pixel gradually decreases as we move away from that point.

Utilizing this characteristic, it is possible to give an image a three-dimensional effect by continuously changing the pixel density and changing the pixel size for an image of equal density. Next, in Figure 2 (a
) and (b), it is clearly seen that the general shapes of the entire image are different, such as a rectangular square and a square containing LllILa. By changing the outline, the image can be made to look like a cylinder even if the density inside the image remains unnatural. Therefore, as mentioned above, it is thought that it is possible to transform a two-dimensional planar image into a 3D-like image by combining the process of changing the pixel density with the process of changing the overall outline.

Now, an example of the method of the present invention, that is, the method of the present invention that transforms a two-dimensional image to look like three-dimensional without using three-dimensional information, will be explained.

In the previous explanation, I said that in order to transform the image into a cylindrical shape, two processes are combined: changing the pixel density and changing the overall shape of the image, but in reality, each process is a combination of simpler processes. It consists of Figure 1 is similar to Figure 2 (
This figure shows how several deformation processes are applied one by one to the original image in a) until the final deformed image in FIG. 2B is obtained. The process will be explained along the flow of the figure.

FIG. 1(a) is the original image, which is the same as FIG. 2(a).

[A] First, processing to change the pixel density in the horizontal direction is performed on the original image shown in FIG. 1(a). This expresses that the density increases from the region closest to the viewpoint of the cylindrical image toward the end in the direction around the axis. In FIG. 2(b), it refers to the density change in the direction around the axis from the ρ side of the point Ql-Q2 to the side of the points Q to Q4. The formula for this process is (1
)formula? This is shown.

In the formula, x and y are the input coordinate values before this process, and X'
+y+ is the output coordinate value after processing.

Also in the following equations, Xy y* X'+'I' represents the same thing for each process. Function f, (
x) is a function that changes the density distribution depending on the horizontal position, and uses trigonometric expressions related to horizontal coordinate values. The image obtained by this modification is shown in FIG. 1(b).

x'=f+ (x) ly'=y (1) [
Iko 2nd 1 Performs processing to change the pixel density in the vertical direction. This means that the density becomes higher < 1 in the direction along the circle axis, from the side of points Q, ~Q, in Figure 2 (b) toward the side of points Q2 ~ Q3. It is something to express. In this method of changing the density, the image is scaled while continuously changing the scaling factor in the vertical direction.The size of the pixels in the vertical direction above the 0 sides Q and Q remains the same size, and the size of the pixels in the vertical direction on the 0 side Q *
Q, the size of the top in the same direction is l compared to the side Q1Q4
Processing is performed so that QIXQ4X l /1QaxQsxl. The equation for this process is shown in equation (2). The function f*(y) is a function that changes the magnification in that direction depending on the vertical position, and the calculation formula fx(y)Xy is the vertical M
This is a quadratic function equation related to the target price. The image obtained by this modification is shown in FIG. 1(C).

y'= r2(y)Xy, x°=x (2) [
] Step 33: Perform processing to change the size of the image. This is to adjust the size of the entire image, which has changed in size after completing the processing in [A, B], to the size of the cylindrical target image, and uses vertical and horizontal independent scaling. The size after scaling is set to be IQl-Qawl in the vertical direction and IQl-Ql-1 in the horizontal direction. The equation for this process is shown in equation (3). The functions f and f4 are constants.

The image obtained by this transformation is shown in FIG. 1(d).

X'=fsXXx y'=f<xy (3) The third process is simply scaling, but the processes up to this point are for changing the pixel density.

Next, processing is performed to change the general shape of the entire image.Since the upper and lower sides of the target image, which has a cylindrical shape, are curved, processing is performed here to give that effect. Focusing on the shape of the lower side of the target image, processing is performed to shift the entire image along the curved shape of the lower side. However, the shapes of the upper and lower sides of the target image are different. Specifically, since the horizontal and vertical lengths of the two sides are different, a simple shift process is insufficient. Therefore, processing is performed to match the heights of the two curves in the vertical direction.

[Engineer] Fourth, the magnification is changed in the vertical direction using a vertical magnification ratio that has a different value depending on the horizontal position.

In other words, the vertical length is changed depending on the horizontal position. The equation for this process is shown in equation (4). Seki v!
If a, the horizontal axis is Ql-Ql-1, and the vertical axis is I(!Q+-Q*yl-l QswQa
v l ) This is an equation including an elliptic equation with l. In this equation, when the value (I Ql-Qawl -l Qs-Qa-1) is positive, the upper half of the ellipse is used, and when it is negative, the lower half is used. The image obtained by this transformation is shown in Figure 1(e).
Shown below.

y'=fs(x+y)Xy+ x'=x (4) [
Oko Fifth, shift the entire image along the same curved line as the bottom edge of the cylindrical target image. The formula for this process is (5)
As shown in the formula. The function f is the horizontal axis I Ql, Ql
, l, and the vertical axis wheels are Ql, Ql, l. The image obtained by this transformation is shown in Figure 1 (f
).

y'= fs (x+ y) +y+ x'=x
(5) [Force] Sixth, change the magnification depending on the difference in vertical position and change the magnification in the horizontal direction. In other words, a process is added to change the width of the image in the horizontal direction, thus making it trapezoidal. The equation for this process is shown in equation (6). function f
, is an equation for trapezoidization and is a quadratic function equation including xy.

The image obtained by this transformation is shown in FIG. 1(g), and is the same as the finally obtained image in FIG. 2(b).

y'=fv (X, y)+:/+ y''=y (8)
As described above, a final cylindrical image can be obtained by combining the process of changing the pixel density and the process of changing the general shape of the entire image. Specifically, a combination of simple processing in one-dimensional direction is used. In actual processing, detailed processing is carried out 1
Rather than going one step at a time and getting a slightly deformed image,
Obtain a deformed image in one go.

An example of a hardware configuration for executing the method of the embodiment of the present invention detailed above will be described.

31st! I indicates its hardware configuration, and in the figure, 31 is a computer, 32 is a central processing unit, and 3 is a computer.
3 is an image transformation processing unit, 34 is an image memory, 35 is an input device, 36 is a display, 37 is a scanner, 38 is a printer, and 39 is a bus.

The input device 35 is for giving commands etc. to the computer. The display 36 outputs and displays images. The scanner 37 is for inputting images, and the printer 38
outputs an image.

The path 39 serves to transfer image data and control information. The image memory 34 stores image data, and the central processing module 132 controls the entire image processing apparatus and performs general calculations.

The image deformation processing section 33 performs processing for image deformation, which is a feature of the present invention.As shown in FIG. A value input section 41, an inverse mapping calculation section 42 that calculates an inverse mapping function of the deformation function formula from the input initial value, and a An inverse mapping coordinate calculation unit 43 that calculates coordinate values, an interpolation processing unit 44 that calculates new pixel values on the transformed image from the calculated coordinate values by interpolation, and a pixel input unit that writes and reads pixel values. It is composed of an output control section 45. 46 is an image memory in which image data before and after transformation is stored.

In the above configuration, the overall processing flow from reading out pixel values to performing coordinate calculations and writing will be described. FIG. 5 shows the processing flow of the calculation procedure.

(2) The coordinate values of the vertices of the four corners of the image before and after transformation, which will be the initial values, are input using the transformation initial value input section 41.

(2) In the inverse mapping function calculating section 42, a deformed coordinate function is first calculated from the coordinate values input as initial values. The initial values are only the coordinate values of the four vertices, and the coordinate function is divided into six types of equations (1) to (6) described above, but the count of each calculation equation is uniquely determined.

Next, an inverse mapping function formula is determined for each calculation formula of this coordinate function. As mentioned above, since the forward coordinate function formula is a 0* formula using linear functions, quadratic functions, and trigonometric functions, the inverse mapping function formula can be found.

(2) The inverse mapping coordinate calculation unit 13 first starts tracing the area of the transformed image.

(2) Next, the inverse mapping coordinate calculation unit 43 calculates coordinate values on the original image by an inverse mapping function using the traced coordinate values of the transformed image area.

(2) The interpolation processing unit 44 first reads out a plurality of pixel values in the vicinity of the coordinate values determined in step (2).

(2) Next, the interpolation processing unit 44 performs interpolation processing based on the read pixel values to calculate new pixel values.

An appropriate interpolation method may be selected depending on the required image quality and processing speed. For example, four-point linear interpolation using pixel values at four points around the calculated coordinate value is given as an example.

(2) The pixel input/output control unit 45 writes the new pixel value obtained by the interpolation processing unit 45 to the coordinate position of the traced deformed image area in the image memory 46.

(2) Determine whether tracing in the image area after deformation has been completed. If Yes, the process ends; if No, the process returns to step (2).

Although this processing flow shows an example in which the coordinates are calculated by tracing the deformed image area using the inverse mapping function expression of the deformed coordinate function, this method is not necessarily required. for example,
Similar to the method used in special effects equipment, the original image area is divided into small plane patches, and the coordinate values on the deformed image are calculated using a forward deformation coordinate function for the vertex coordinate values of each patch. The interpolation process may be performed by calculating the coordinate values on the original image from the patch again using the inverse mapping function formula. The explanation of the method will be omitted here.

In the above embodiment, the shape of the image to be deformed is cylindrical, but the present invention can also be applied to a conical shape. The processing method for deformation into a conical shape is simply to change the last of the equations (1) to (6) above, formula (6) for trapezoidalization, to one for triangularization, and the only difference in the calculation formula is the coefficients. .

(Effects of the Invention) As described in detail above, according to the present invention, processing for continuously changing the pixel density in the horizontal and vertical directions for a rectangular two-dimensional bitmap original image of equal density, and By combining this with processing that changes the outline of You will be able to paste images into images with simple operations.

[Brief explanation of drawings]

FIGS. 1(a) to 1(g) are diagrams showing the deformation process according to the present invention from a planar image, which is an original image, to obtaining a final cylindrical image. FIGS. 2(a) and 2(b) are diagrams showing examples of images before and after transformation processing from a planar image to a cylindrical image. FIG. 3 is a diagram showing an example of a hardware configuration for implementing the present invention. FIG. 4 is a block diagram showing the configuration of the image transformation processing section. FIG. 5 is a processing flow of the overall calculation procedure from reading out pixel values to calculating coordinates and writing. 41... Deformation initial value input section, 42... Inverse mapping function calculation section, 43... Inverse mapping coordinate calculation section, 44... Interpolation processing section, 45... Pixel input/output control section, 46. ...Image memory.

Claims (1)

[Claims] For a rectangular two-dimensional bitmap original image, there is a process to convert the pixel density in the horizontal direction, a process to convert the pixel density in the vertical direction, a process to convert the image size by vertical and horizontal independent scaling, and a process to convert the pixel density in the vertical direction. The image is created by a combination of processing that changes the size of the image depending on the difference in horizontal position, processing that shifts the entire image vertically along a curve, and processing that changes the horizontal image width to create a trapezoid. A method of transforming a two-dimensional bitmap image, the method comprising transforming a two-dimensional bitmap image into a cylindrical shape.