JPH0542708B2 - - Google Patents

Description

Detailed Description of the Invention [Technical Field of the Invention] The present invention relates to a quantization projection method for projecting a continuous function curve onto a quantized coordinate plane and generating coordinates of the curve on the coordinate plane. In particular, it relates to a quantized projection method that determines the necessity of intermediate projection based on data after projection on a coordinate plane and generates coordinates on a curve.

[Traditional background]

In image processing simulations, curve display on screen, etc., it is necessary to project the continuous function curve FC onto a quantized coordinate plane (for example, an X-Y plane in memory) PLN as shown in FIG. Generally, when performing this projection, a continuous curve and its projection function onto the coordinate plane are given, and if the projection function is applied to all points on the curve and quantized on the coordinate plane, the curve on the coordinate plane is can get.

[Conventional technology and problems]

Conventionally, a method as shown in FIG. 2 has been used to generate this curve. That is, in order to project the continuous function curve FC in Figure 2A onto the quantized coordinate plane PLN of a memory, etc., the curve FC in Figure 2A is converted into a series of points as shown in Figure 2B, and the curve is converted into a fine point series. This was then projected onto the quantization coordinate plane PLN and quantized as shown in FIG. 2C. In other words, first the continuous curve FC
curve FC based on the function (x=g(t), f=h(t))
The continuous curve was obtained by calculating the coordinates of each point and writing "1" (mark) in the unit pixel of the quantized coordinate plane PLN based on the coordinates.

In such a conventional method, FIG. 2C of FIG. 2D
As shown in the partially enlarged view of pixel NP, even though the curve FC passes through the pixel NP, "1" (mark) is not placed between the points, so accurate projection cannot be performed. There was a problem. In order to solve this problem, it is necessary to make the point interval of the point sequence, ie, the variable t of the function, finer, which causes the problem that curve generation, ie, projection, takes a long time.

[Purpose of the invention]

An object of the present invention is to provide a quantization projection method that can perform highly accurate quantization projection in a short time.

[Structure of the invention]

In order to achieve the above-mentioned object, the present invention calculates a projection point of a continuous line segment from an arbitrary function representing the continuous line segment, and develops the projection point in a bitmap memory. In the quantization projection method of projecting a line segment onto the bitmap memory, a first step of inspecting the adjacency of both end points of the line segment on the bitmap memory by the data processing unit; a second step of dividing the line segment and calculating the end points of the divided line segment as the projection point by the arbitrary function if the two end points have no adjacency in the step; In a second step, the first step is performed on each of the divided line segments, and in the first step, the first step is performed on each of the divided line segments until both end points of each divided line segment have adjacency. The method is characterized in that the projection point in the second step is calculated, and the calculated end point is written in the bitmap memory.

[Embodiments of the invention]

Hereinafter, the present invention will be explained in detail using examples.

FIG. 3 is a diagram explaining the principle of the present invention.

First, find both end points P ₁ and P ₂ of the continuous function curve l ₁ as shown in Figure 3A, and use these as the projection points as shown in Figure 3B.
Write in the coordinate plane PLN as follows.

Next, the adjacency of both end points P ₁ and P ₂ on the coordinate plane PLN, that is, whether or not the pixels of both end points P ₁ and P ₂ are adjacent to each other is checked.

If they are not adjacent, the image shown in Fig. 3 A as shown in Fig. 3 C.
Divide the curve l ₁ into curves l ₂ and l ₃ , and find the end points of curves l ₂ and l ₃ .
Find P ₃ by calculation. Then, the end point _P3 is written on the coordinate plane PLN as a projection point as shown in FIG. 3D.

Similarly, both end points P ₁ of curve l ₂ on coordinate plane PLN,
Examine the adjacency of P ₃ and both end points P ₂ and P ₃ of curve l ₃ .

If these end points are not adjacent, then
As in, curve l ₂ becomes curve l ₄ , l ₅ , curve l ₃ becomes curve l ₆ ,
The end points P ₄ and P ₅ are obtained by calculation, and the end points P ₄ and P ₅ are written on _the coordinate plane PLN as projection points as shown in FIG. 3F.

Similar processing is repeated, and finally, when the end points of all the divided curves have adjacency as shown in FIG. 3G, a projected curve is obtained on the coordinate plane PLN as shown in FIG. 3H.

In this way, the present invention basically stores the end points of a curve as projected points on a coordinate plane, divides the curve on the coordinate plane, finds the end points of the divided curves as projected points, and stores them in the coordinate plane. I will store it. Then, the end points of the divided curves have adjacency on the coordinate plane, thereby completing the target projection curve.

In other words, the points at both ends of the projected curve are projected and quantized onto the coordinate plane, the necessity of intermediate projection of the curve is determined based on the projected points on the coordinate plane, and the original curve is divided by feeding back to the original curve. The end points are calculated.

Therefore, the method of the present invention is a method of calculating a new projection point of the original curve based on the projection point on the coordinate plane, unlike the conventional method of calculating a projection point without considering the coordinate plane. Since it is also a sequential method,
The accuracy of the projection curve on the coordinate plane is improved, and high-speed projection becomes possible.

FIG. 4 is a processing flow diagram of one embodiment of the method of the present invention.

Here, the functions of the curve are set as X=g(t) and Y=h(t), that is, the two-dimensional coordinates (X, Y) on the curve are determined by the variable t (for example, rotation angle θ). shall be carried out.

The left side of FIG. 4 is the main routine, and the right side is the subroutine called by the main routine.

In the main routine on the left side of Figure 4, DRAWf(tn,
tm) is called, the subroutine is executed, and the process ends. When the subroutine on the right side of FIG. 4 is called, it first calculates the coordinates of the end point.

Coordinates P _{1 X} , P ₁ Y of end points P ₁ , P ₂ of Fig. 3A,
Calculate P ₂ Y from the following equation with n=1 and m=2.

PnX=g(tn)...(1) PnY=h(tn)...(2) PmX=g(tm)...(3) PmY=h(tm)...(4) And, Figure 3B Write "1" (mark, shown as a white circle in the figure) in the pixel of the coordinate plane PLN corresponding to this coordinate, as shown in FIG.

Next, the adjacency of end points P ₁ and P ₂ is checked. In this example, as shown in Figure 5 as a test for adjacency, if there is another point Pj in the pixel with the x mark around the pixel of point Pi, the points Pi and Pj have adjacency (adjacent). It has been determined that To do this by calculation, the coordinates of point Pi are (PiX, PiY),
If the coordinates of point Pj are (PjX, PjY), check whether the following equation is satisfied.

|PiX−PjX|+|PiY−PjY|≦1 (5) If formula (5) is satisfied, it is determined that there is adjacency, and if it is not satisfied, it is determined that there is no adjacency.

If it is determined that there is adjacency through this inspection, the line segment is completed, and the process returns to the main routine (RETURN) and ends.

On the other hand, if it is determined that there is no adjacency, it is determined that intermediate projection is required as shown in FIG. 3, and the coordinates of the intermediate point _P3 are calculated. That is, Figure 3C
In order to obtain the coordinates of the midpoint P ₃ of the line segments l ₂ and l ₃ divided as shown, the variable t ₃ is determined by the following equation.

tl=(tn+tm)/2...(6) Since l=3, n=1, and m=2, _t3 becomes _t3 =( _t1 + _t2 )/2.

Next, the command DRAWf (tn, tl) returns to the beginning of this subroutine (i.e. step) and executes the step with tn=t ₁ and tl=t ₃ .
_{The coordinates} (P ₁ X, P ₁ Y) and _{( P 3}
Write the intermediate point _P3 as shown in Figure D.

Similarly, the adjacency of P ₁ and P ₃ is determined by the step, and if there is adjacency, the line segment of the step is
l Move on to step ₃ . On the other hand, if there is no adjacency, the line segments l ₄ , l ₅ which divide the line segment l ₂ into two as in the step
In order to obtain the intermediate point P ₄ of (Fig. 3 E), the variable t ₄ is
(6), and then use the command DRAWf (tn, tl) to find tn=t ₁ , tl=t ₄ , that is, the end point P ₁ of line segment l ₄ ,
Find the coordinates of P ₄ and similarly find the point P ₄ as shown in Figure 3 F.
After writing, the adjacency of P ₁ and P ₄ is checked, and if there is no adjacency, the line segment l ₄ is further divided into two and the same process is performed until they have adjacency. In this way, when all the end points of line segment l ₄ have contiguity, the process is repeated using the command PRAWf (tl, tm) until line segment l ₅ has contiguity. Find each endpoint.

Next, DRAWf(tl, tm), i.e. DRAWf(t ₃ ,
t ₂ ) instruction, division of the line segment, calculation of end points, and inspection of adjacency are repeated for the line segment l ₃ in the same way until the line segment l 3 has adjacency. For example, as shown in Figure 3 E, the line segment
When all end points on the coordinate plane PLN are adjacent at l ₄ , l ₅ , l ₆ , and l ₇ , the above series of processing is performed as follows: first, line segment l ₁ → line segment l ₂ → line segment l ₄ → Line segment l ₅ → line segment l ₃ → line segment
l ₆ − line segment l ₇ , and the coordinate plane PLN
The curve l ₁ will be stored above.

In this way, the same processing procedure can be repeated depending on the presence or absence of adjacency, so the program itself can be simple and the processing time can be shortened.

FIG. 6 is a block diagram of an embodiment for realizing the method of the present invention. In the figure, 1 is an arithmetic unit that executes the series of processes described above, 2 is a projection quantization unit, and The function g of the curve set from
(t) and h(S) are calculated according to the given variables tn, etc.,
One that outputs the quantized coordinates of the end point Pn, 3
is the adjacent inspection part, and the end point from the projection quantization part 2
4 is an intermediate point generation unit that executes the above-mentioned equation (5) based on the coordinates of Pn and determines the presence or absence of adjacency. (6) is executed to calculate the variable tl at the intermediate point, 5 is a stack memory that stores the variables at the end points of each line segment, and 6 is a memory, which corresponds to the quantized coordinate plane PLN mentioned above, and which is projected The end point Pn from the quantization unit 2 is written.

Next, the operation of the embodiment shown in FIG. 6 will be explained based on the operation diagram of the stack memory shown in FIG. 7.

First, the variables t ₁ and _{t 2} of the end points P ₁ and P ₂ of the line segment l 1 in FIG. 7A are initially set in the stack memory 5.

The variables t ₁ and t ₂ of the stack memory 5 are given to the projection quantization unit ₂ , and as mentioned above, the quantized coordinates (P ₁ X, _{P 1 Y} ), ( _{P 2} X, P ₂ Y) are calculated and written into the memory 6 as shown in FIG. 3B.

Along with this, the coordinates (P ₁ X, P ₁ Y), (P ₂ X,
P ₂ Y) is sent to the adjacency checking section 3, and the presence or absence of adjacency is determined by the above-mentioned equation (5). If it is determined that there is no adjacency, the intermediate point generation unit 4 converts the intermediate point t ₃ to the above-mentioned number using the output variables t ₁ and t ₂ of the stack memory 5.
Generated from equation (6), variables (t ₃ , t ₁ ) and (t ₃ , t ₂ ) of line segments l ₂ and l ₃ obtained by dividing line segment l ₁ are written in the stack memory 5 as shown in FIG. 7B. It's crowded. Since the stack memory 5 is designed to output the contents from the beginning (that is, the upper part of FIG. 7), the variables t ₃ and t ₁ are then output to the projection quantizer 2.
The coordinates of the end points P ₁ and P ₃ of the line segment l ₂ are calculated as described above and written into the memory 6 as shown in FIG. 3D.

Similarly, the adjacency check unit 3 checks the adjacency of the end points P ₁ and P ₃ , and if there is no adjacency, the intermediate point generation unit 4 uses the output variables t ₁ and t ₃ of the stack memory 5 to determine the intermediate point t. ₄ is generated from equation (6) above, and the variables (t ₄ , t ₁ ) and (t ₄ , t ₃ ) of line segments l ₄ and l ₅ , which are obtained by dividing line segment l ₂ , are processed in the stack memory 5. As shown in FIG. 7C, the variables (t ₃ , t ₂ ) of the line segment l ₃ that have not been written are stacked and written.

Similarly, the variables t ₄ and t ₁ of the line segment l ₄ are sent to the projection quantization unit 2, which generates the coordinates of the end points P ₁ and P ₄ of the line segment l ₄ , and stores them in the memory 6 as shown in FIG. 3F. Similarly, the adjacency test section 3 performs an adjacency test, operates the intermediate point generation section 4 depending on whether there is adjacency, generates an intermediate point, and writes the variables of the divided line segment to the stack memory 5. It's crowded. For example, if it _is determined that end points P _{1 and} P ₄ of line segment l 4 are adjacent, variables are not stacked in the stack memory ₅ of FIG. , t ₃ ), the output variables of the stack memory 5 are t ₄ and t ₃ and the processing for the line segment l ₅ is performed, and the same process is subsequently performed for the line segment l ₂ as well.

In this way, if the stack memory 5 is used, the data (variables) that need to be processed are stacked up so as to be output in the order of processing, so the above-mentioned series of line segment division processes can be executed sequentially by reading out the stack memory 5. be able to.

In the above example, the arithmetic unit 1 is divided into blocks, but it can also be made common by using a microcomputer or the like.

An application example using line segments obtained by quantized projection as described above will be described next.

FIGS. 8 and 9 are explanatory diagrams of three-dimensional measurement using a spherical camera. As shown in FIG. 8A, when an object l is imaged on an imaging surface 10a as shown in FIG. 8B by a camera 10 having a spherical lens 10b such as a fisheye lens, the object l is obtained as a spherically projected image. That is, as shown in FIGS. 9A and 9B, the straight lines l ₁ , l ₂ , l ₃ that are objects are images l ₁ ′, l ₂ ′,
l ₃ ', and straight line projected images l ₁ ', l ₂ ', l ₃ ' as shown in FIG. 9C are obtained on the imaging surface 10a.

When spherical projection is performed in this manner, even a straight line becomes a curve as shown in FIG. 9C, so even if the lines are parallel, the intersection point at infinity can be measured. Of course, straight lines that intersect on a plane also have points of intersection on the spherical surface, so by finding the points of intersection on the spherical surface, the three-dimensional position of the straight lines can be measured.

In such a case, when simulating a processing device that performs three-dimensional measurement, a spherical projection image as shown in FIG. 9C is generated by the quantization projection method according to the present invention. Therefore, such a spherical projection image can be generated easily and in a short time, so that such simulation can be performed efficiently and accurately.

In addition, it can also be used to detect distortion of a spherical lens. That is, according to the present invention, the projection image shown in FIG. 9C is generated and compared with the image of the reference straight line taken by the camera 10 to detect the distortion of the spherical lens. Further, such distortion can be measured as data and used to correct the projected image captured by the camera 10 to remove the distortion.

In the above embodiments, an example in which a line segment is divided into two was explained, but the line segment may be divided into n, such as three.

Although the present invention has been described above using one embodiment, the present invention can be modified in various ways according to the gist of the present invention, and these are not excluded from the present invention.

〔Effect of the invention〕

As explained above, according to the present invention, the following effects are achieved.

Since the projected point is calculated by feeding back to the original line segment based on the end point projected on the coordinate plane,
Accurate quantized projection images can be obtained.

The number of divisions of the original line segment is determined based on the adjacency of the projection points, so there is no need to find unnecessary projection points, and the projection image can be processed at high speed, especially for curves with complex shapes. Since a quantized projection image can be obtained accurately and quickly, it is suitable for use in image processing.

Since the processing method is sequential (i.e. recursive),
This can be easily realized and the program etc. can be simplified.

[Brief explanation of the drawing]

Fig. 1 is an explanatory diagram of quantization projection, Fig. 2 is an explanatory diagram of the conventional quantization projection method, Fig. 3 is an explanatory diagram of the principle of the present invention, and Fig. 4 is a processing flow diagram of an embodiment of the method of the present invention. , FIG. 5 is an explanatory diagram of the adjacency test in the flow of FIG. 4, FIG. 6 is a block diagram of an embodiment for realizing the method of the present invention, FIG. FIGS. 8 and 9 are explanatory diagrams of application examples using the method of the present invention. In the figure, _l1 to _l7 ... line segment, _P1 to _P5 ... end point, PLN... quantization coordinate plane, 1... calculation section, 2... projection quantization section,
3...Adjacent inspection unit, 4...Intermediate point generation unit, 5...Stack memory, 6...Memory.

Claims (1)

[Scope of Claims] 1. A data processing unit calculates a projection point of a continuous line segment from an arbitrary function representing the continuous line segment, and develops the projection point in a bitmap memory, thereby converting the line segment into a bitmap memory. In the quantization projection method for projecting onto a map memory, a first step in which the data processing unit checks the adjacency of both end points of the line segment on the bit map memory; A second method that divides the line segment when the points have no adjacency and calculates the end point of the divided line segment as the projection point using the arbitrary function.
In the second step, the first step is executed for each of the divided line segments, and in the first step, both end points of each divided line segment are A quantization projection method characterized in that the projection points of the second step are calculated until the projection points have adjacency, and the calculated end points are written in the bitmap memory.