JPS6234283A - Two-dimensional distance calculating device - Google Patents

Abstract

PURPOSE:To attain the approximation of a two-dimensional Euclid distance with high accuracy by providing the 3rd arithmetic part which adds and normalizes the Chebyshev distances obtained by the 1st and 2nd arithmetic parts. CONSTITUTION:The 1st Chebyshev distance arithmetic part 14 calculates the Chebyshev distance based on an equal Chebyshev distance curve as shown in (a). While the 2nd Chebyshev distance arithmetic part 15 calculates the Chebyshev distance based on an equal Chebyshev distance curve turned by 45 as shown in (b). These obtained Chebyshev distances are given to an addition/ normalization part 16 to be synthesized there. Thus the result obtained from a synthetic equal Chebyshev distance curve is delivered as shown in (c). This synthetic equal Chebyshev distance curve has a right octagonal shape and therefore the approximation error can be reduced down to about 8% or less.

Description

[Detailed Description of the Invention] [Summary] When the two-dimensional Euclidean distance between two points is simply approximated by the Chebyshev distance, the calculation speed is fast, but there is a drawback that the error is large. Therefore, we approximated the Chebyshev distance of the two points rotated by 45 degrees and added them to the Chebyshev distance of the original two points, in order to improve accuracy without significantly impairing calculation speed.

[Industrial application field]

The present invention relates to a two-dimensional distance calculation device for quickly determining the distance between two arbitrary points, which is useful for an image processing device that processes patterns such as two characters or figures.

[Conventional technology]

Generally, in one image processing, there is often a processing request to find the distance between two arbitrary points given on nine planes. 2
The distance between points can be found as follows.

As shown in Figure 4, when the coordinates of two points P, , P2 on a plane are (x,, Yl), (xz, yz), P
, , P2 is the coordinate (X, -Xi).

It is equal to the distance between the point P of Yl　Yz) and the origin.

Therefore, when defining the distance between any two points, one point (
It is sufficient to define the distance between (X, Y) and the origin (0,0).

Here, the distance between the two points (X, Y) and the origin (0, 0) is expressed as d (X, Y). Below d(X,Y)
discuss.

By the way, the straight-line distance between two points is called the Euclidean distance and is defined as a (X, Y)=, E"'+Full 1.

Figure 5 shows the curve of the locus of points showing the second Euclidean distance.
In other words, it represents a circle centered at the origin. but,
When calculating this Euclidean distance on an actual distance calculation device, approximation calculation of the square root using Newton's method is required, which has the drawback of increasing calculation time.

Therefore, if high-speed processing is required, score 1 point (X).

The distance between Y) and the origin (0,0) is the coordinate value X.

Chebyshev distance d (
X, Y)=lXl+lYl is often used approximately.

Figure 6 shows the locus of points showing the first order Chebyshev distance.

In other words, it represents a square rotated 45 degrees around the origin.

By using this Chebyshev distance, basically only one addition operation is required.

High-speed processing becomes possible.

[Problem that the invention seeks to solve]

In a conventional two-dimensional distance calculation device, when calculating the distance between two points using the Chebyshev distance, in terms of wood, the circle of the iso-Euclidean distance curve shown in Fig. 5 and the circle of the iso-Chebyshev distance curve shown in Fig. 6 are used. An error occurs based on the difference from the square, and for example in FIG. 6, the closer to the x and y coordinate axes, the smaller the error is.

There was a problem in that the further away from the coordinate axis, that is, the closer to 1Xl=lYl, the larger the error became, reaching a maximum of about 40%.

[Means for solving problems]

The purpose of the present invention is to improve the approximation error of a two-dimensional distance calculation device that uses Chebyshev distance, and therefore calculates the Chebyshev distance between two given points and rotates the coordinates of the two points by 45 degrees. The configuration is such that the Chebyshev distance is also determined for the two Chebyshev distances obtained, the two obtained Chebyshev distances are added, and the normalized result is output.

FIG. 1 is a diagram showing the basic configuration of the present invention.

In the figure, 11 is a first point input section, 12 is a second point input section, 13 is a relative position conversion section, 14 is a first Tievisiev distance calculation section, 15 is a second Tievisiev distance calculation section, and 16 is an addition and normalization section. represents the division.

In the first point input section 11 and the second point input section 12.

One of the first point and the second point for which the distance is to be calculated is input and set. Here, the coordinates of the first point and the second point are (
X+, YI), (Xz, Yz).

The relative position conversion unit 13 converts the first point and second point set in the first point input unit 11 and second point input unit 12, respectively.
The relative coordinates of the point are determined and the process of moving the second point to the origin position is performed. As a result, the coordinates of the first point are (X+X
z, YI Y2).

The coordinates of the second point are (0, O).

The first Chebyshev distance calculation unit 14 calculates the Chebyshev distance d (X, Y) between two points at the reference position without one rotation.
-1Xl+lYl...(1) is calculated.

Second Chebyshev distance, the throat fold 15 is the Chebyshev distance d between two points rotated 45 degrees with respect to the origin (X, Y) = - (lx + yl + 1X - yl)...
・(2) Find π.

The addition and normalization unit 16 includes the first . By adding the two Chebyshev distances output from each second Chebyshev distance calculation unit and normalizing by multiplying by a constant so that the input value on the coordinate axis and the result value match.

d (X, Y) −(ff−1) (lXl+lY
I+ (1--) (lX+Yl+1X-Yl)...
- Output (3) as the result value.

[Effect]

In FIG. 1, the first Chebyshev distance calculation unit 14 is
The Chebyshev distance is calculated based on the iso-Chebyshev distance curve shown in FIG. Calculate Chebyshev distance based on a curve.

The addition and normalization unit 16 in FIG. 1 combines these results and outputs a result based on the combined Chebyshev distance curve shown in FIG. 2(c).

The composite iso-Chebyshev distance curve in Figure 2(c) is.

It has a regular octagonal shape, and has the same shape as shown in Figure 5.
The approximation error is reduced because it is closer to the distance curve.
It can be suppressed to within about 8%.

Next, the process of obtaining equation (3) from the above equations (11 and (2+) will be explained.

Equation (2) is obtained by subjecting Equation (1) to the following coordinate rotation transformation.

...(4) Now, add equations (1) and (2).

d (1,0) -1...(5) Normalize by setting constants for the coefficients so that

...(6) is obtained. Furthermore, remove the square root from the denominator of the constant.

By rearranging the equation, (3) 2 can be obtained.

〔Example〕

FIG. 3 is a block diagram of an apparatus according to an embodiment of the present invention.

The coordinates of the first point (Xl) are entered in the first point coordinate input section 31.

YI), and input the coordinates (Xz, Yz) of the second point into the second point coordinate input section 32.

From the first point coordinate input section 31 to the first point X coordinate storage section 33
I and y in the first point X coordinate storage section 35.

are transferred and stored respectively. Similarly, the second point coordinate input section 3
2 to the second point X coordinate storage section 34.

Further, Y2 is transferred and stored in the first point X coordinate storage section 36, respectively.

Next, transfer X, , X2 from 33.34 to the subtraction unit 37,
The difference value X=X, -X2 is determined, and X is stored in the difference value X storage section 38. Similarly, from 35.36, subtracter 37 inputs Y, , Y2
is transferred, the difference value Y=Y, -Y2 is calculated, and the difference value Y storage unit 3
Store Y in 9.

Next, X is transferred from 38 to the absolute value calculation section 40 to obtain the absolute value and stored in the IX1 storage section 41. Similarly from 39 to 4
Transfer Y to 0, find the absolute value IYI, and store IY1 storage section 4.
Store in 2.

Next, from 38.39, the adder 43. Transfer X and Y to the subtraction unit 44. After determining XIY in step 43, it is transferred to step 40, where the absolute value I XIY l is determined and stored in l XIY 1 storage section 45 . Also, after finding X-Y at 44, transfer it to 40,
Find the absolute value I X-Y l.

l　XY　l Store in the storage section 46.

Next, from 41.42, IXl and IYI are transferred to the adder 47, lXl+lYl is obtained, and lXl+IYI storage unit 4
8, and from 45.46 lX+Yl, IX-Y
l is transferred to the addition section 47.

l XIY l + l X-Y Find l, lX+Y
l+1X-Y Store in l storage section 49.

The first constant storage section 50 stores a constant value of 5 ((2)-1), and the second constant storage section 51 stores a constant value of (1π m-).

Here, each item stored in 50, 48, 49, and 51 is transferred to the sum-of-products calculating section 52. 52, the product IXI+lYl of the value from 50 (old -1) and the value from 48, and 49
Find the sum of the products of the value I XIY l + l Xl - Y l 51 and the value (1--) from.

The result is stored in the result storage section 53.

In this way, the result of equation (3) described above is obtained.

〔Effect of the invention〕

According to the apparatus of the present invention, a two-dimensional Euclidean distance can be approximated with higher precision without reducing the calculation speed at all compared to the conventional approximation based on a simple Chebyshev distance.

[Brief explanation of drawings]

Figure 1 is a diagram of the basic configuration of the present invention, Figure 2 (a) is a graph of the equal Chebyshev distance curve, Figure 2 (b) is a graph of the equal Chebyshev distance curve rotated by 45 degrees, and Figure 2 (c) is a graph of the equal Chebyshev distance curve. 3 is a graph of a synthetic equivalent Chebyshev distance curve, and FIG. 3 is a configuration diagram of an embodiment of the present invention. FIG. 4 is an explanatory diagram of the distance between two points, FIG. 5 is an explanatory diagram of the equi-Euclidean distance curve, and FIG. 6 is an explanatory diagram of the equi-Chebyshev distance curve. In Figure 1. 11: First point input section 12: Second point input section 13: Relative position conversion section 14; First Thiebishev distance calculation section 15: Second Thievishev distance calculation section 16: Addition and normalization section

Claims (1)

[Claims] A first calculation unit (
14), a second calculation unit (15) that calculates the Chebyshev distance between the two points rotated by 45 degrees with respect to the coordinate system, and a first calculation unit (14) and a second calculation unit (15). A two-dimensional distance calculation device characterized by comprising a third calculation unit (16) that adds and normalizes the Chebyshev distances determined respectively.