JPH04205676A - Method for approximating polygonal of point sequence data - Google Patents

Abstract

PURPOSE:To allow the execution of the approximation processing of a polygonal by expressing the deviation between partial point sequence data and provisional approximation segment by the height of a triangular shape and deciding whether the deviation is a polygonal point or not by comparing the height thereof with the threshold. CONSTITUTION:The deviation between the data of the partial point sequences P1,..., Pn and the provisional approximation segment Ln is expressed by the height h of such a triangular shape HP1Pn which is equal in area to the area Sn of the part enclosed by the provisional approximation segment Ln and the partial point sequences P1,..., Pn and the base of which is the segment Ln with out expressing the same with the max. distance to the segment Ln from the partial point sequence P1,..., Pn. Whether the deviation is the polygonal point or not is decided if the height h of the triangular shape HP1Pn is compared with the threshold. The time for the approximation processing of the polygonal is shortened in this way.

Description

DETAILED DESCRIPTION OF THE INVENTION (Industrial Application Field) The present invention relates to a polygonal line approximation method for point sequence data, which performs polygonal line approximation at high speed within a predetermined tolerance without storing the point sequence data all at once. It is something.

(Prior art) Conventionally, as a technology in this field, Japanese Patent Application Laid-Open No. 1-96
There was one described in Publication No. 771.

Generally, an approximate line is calculated from the coordinate point sequence data of the boundary line obtained by performing boundary point tracking of a binary image of an object or the coordinate point sequence data of the edge line obtained by performing edge point tracking in an edge image. Create shapes, compress point sequence data,
When attempting to recognize the shape of an object from an approximate figure of its outline or edge, polygonal line approximation of point sequence data is often used from the viewpoint of processing simplicity. An example is shown in FIG.

FIG. 2 is a diagram showing the conventional method of polygonal line approximation of point sequence data described in the above-mentioned literature.

As shown in this figure, the conventional method for polygonal line approximation of point sequence data requires a threshold (
Tolerance) When ε is specified, the point sequence data is Pl, ..., Pi in the XY coordinates.

. . , P , P P , . . . is a tentative approximate line segment from the starting point Pn-1n' n+1 1 to the current point P. think of.

Then, partial point sequence P1. ..., P, line segment L from each point
Calculate the maximum distance d, to the maximum distance d. If is less than the threshold ε, move to the next point P1+1 and repeat the above process. Also, the maximum distance d.

is greater than the threshold ε, then the previous point P. −1 is extracted as a breaking point, that is, partial point sequence P , ..., Pn-1
The approximate line segment is set as the line segment L from point P1 to point P, -1, and the above process is repeated using the immediately previous point (break point) Pn-1 as a new starting point to create a point sequence pig P1,... , P ,
... was approximated as a polygonal line.

(Problem to be solved by the invention) However, in the conventional method of polygonal line approximation, the polygonal line
. −1 is found, that is, until the maximum distance d, is greater than the threshold ε.

Every time you move from point P1 to point P0,
For all points up to 1, it is necessary to calculate the distances up to +1, which are temporary approximate line segments, every time, and find the maximum distance dn+1. Therefore, as the partial point sequence P1° .

The present invention provides a method of polygonal line approximation of point sequence data that solves the problem of the prior art, which is that the processing time increases as the partial point sequence becomes longer.

(Means for Solving the Problems) In order to solve the above-mentioned problems, the present invention provides a method for polygonal line approximation of point sequence data. Based on only three points: the existing point, the point immediately before it, and the starting point, a temporary approximate line segment connecting the starting point and the current point and partial point sequence data from the starting point to the current point are generated. Find the height of a triangle that has an area equal to the area surrounded by and has the tentative approximate line segment as its base. Then, the height of the triangle is compared with a threshold value input in advance as an index representing the deviation between the tentative approximate line segment and the partial point sequence data. As a result, if the index is larger than the threshold, the immediately preceding point is extracted as a breaking point of the approximate line segment, and the immediately preceding point is set as a new starting point, and the current point is set as a new immediately preceding point. By repeating the calculation and comparison process of the height of the triangle until the end point of the point sequence data, the entire point sequence data is approximated by a polygonal line.

(Function) According to the present invention, since the method of polygonal line approximation of point sequence data is configured as described above, as shown in the principle diagram of FIG. 1(a), partial point sequences P, ..., Pn data and tentative approximate line segments. Which deviation is not expressed by the maximum distance dn from the partial point sequence P 1 , . . .
...The area S of the part surrounded by 2Pn. With an area equal to
Height h of triangle HP1P whose base is a line segment
The deviation is expressed by . Then, by comparing the height I] of the triangle HP1Pn with the threshold ε, it is possible to determine whether it is a break point or not, thereby shortening the processing time of the broken line approximation.

Therefore, the above problem can be solved.

(Example) FIGS. 1(a) and 1(b) are diagrams showing the principle of a method of polygonal line approximation of point sequence data showing an example of the present invention, and the principle of this example will be explained with reference to this figure. do.

In the XY coordinates of Fig. 1(a) and (b), Fig. 1(a)
) shown in the partial point sequence P1. ..., P,, ..., the three points P1-(Xl
, Yl), Pn-1= (Xn, , Yn-1
)- and P-(Xo, Y, ) is the area of the triangle surrounded by ΔSo. And the sign of the area ΔS is
Point Pn-1 is a vector V pointing from point P1 to point Pn, =
If it is on the left hand side of (Xn Xl , Yn Yl ), it is positive, and if it is on the right hand side, it is negative. Then,
The area of the triangle ΔSo, the area of the triangle, Vn and Vn-1-
(Xn-1-Xl' Yn-1-Yl)
The following equation (1) holds true between the cross products V, , xVn.

2ΔS, =V, −I XV, ・” (1) Therefore, the partial point sequence P1.

P data and tentative approximate line segment. Let the area of the area surrounded by The following recurrence formula holds.

2S -2So-1+2ΔSn “2S, -1+Vn-1xV.

...(2) Now, if the length of the line segment is d, the base is the line segment. The height l of triangle HP1P2 whose area is l501 is
Since h=21 S, l/d, point Pn-1 can be determined to be a breaking point when the following discriminant formula (3) holds true.

Therefore, the processing necessary for determining a break point using the present broken line approximation method is as follows: partial point sequence P1. ..., P, and can be processed faster than conventional methods.

FIG. 3 shows an example of the case where the present invention is applied to a pre-fold extraction device that approximates sequentially sent point sequence data to a broken line based on the above principle and sequentially outputs the broken point sequence data.

FIG. 3 is a block diagram of the structure of the fold front extraction device.

This fold-edge extracting device has a control circuit 1 composed of a central processing unit (hereinafter referred to as CPU) and the like that controls the entire device. The control circuit 1 includes a line segment vector calculation circuit 2.
A bending point determination circuit 4 is connected via the cross product summation circuit 3.

The control circuit 1 also includes a start point register 5 that stores the XY coordinates of the starting point P1 (or break point) of the point sequence data, a current point register 6 that stores the XY coordinates of the currently read point P1, and a current point register 6 that stores the XY coordinates of the currently read point P1. Point P read immediately before point Pn. -1
The immediately preceding point register 7 stores the XY coordinates of the point P1 immediately before the starting point P1.

A straight line register 8 that stores the XY acid components of the vector Vn-1 directed toward 1 is connected. Furthermore, starting point P1
A vector ■ heading from to the current point Pn.

A current line segment register for storing the XY acid components of
It is connected to the control circuit 1.

Here, the error ε2 of the polygonal line approximation and the input point sequence P1 to perform the polygonal line approximation. P2. ..., P, ..., Po. (However, the length is 2 or more) is read from the control circuit 1 to this device and subjected to polygonal line approximation, resulting in a polygonal point sequence (partial point sequence of the input point sequence) Pl, . . .
It is assumed that the data of Po are sequentially output from the control circuit 1.

FIG. 4 is a flowchart showing the operation of FIG. 3,
The operation of the fold-edge extraction device will be described with reference to this figure.

First, the control circuit 1 reads the threshold value ε2 of the polygonal line approximation and the starting point P1 of the point sequence data into the threshold value register 0 and the immediately preceding point register 7, respectively (step S1). Then, as a process after extracting the bending point (the starting point of the input point sequence is also one of the bending points), the control circuit 1 outputs the value of the immediately preceding point register 7 as the bending point data (step S2), and at the same time The value is copied to the starting point register 5, and the values of the immediately preceding line segment register 8 and the outer product sum register 2 are set to ○ (step S
3>.

After step S3, the control circuit 1 reads the next point P of the input point sequence data into the current point register 6 (step S4
), it is determined whether the input point sequence data is complete (step S5). If the input point string data is finished, the value of the current point register 6 (end point P of the input point string) is output as the end point of the break point string data (step 513), and all processing is completed.

On the other hand, in step S5, if the input point sequence is not completed, the line segment vector calculation circuit 2 calculates a line segment vector V from the starting point P1 to the current point P, based on the values of the current point register 6 and the starting point register 5. is calculated and stored in the current line segment register 9 (step S6). Next, the cross product sum calculation circuit 3 calculates the vector cross product ■ from the value of the current line segment register 9 (vector ■.) and the value of the immediately preceding line segment register 8 (vector V. -1). -1×Vo is calculated, and the foreign debt value is added to the value of the outer product sum register 1 to update the value of the outer product sum 2So (step S7). The bending point determination circuit 4 calculates the square d2 of the length of the line segment vector V, ) from the starting point P1 to the current point P based on the value of the current line segment register 9. The determination condition of the equation (4) is evaluated from the value 2S of 1 and the value ε2 of the threshold register 0 (step S9).

In step S9, if the determination condition of equation (4) is not satisfied, the control circuit 1 determines the value P of the current point register 6.
In step 5, copy the values of the current line segment register 9 and the current line segment register 9 to the previous point register 7 and the previous line segment register 8, respectively.
10), return to step S4. On the other hand, in step S9, if the condition of equation (4) is satisfied, the value Pn-1 of the immediately preceding point register 7 is output as the breaking point.
1), and its value P. After copying -1 to the starting point register 5 (step 512), the process returns to step S3.

Therefore, the point sequence P1 to be approximated by a polygonal line. P2,...

There is no need to store all the data of Pn,...
By sequentially scanning only once, the point sequence data can be approximated by a broken line with an error less than a given threshold value, and the extraction process of the broken point sequence data can be performed at high speed with a small number of steps.

It should be noted that the present invention is not limited to the above embodiments, and for example, the first embodiment
Partial point sequence P1 in figure (a). . . , P, . Various modifications are possible, such as execution using program control.

(Effects of the Invention) As described above in detail, according to the present invention, the deviation between partial point sequence data and a temporary approximate line segment is represented by the height of a triangle, and the height is compared with a threshold value. Since it is decided whether or not it is a break point by The process of approximating the line to a polygonal line and extracting the polygonal point sequence data can be performed at high speed with a small amount of processing.

[Brief explanation of the drawing]

Figures 1 (a) and (b) are diagrams showing the principle of the polygonal line approximation method according to the present invention, Figure 2 is a diagram showing the conventional polygonal line approximation method for point sequence data, and Figure 3 is a diagram showing the implementation of the present invention. FIG. 4 is a block diagram illustrating the configuration of a bending point extracting device showing an example, and FIG. 4 is a flowchart showing the operation of FIG. 3. ■〕... Height of triangle, L... Line segment, P...
・, Pn1 n, Pn+1... Partial point sequence, S, ΔS,... Area, ■n-1, "n... solid 1 ~ Ru. Applicant: Mitsubishi Heavy Industries, Ltd. (Kari name) Agent Patent Attorney Kakimoto Kyo Seikaisumon “3 〒 ζ (:) ')−.

Claims (1)

[Claims] Every time the coordinate data of each point in the point sequence data is inputted sequentially, the coordinate data of each point in the point sequence data is calculated based on a recurrence formula from only the inputted current point, the point immediately before it, and the starting point. The height of a triangle with an area equal to the area surrounded by the tentative approximate line segment connecting the starting point and the current point and the partial point sequence data from the starting point to the current point, and whose base is the tentative approximate line segment. The height of the triangle is compared with a pre-input threshold value as an index representing the deviation between the tentative approximate line segment and the partial point sequence data, and if the index is larger than the threshold value, Extracts the previous point as a breaking point of the approximate line segment, and performs the calculation and comparison process of the height of the triangle using the previous point as a new starting point and the current point as a new previous point. A method for polygonal line approximation of point sequence data, characterized in that the entire point sequence data is approximated by a polygonal line by repeating the process until the end point of the point sequence data.