JPH01297775A - Circle and circular arc extracting method - Google Patents

Abstract

PURPOSE:To perform the extraction of a circle and a circular arc at high speed by approximating an original picture with a polygonal line, finding an approximated circle from two adjacent polygonal lines, and approximating the original picture with the circle or the circular arc when distance between the approximated circle and the polygonal line is within a prescribed value. CONSTITUTION:The original picture read by a scanner is approximated with the polygonal line and obtained vector data is stored in a memory. And two adjacent vector data are read out by a vector tracing part, and the circle approximated to the two vector data is found at a circular arc vector decision part, and the maximum value (h) of the distance between the vector and the circle is compared with the prescribed value. When the distance between the vector and the circle is less than the prescribed value, it is judged as the circle or the circular arc, and the vector data is replaced by circle data or circular arc data.

Description

[Detailed Description of the Invention] [Summary] An original picture is approximated by directed polygonal lines so that the distance between the line forming the original picture and the directed polygonal line is within a predetermined threshold, and a polygonal line is assembled from continuous directed polygonal lines. Regarding a circle/arc extraction method that judges whether a group of polygonal lines forms an arc or not, and when it is determined that a group of polygonal lines forms an arc, approximates the group of polygonal lines with a circle or an arc to extract the circle or arc from the original image. Or, the purpose is to provide a circle/arc extraction method that can extract a circular arc, and the radius of the circular arc obtained when a polygonal line pair assembled with two adjacent directed polygonal lines is approximated by a circular arc, It is determined whether or not a predetermined evaluation value determined based on the length of each polygon line that composes the polygon line pair and the threshold value is within a predetermined tolerance range, and it is determined that it is within the range. In this case, the group of broken lines assembled from the pair of broken lines is approximated by a circle or an arc.

[Industrial application field]

The present invention relates to a method for extracting circles and arcs for the purpose of compressing and cleansing data of line drawings approximated as polygonal lines (petals) among techniques for approximating figures when inputting drawings into a computer. In particular, the original image is approximated by directed polygonal lines using a predetermined threshold value, and it is determined whether or not the polygonal line group assembled by continuous directed polygonal lines forms an arc. Extract a circle or arc
Concerning an arc extraction method.

[Conventional technology]

In recent years, with the computerization of graphic processing approximation techniques such as CAD systems and mapping systems, there has been an increasing demand for inputting existing graphics into computers.

Since drawings input using a scanner or the like are image data expressed in pixels, it is necessary to convert this into directed polygonal line data (vector data) suitable for processing by a computer. At this time, it is preferable to extract the parts of the original drawing as circles and arcs, rather than simply using data approximated by polygonal lines, in the sense that a more faithful representation of the original drawing's intent can be obtained. This method also has the advantage of reducing the amount of data.

Conventionally, in order to extract a circle or an arc from an original drawing, the original drawing is first approximated to a directed polygonal line, and then the angles formed by adjacent directed polygonal lines are determined, and the polygonal lines assembled by the polygonal lines form a circle or arc. I was deciding whether to do it or not.

Or, the original image or an image image created by converting the original image into a core line.
A method was used to extract circles or arcs using the rays.

[Problem to be solved by the invention]

By the way, in the conventional method, the angle between each adjacent polygonal line is calculated, or the circle or arc part is extracted using image data obtained by converting the original image into core lines, so the circle or arc can be extracted with high accuracy. However, since there are many pixels to be used for angle detection or reference, there is a problem in that the processing takes time.

Therefore, the technical object of the present invention is to solve the above-mentioned problems, and has been made with the purpose of providing a circle/arc extraction method that can extract circles or arcs at high speed. be.

[Means to solve the problem]

In order to solve the above technical problems, the present invention, as shown in FIG. S
L) Determine whether or not a polygonal line group assembled from continuous directed polygonal lines forms an arc, and if it is determined that it forms an arc, approximate the polygonal line group with a circle or arc and create a circle or arc from the original image. In the circle/arc extraction method that extracts, the radius of the circular arc obtained when a polygonal line pair assembled from two adjacent trees of the directed polygonal lines is approximated by a circular arc,
It is determined whether a predetermined evaluation value determined based on the length of each polygonal line that composes the polygonal line pair and the threshold value is included within a predetermined tolerance range (S2), and whether it is included within the range. If it is determined that this is the case, the polygonal line group assembled from the polygonal line pair is approximated by a circle or an arc (S3).

[Effect]

When extracting a circle or an arc according to the present invention, in step S1, the original image is approximated by a directed polygonal line based on a predetermined threshold value.

Here, the threshold value refers to the longest distance at which approximation between the line of the original image and the approximated polygonal line is allowed.

Next, in step S2, the radius of the arc obtained when the polygonal line pair assembled from the two adjacent trees of directed polygonal lines is approximated by a circular arc, the length of each polygonal line that composes the polygonal line pair, and the threshold value. It is determined whether a predetermined evaluation value determined based on the above is included within a predetermined tolerance range.

This takes advantage of the fact that when a circular arc with a certain radius is approximated to a directed polygonal line using a certain threshold, the length of each polygonal line created falls within a certain range determined by the radius.

Here, the predetermined evaluation value and the predetermined range are, for example, the fourth
As shown in the figure, if the radius is r, the length of the directed polygonal line is text, the threshold is d, and the distance between the arc of the original drawing and the polygonal line is 11, then h≦d; , as is clear from Figure 4, (cross/2)2
+ (r-h)2=r2 (2).

Therefore, by rearranging ■ and ■, the following relational expression can be obtained: Sentence 2 = 4h (2r-d) ≦4d (2r-d) ■.

Therefore, for example, the predetermined evaluation value is 12/4d (2r-
If d) is taken, the value must fall within a predetermined tolerance range of 1 or less in order for the polygonal line pair to form a circle or an arc.

Subsequently, if it is determined in step S3 that the polygonal line group is within the range, it is determined that the polygonal line group assembled from the polygonal line pair forms a circle or an arc, and is approximated by a circle or an arc.

〔Example〕

Next, embodiments according to the present invention will be described.

FIG. 2 shows a device for realizing the circle/arc extraction method according to this embodiment.

A scanner 1 that reads an original image as an image formed from pixels, a polygonal line approximation unit 2 that approximates the image with a directed polygonal line (hereinafter referred to as a "vector") based on a certain threshold, The vector table storage unit 3 serves as a memory for storing the set of position coordinates of If the vector determining unit 5 determines that it is a circular arc, a center coordinate deviation test is performed, and if both are determined to be circular arcs, the circular arc vector is sent to the circular arc vector storage unit 6, which will be described later, to confirm that both are circular arcs. If the determination is not made, the arc vector tracking unit 4 newly reads the Muku 1 health data from the vector table storage unit 3, and calculates the radius and center of two adjacent vector pairs when approximated by length arcs. an arc vector determination unit 5 that calculates coordinates and inner product values, determines whether or not it can be an arc, and sends the result to the tracking unit 4; and when the arc vector tracking unit 4 determines that it is an arc, the data is It has an arc table storage section 6 that stores the arc table storage section 6, and an arc approximation section 7 that outputs the final arc approximation result stored in the arc vector storage section 6.

Next, the operation of this embodiment will be explained.

In this embodiment, as shown in FIG. 3, the image data read by the scanner 1 is vectorized (approximated by directed polygonal lines) at the threshold value d in the polygonal line approximation unit 2 in step SJI as shown in FIG. ) and then stored in the vector storage section 3.

In step SJ2, the arc vector tracking unit 4 reads out the vector data if there is unprocessed vector data stored in the vector storage unit 3.

The vector read in step SJ3 is set as the hector of interest.

In step SJ4, the arc hector tracking unit 4 finds connection vector data adjacent to the end point (start point or end point) of the vector of interest.

In step SJ5, it is determined whether the pair of broken lines assembled from the vector of interest and the connected vector can form an arc.

Here, it is determined whether or not a pair of polygonal lines forms an arc as follows.

In the above-mentioned case (2), since the vectorization threshold d is generally quite small compared to the radius r of the circle to be extracted, the case (2) is simplified to 2≦8dr (2). This value means that a circle of radius r that is vectorized using a certain threshold value d will not exceed a certain length.

By rearranging (2), E=sentence 2/8 dr≦1 is obtained, and E is used as the evaluation value of the arc for two consecutive tree vectors.

Also, if the value is within the range of 1 or less, the group of polygonal lines forms a circle or arc, but in actual drawings, it is problematic to set the value of E to 1 due to handwritten distortions, etc. Yes, it is necessary to change the value depending on the degree of distortion of the circle/arc drawn on the original picture. Therefore, equation (2) needs to satisfy E=12/8dr≦.

Here, the case of k or less corresponds to the above-mentioned tolerance range, and there is a parameter determined depending on the degree of distortion of the arc drawn on the original drawing.
Use as a.

By finding this value for consecutive vectors and determining whether it is within a certain threshold, it is possible to easily determine whether the vector forms an arc.

In addition to the evaluation value E obtained above, the following judgments are obtained.

(a) The inner product of two consecutive tree vectors is D≧0 (b) The obtained temporary radius r is r≦l'maX (
C) The deviation of the center coordinates determined from the two vectors so far is within a certain range.

Here, (a) is a process that excludes cases where the angle formed by the two-tree vector is an acute angle, and (b) is a process that excludes cases where the angle formed by the two-tree vector is an acute angle.
The process for removing it (C) is a process for separating two circular arcs by shifting their center coordinates when they touch at their end points.

Note that the radius and center position when two vectors are approximated by circular arcs can be obtained by drawing a perpendicular bisector from the two vectors and finding the intersection.

A specific example is shown in FIG.

Vector sentence. , kiln, (u.9 sentence 1 represents each vector length) has already been extracted as a candidate for forming an arc. Attention beta 1 hell barbarian, 1 anbl to the connection vector connected to. If there are three trees, calculate the evaluation value E of the arc, the inner product of the vector, and the radius range for each of these three trees. , λ□.

For example, barbarism. When making a judgment, as shown in FIG.
, when the threshold value is d and the range is k, it is barbaric if the following relationship holds. It is determined that it can be an element of an arc formed by a pair of broken lines assembled by , , and .

i.e. flx”/8dria, la’/8dr
ta≦k(bun,・kiln,)≧0 (i.e. 1θ181≦9
0°) 1”min≦rla≦rmax (+-min indicates the radius of the smallest circular arc that can be approximated by a vector).

In this way, returning to FIG. 3, when the above judgment is made in step SJ5, if it is determined that it will not be a circular arc, the process will proceed to step SJ2 again, but if it is determined that it can be a circular arc, the process will proceed to step SJ6. Then, the vector of interest and the connected solid 1 hell are newly registered in the arc table storage section 6.

Next, the process proceeds to step SJ7, and the connection vector is newly set as a vector of interest.

In step SJ8, the arc vector tracking section 4 discovers a vector connected to the end point of the vector of interest.

In step SJ9, the arc vector determination unit 5 determines whether the vector of interest and the connected vector can form an arc using the method described above (step SJ5).

If it is not an arc, the process proceeds to step 5J13, and the registration in the arc table storage unit 6 for the polyline group assembled by the vector pair (broken line pair) is completed.

On the other hand, if it is determined that it can be a circular arc, step 5J
Proceeding to IO, the arc hector tracking unit 4 determines whether the deviation of the center coordinates up to now is within a certain range for the arc.

That is, vector versus stem as shown in FIG. , kiln, and the center coordinates of the arc approximated by oo1(x,y) and peklhel vs. kiln1. The deviation of the center coordinate (ΔX,
It is determined whether Δy) is within a certain range of the arc.

If this does not result in a circular arc, the process proceeds to step 5J13, where the registration in the circular arc table is completed, and the process proceeds to step SJ2 again, where the circular arc vector tracking section 4 searches the vector storage section 3 for unprocessed vector data and performs the above process. You will have to repeat the procedure.

If the arc vector tracking unit 4 cannot find unprocessed solid 1 hell data in step SJ2, step 5J
The process proceeds to step 14, where arc approximation processing is performed by the arc approximation section 7.

On the other hand, if it is determined in step 5JIO that it can be an arc, the process proceeds to step 5JII, where the arc vector tracking section 4 registers the connected vector in the arc table storage section 6.

Further, the process proceeds to step 5J12, and the arc vector tracking unit 4 again sets the connection square 1-1 as the focus of attention, and proceeds to step SJ8 to repeat the above procedure.

Incidentally, when the arc vector tracking section 4 searches for a connection vector with respect to the vector of interest, the search is performed in two directions: the starting point side and the ending point side of the vector.

In this way, all of the above determinations can be easily made, and high-speed processing is possible.

Also, since the maximum value rmaX of the radius of the circle/arc to be extracted is given in advance, the maximum allowable vector length can be found from the above inequality, so by first excluding unnecessary vectors from the vector length, Faster processing is possible.

Furthermore, in this embodiment, by calculating the inner product between adjacent vectors, determining whether the sign is positive or negative, and determining whether the change in direction of the vector is an acute angle, it is possible to create a circle or arc without knowing the angle of adjacent vectors. Since cases that cannot be approximated are excluded, high-speed processing is possible.

〔Effect of the invention〕

As explained above, the present invention uses the threshold value used when approximating a polygonal line to determine whether a group of polygonal lines forms a circle or an arc, so that the length of each approximated polygonal line is within a predetermined range. It takes advantage of the fact that it fits inside.

Therefore, circles or arcs can be extracted at high speed without referring to complicated data such as changes in angles of adjacent directed polygonal lines.

[Brief explanation of the drawing]

Fig. 1 is a flowchart of the principle of the present invention, Fig. 2 is a block diagram of the embodiment, Fig. 3 is a flowchart of the embodiment, Fig. 4 is an explanatory diagram of the arc evaluation value of the embodiment, and Fig. 5 FIG. 2 is an explanatory diagram of arc approximation according to the embodiment. 1... Scanner 2... Broken line approximation unit 2... Broken line approximation unit 3... Vector table storage unit 4... Arc vector tracking unit - 5... Arc vector determination unit 6... Arc table Storage section 7...Circular arc approximation section

Claims (1)

[Claims] The original picture is approximated by directed polygonal lines so that the distance between the lines forming the original picture and the directed polygonal lines is within a predetermined threshold (S1), and a polygonal line group assembled from continuous directed polygonal lines is created. In the circle/arc extraction method, which judges whether or not the line forms an arc, and if it is determined that it forms an arc, approximates the group of polygonal lines with a circle or arc to extract the circle or arc from the original image. A predetermined evaluation value that is determined based on the radius of the arc obtained when the polygonal line pair assembled with the directed polygonal lines is approximated by a circular arc, the length of each polygonal line that composes the polygonal line pair, and the threshold value is predetermined. (S2), and if it is determined that it is within the range, the group of broken lines assembled from the broken wire is approximated by a circle or an arc (S3). ) A method for extracting circles and arcs.