JPS6286468A - Polygonal line approximation circuit for line picture - Google Patents

Abstract

PURPOSE:To allow the titled circuit to withstand noise by approximating a line picture expressed in a chain code by a polygonal line so as to make the distance between a long line segment and a picture element to a prescribed value or below thereby compressing remarkably the data quantity. CONSTITUTION:In tying a start point A (x0, y0) and an end point B (x1, y1), a line segment AB gives the 0th order approximation of the line picture. Assuming that a distance between an optional i-th picture element constituting the line picture and the line segment AB is di, then the distance di is obtained as to all picture elements, the maximum value is taken as dj and the picture element giving a maximum value as (j), a point C (Xj, Yj) is referred to as the maximum distance point. In giving a distance (l) deciding the degree of approximation in advance and it is referred to as the approximation length (l). The distances dj and (l) are compared and when the distance dj is smaller than the distance (l), the approximation operation is stopped, and when the distance dj is larger than the distance (l), the start point A, the end point B and the maximum distance point C (Xj, Yj) are tied, then the line picture is approximated by two line segments AC, CB. This is the 1st approximation and the procedure above is repeated.

Description

DETAILED DESCRIPTION OF THE INVENTION Field of the Invention The present invention relates to an image processing apparatus that converts a grayscale image represented in space into a line drawing. In particular, the present invention relates to a polygonal line approximation circuit that compresses data from line images without losing useful information.

(Company) Conventional technology and its problems Characters, figures, objects, etc. are imaged with a TV camera, divided into pixels, compared with a certain threshold value for brightness and darkness, binarized, and thinned. A line image is obtained.

The thinning process is a process of erasing unnecessary black pixels in order to obtain a continuous thin outline.

There are several methods for the thinning process, which will not be explained here. The number of remaining black pixels varies depending on the thinning method. A line image is a collection of continuous black pixels.

A line image has a starting point and an ending point. The starting point and the ending point are continuously connected by pixels.

Line image data is completely described by specifying the x%y coordinates of all pixels. However, in this case, the amount of data is too large, making subsequent image processing and data storage difficult.

Therefore, it is possible to compress the data.

FIG. 1 shows an example of a line image.

The starting point and the ending point are continuously connected by pixels, and there is only one continuous line. Therefore, instead of the black pixel itself, the direction of change and the slope of the border line can be used as data.

FIG. 2 shows eight directions of change around a certain pixel. A change from one pixel to the next pixel is a change to any of the eight surrounding pixels. These are numbered from 0 to 7 and called chain codes.

Movement directly upwards is 01, movement diagonally to the upper left is 1, and from then on, chain codes are associated in a counterclockwise direction.

The chain code is 3-bit data. To specify a certain pixel, the XSy coordinates must be given. If these are m bits (for example 8 bits or 16 bits), then a data amount of 2m bits is required. However, since the chain code is 3 bits, the amount of data for specifying one point is reduced by (2m-8) bits.

Therefore, in order to specify a line image, the coordinates of the starting point (xo s
3'o) and the subsequent direction of change using a series of chain codes.

FIG. 8 shows the line image of FIG. 1 expressed by a series of chain codes.

Since the change from the starting point to the second point is diagonally to the upper right, the chain code is 7. Since the change from the second point to the third point is directly upward, the chain code is 0. Since the change from the third point to the fourth point is directly upward, the chain code is O. In the same way, the chain codes are arranged until the end point is reached. Depending on the starting point and chaincode column,
Line images can be uniquely specified.

Even if this is done, there is still too much line image data, so it is desirable to compress the data.

For this reason, a broken line approximation is used.

In this method, a line image is divided into parts that can be regarded as straight lines, and each part is approximated by a line segment.

Since the approximation is performed using line segments rather than curves, the image after approximation will be a broken line. For this reason, it is called a broken line approximation.

When the polygonal line approximation is applied, the data is reduced to only those specifying the intersections of the polygonal lines. Therefore, the amount of data will be significantly reduced.

In the conventional broken line approximation method, the main method was to trace a line image from a starting point, detect a point where the direction of change changes (referred to as a turning point), and connect the turning points with line segments.

Since the direction of change is represented by eight chain codes, changes in the direction of change can be determined by looking at changes in the chain codes. Therefore, it is easy to sequentially detect turning points.

Since this method is, so to speak, a differential method, it has the disadvantage of being vulnerable to local noise.

To obtain a line image, the object is illuminated and the reflected light is transmitted to the TV.
It is necessary to capture an image with a camera, divide it into vertical and horizontal pixels, and then binarize the brightness and darkness of the pixels. Therefore, noise may occur depending on the lighting conditions. Further, noise may be generated by the line thinning process.

Since the conventional method detects all turning points, noise is included as is. It is better to eliminate local noise.

Further, although the differential method described above can compress data, the shape of the line image remains unchanged, so it cannot be said to be an approximation in terms of the image.

The main purpose of approximation is to compress data, but it is also used to reduce noise.

(+7) Purpose In order to compress the amount of data of a line image, the first objective of the present invention is to provide a line image approximation circuit that is strong against local noise and capable of approximating a line image with an arbitrary degree of approximation. This is the purpose of

A second object of the present invention is to provide a broken line approximation circuit that can quickly find the coordinates of pixels forming a fold using a relatively simple circuit.

A third object of the present invention is to provide a broken line approximation circuit which is a circuit consisting of a combination of relatively simple elements and which can be easily integrated into an LSI.

B) Principle of broken line approximation In contrast to the conventional differential broken line approximation, the present inventor has established a so-called integral broken line approximation method. This is a method that can be used extremely effectively for line images stored as chain codes.

First, a broken line approximation method invented by the inventor will be explained.

First, start point A (Xolyo) and end point B (xl, yl) are connected. Line segment AB is obtained. Line segment AB gives the 0th approximation of this line image.

Straight line AB is a straight line obtained by extending line segment AB infinitely to both sides. The distance between a point and a straight line is the length of the perpendicular line drawn from that point to the straight line. Even if the foot of the perpendicular line is outside the line segment, the distance can be defined uniquely in the same way.

Let di be the distance between an arbitrary first pixel constituting the line image and straight line AB.

Figure 4 shows these relationships.

Distances dtf are determined for all pixels, and the maximum value among them is set as dj. Let j be the pixel that gives the maximum value.

This is set as 0 point (Xj, Yj). The 0 point is called the maximum distance point.

A distance l is given in advance to determine the degree of approximation.

This is called the approximate length l.

Compare dj and 4. If dj is smaller than l, the approximation operation is aborted. If dj is larger than l, the starting point A1 and ending point B are connected to the maximum distance point C (Xj, Yj).

This is shown in Figure 5. The line image is approximated by two line segments AC10H. This is the first approximation.

Next, the distances between the straight line AC and all the pixels sandwiched by the end points A and C are calculated, and the maximum value thereof is determined.

Also find the point that gives the maximum value. Assume that this is point D.

The distance between point D and straight line AC and the approximate length l are compared. Suppose l is longer. In this case, we can no longer proceed with the approximation.

Do not connect point fi, A, 0 and point D, leaving the line segment AC as it is.

The same thing is done for line segment CB.

The distance between the straight line CB and all pixels of the line image 1 sandwiched by points C and B is determined. Let do be the maximum value of the distance, and let E be the point that gives the maximum value. The maximum distance de and the approximate length l are compared. It is assumed that deO is larger by 6.1. In this case, the end point C
, B and the maximum distance point E. The line segments GE and EB are the second approximation.

Furthermore, the maximum distance between CE and between EB is determined, and this is compared with the approximate length l.

It is assumed that both maximum distances are shorter than the approximate length l. The approximation is discontinued here. This is shown in Figure 6.

In this way, the point that gives the maximum distance is detected, and if this point is longer than 4, this point and both end points are connected by a line segment. The new line segment gives a better approximation.

The maximum distance between the straight line containing this line segment and all the pixels sandwiched by the end points of the line segment is found, and if this distance is longer than l, a line segment is drawn in the same way to improve the approximation.

Thereafter, such operations are repeated until the maximum distance becomes shorter than the approximate length l.

When the maximum distance becomes shorter than l, the approximation operation ends.

In this way, any line image can be approximated by broken lines.

If the approximation length l is long, the approximation will be rough, but the time required for the approximation operation will be short.

If the approximation length l is short, the approximation will be finer, but the time required for the approximation will be longer. Furthermore, if l is too short, there is a drawback that noise cannot be reduced. An appropriate approximate length l is determined depending on noise, required time, required figure, etc.

Group Necessary Calculation Formulas Next, a method for calculating pixel j and distance dj will be explained.

The pixel plane is specified by xy coordinates.

A straight line passing through the starting point (X8% yo) and the ending point (Xl, yl) is represented by ax −1−by 〇=Q.

The distance di between this straight line and pixel 1 (xi, yt) is given by the following equation.

The parameters a%b, c can be determined by entering the coordinates of the starting point and ending point into the above straight line equation.

Although the value of the ratio of the parameters is determined, the absolute value is not.

Therefore, simply a = yl-yo (2) b"'
Xo Xt (8)C”
13'OXO3'l (4' can be used. Of course, these can be multiplied by a constant.

When finding the pixel j with the maximum dl, use the denominator d'i
== l aXi + byi + CI (Define 51 and find the pixel j where this is the maximum.

In any connection of line images, a certain pixel (xi % y
i) and the immediately preceding pixel (xi-1, yi-1) is mi.

Suppose that it is represented by ni. ml, ni is 01+1, -1
There is a one-to-one correspondence between chain codes. None of them are O.

For these values, xt = Xl-1+mt (61
yi = yi-1-1-ni (
7) holds true. Since m is the increment in the X direction and n is the increment in the Y direction, the following relationship exists for the chain code defined in FIG.

This is shown in Table 1. The multiplexer output in the right column will be described later.

Table 1 Chain code, m, n values, multiplexer output axi-1-byi +c = aXo+1)
It becomes 3'o +C. The starting point (aoSyo) is the straight line ax
+by −t−c = 00, so the first term on the right side of equation (8) is 0.

Therefore, the value of dl is becomes. The same formula can also be expressed as:

Δ = amh + bnst (1
0) Σk = ΣΔh (11) h
=1 Here, the absolute value of Σ1-1 is d'i-i.

Two integers mk and nk are given by the chain code, and Δ is determined by these. Δk is m, n is 0
It is given as 1+1, but the following eight values a, -b,
-a, b, a+b, -a tensu, a-b
.

-a-b'ff: Take.

After all, the algebraic distance Σi is a, -b in the previous Σ1-1.

It can be found by adding -a, etc.

When tracing the chain code sequence, the previous value Σ
If il is maintained, Σi can be found just by addition to Δ.

Also, at this time, if we calculate the value of xly in parallel and save the value (Xj S'fj) when d'i becomes maximum, we get (1
(2) Then, d't can be obtained quickly using a simple method, and the coordinates of that pixel can be found. If the coordinates of the maximum distance point are known, the line segment connecting the starting point, end point, and maximum distance point can be immediately determined. One can quickly proceed to the next stage of approximation.

□□□) Configuration of the Invention Since the present invention relates to a circuit configuration for quickly performing the above-mentioned calculation, this will be explained with reference to FIG.

Constant registers 1 to 8 are the starting point (xos yo),
a calculated from the coordinate values of the end point (Xl,'/x),
b.

-a, -b, a-b, -a+b, Ia tensu, -a
-b (7) A group of registers in which values are stored in advance prior to calculation.

The outputs of constant registers 1 to 8 are input to multiplexer 9. This is an 8-power, 1-output multiplexer into which a chain code is input and the contents of one of the constant registers (a) corresponding to the chain code value according to Table 1.
lbl-al-bl...) is selected and output.

The output of multiplexer 9 is input to adder 10.

The output of the multiplexer should be the value corresponding to the above-mentioned Δk,
This and the algebraic sum Σk-1 up to the immediately preceding pixel held in the register 11 are added to obtain Σk.

This value is input to the register 11 and temporarily held there.

In the end, the adder 10 and the register 11 function as an accumulator for obtaining the value of ΣΔ input to the adder 10. After the kth chain code is input,
The value of Σk appears at the output of the adder.

The absolute value calculation circuit 12 is a circuit that calculates the absolute value Σk of the adder output. This is equal to the distance d'k.

The output of the absolute value calculation circuit 12 is sent to the register 14 and the comparator 1.
given to 5.

When the fifth distance d'i is input, the comparator 15 compares it with the value held in the register 14, and if d/i is greater or equal, loads d'i into the register 14. Issue a control signal. d't is stored in the register 14. When d't is smaller, no control signal is output. The contents of register 14 remain unchanged.

Therefore, if register 14 is initially set to 0,
This means that the maximum value of the distance to the i-th distance is always stored. That is, register 14 and comparator 15
functions as a maximum value detection circuit.

The counter 13 is a counter that counts the number of chain codes, and increments its contents by 1 every time a chain code is input. The register 16 to which the output of the chain code counting counter 13 is input loads the value of the counter 13 in response to the control signal of the comparator 15. The register 16 temporarily stores the number of the pixel that provides the maximum distance among the pixels up to the i-th pixel.

The decoder 17 outputs the amounts of change m and n in the x1y direction for the chain code value (θ to 7) according to Table 1. The value of m is given to the X direction counter 18. The X-direction counter 18 is an up/down counter that adds up the value of m. Since m is O1+1, -1, it can be integrated by a counter.

The value of n is given to the counter 19 in the X direction.

The X-direction counter 19 adds up the value of n.

These counters 18 and 19 are programmap/L/(brisera tab/L/) counters, and initial values can be set therein. As an initial value, the coordinates Xo s 7o of the starting point (xo s 3'o) are given. After this, changes in the X direction, mk, and nk in the X direction are added in order, so when the first chain code is input, counter 1g holds the XtO value, and counter 19 holds the YiO value. . From this, the coordinates (Xi, Yi) of the first pixel can be found.

The X direction register 20 and the X direction register 21 are the comparator 1
5 issues a control signal, the outputs of the X-direction counter 18 and the X-direction counter 19 are loaded, respectively. Comparator 1
5, when d'i is larger than the value held in the register 14, a control signal is issued when d'1 is the maximum value up to the first, so the X direction register 20,
The X direction register 21 holds the X and Y coordinates of the pixel that provides the maximum distance.

Therefore, when all chain codes are read up to the end point, d
'xjlYj, which is the X1y coordinate of pixel j that gives the maximum value d/j of 1, is held. The value of j is stored in register 16.
is maintained. The value of d'j is held in register 14.

From the value of d'j, dj is determined according to equation (1), and this is compared with the approximate length l.

If djO is larger than l, the start point, end point, and maximum distance point (XIYj) are connected by a line segment. If djO is smaller than l, then the approximation operation is terminated.

If you connect the starting point, ending point, and maximum distance point with a line segment, one line segment becomes two line segments, which means that you have a higher order approximation.

Next, since the starting point and ending point of the new line segment are determined, the values of a and b are determined based on this. Once the values of a and b are determined,
Since the values of constant registers 1 to 8 are also determined, the previous held values,
a% 5% '1-b%... Make the controller input the newly calculated holding value into the constant register. Then, similarly, the chain code is input to the multiplexer 9 and the decoder 17 to obtain a new maximum value.

However, in the latter half, the (j+1)th pixel becomes the first pixel in the chain code. This is because the fifth pixel is the starting point.

Prior to any calculation, the register 11.14 and counter 16 are cleared, and the counter 18.19 is loaded with the coordinate Xos'10 of the start point of the calculation.

(To) Effects of the invention (1) Since the line image expressed by the chain code is approximated by a broken line, the amount of data can be significantly compressed.

(2) Rather than finding a turning point, a broken line approximation is performed so that the distance between a long line segment and a pixel is equal to or less than a certain value, so it is robust against noise. If l is larger than the noise fluctuation, the noise will drop.

(3) The approximate length l is a parameter. Since this is a controllable parameter, polygonal line approximation can be performed with any precision.

You can specify the degree of approximation. It can also be considered that l expresses the degree of approximation.

(4) In a relatively simple circuit, the pixel number j that forms the crease
and the coordinates Xj1Yj are found at high speed.

(5) Since this circuit can be created by combining elements with simple functions, it is easy to implement the entire circuit as an LSI.

[Brief explanation of drawings]

FIG. 1 is a diagram showing an example of a two-dimensional line image. FIG. 2 is an explanatory diagram of the correspondence between the direction of change from one pixel to the next pixel and the chain code. Figure 3 is an example of displaying the line image in Figure 1 as a chain code. FIG. 4 is an explanatory diagram of the principle of broken line approximation used in the present invention, and is a diagram showing the O-th approximation. FIG. 5 is a diagram showing the first approximation. FIG. 6 is a final approximation diagram after the second approximation. FIG. 7 is a diagram showing the configuration of a broken line approximation circuit according to the present invention. 1 to 8...Constant register 9...Multiplexer 10...Adder 11...Register 12...Absolute value calculation circuit 13...Counter 14...Register 15... ... Comparator 16 ... Register 17 ... Decoder 18 ... X direction counter 19 ... X direction counter 20 ... N direction register 21 ... Y direction register Inventor Asaina Takumijo Kunio

Claims (1)

[Claims] In order to divide a line image expressed by a chain code into parts that can be considered straight lines and approximate each part with a line segment, we connect the starting point and end point of the line image with a line segment and calculate the distance between the straight line and the pixel. maximum value d_j, pixel j giving the maximum value and coordinate X_
j, Y_j, and d_j is a predetermined approximate length l.
If it is larger, connect the start point, end point, and maximum distance point j with a line segment to improve the approximation, and then calculate the maximum distance between the straight line that includes these line segments and the pixels sandwiched by the end points of the line segment, and the maximum distance. Find the pixel and its coordinates that give The line image is approximated by a broken line until ,a
-b, and a multiplexer 9 that selects one of the constant registers 1 to 8 by inputting a chain code representing a line image;
An accumulator that adds and accumulates the output Δ_k of the multiplexer 9, an absolute value calculation circuit 12 that calculates the absolute value d_k' of the output Σ_k of the accumulator, and the maximum value up to the (k-1)th output of the absolute value calculation circuit 12. The holding register 14 and the output d_k' of the absolute value calculation circuit 12
and the value held in the register 14, and when d_k' is greater or equal, a comparator 15 generates a control signal to load the value of d_k' into the register 14, and a counter 13 counts the number of chain codes. , a register 16 that loads the value of the counter 13 according to a control signal from the comparator 15, a decoder 17 that calculates the change m_k in the x direction and the change n_k in the y direction of the line image from the chain code, and the coordinates of the starting point. x-direction counter 1 which inputs x_0, y_0 in advance and adds x-direction change m_k and y-direction change n_k to these to obtain the coordinates X_k, Y_k of the k-th pixel.
8. A y-direction counter 19, and an x-direction register 20 and a y-direction register 21 that load the values of the x-direction counter 18 and y-direction counter 19 according to the control signal from the comparator 15.
A broken line approximation circuit for line images characterized by the following.