JP2847987B2 - Vector data smoothing method and apparatus - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention detects a contour shape of a part from a sequence of points passing over the contour of the part obtained from an edge image synthesized by, for example, operating an edge detection operator on an image of the part. The present invention relates to a vector data smoothing method and apparatus for smoothing a curve represented by a point sequence, which is required in a process for reducing noise included in the point sequence.

[0002]

2. Description of the Related Art As a prior art of this kind, a document [Kentaro Yano (ed.): Mathematical Dictionary, PP, 232-233, Kyoritsu Shuppan Co., Ltd., November 1, 1968, first edition, 6th edition] Using the indicated center of gravity, for example, vector data as a sequence of points through which the contour 100 illustrated in FIG. 3 passes

[0003]

(Equation 1)

There is a technique for smoothing the data. In this conventional method, for example, using an appropriate positive even W

[0005]

(Equation 2)

The local calculated by

[0007]

(Equation 3)

[0008]

[0009]

(Equation 4)

The vector data after the smoothing is used.

[0011]

However, in the prior art described above, for example, W = 2

[0012]

(Equation 5)

In the case where is smoothed, for example, it is calculated by equation (2).

[0014]

(Equation 6)

Regarding

[0016]

(Equation 7)

Since the following holds, for example,

[0018]

(Equation 8)

When is distributed on the circumference of radius R,

[0020]

(Equation 9)

The smoothed contour shape 10
No. 1 has a problem that the area becomes small as illustrated in FIG.
Occurs.

An object of the present invention is to reduce the area of a contour shape represented by vector data without reducing the area.

[0023]

(Equation 10)

Is to provide a technique for smoothing the image.

[0025]

According to a first aspect of the present invention, there is provided a method of smoothing vector data, wherein an average value of a radial component group of a vector group existing near a vector of interest is defined as a radial component;
Sort the angle component group of the vector group, and
Polar coordinates are divided into multiple angle sections from the angle component group
Later, assuming that an angle average exists in the angle section, the angle
Calculated and calculated the angle average value that is the average value of the degree component group
Calculating a variance value corresponding to the angle average value;
The process of determining whether the variance value is valid or invalid
After repeating for each interval, the plurality of valid variance values
Further, a vector represented by polar coordinates having an angle average value corresponding to a minimum variance value as an angle component is a vector obtained by smoothing the vector of interest.

According to a second aspect of the present invention, there is provided a vector data smoothing apparatus, comprising: a polar vector storage means for storing vector data in a polar coordinate format; and a radial component group related to a neighborhood vector group of each output vector data of the polar vector storage means. Neighborhood data extracting means for extracting each of the angle component groups; radial average value calculating means for calculating an average value of the radial component groups; sorting means for sorting the angle component groups; and output data of the sorting means a plurality of each angular interval, from the angle component groups after sorting, the polar plurality of angles determined by
After being divided into sections, there is an angle average value in the angle section
And calculate the angle average value, which is the average value of the angle component group.
Out, and calculate a variance value corresponding to the calculated angle average value,
Processing for determining whether the angle average value and the variance value are valid or invalid.
After repeating the process for each of the angle sections,
Angle average value calculating means for calculating an angle average value corresponding to the minimum variance value among the various variance values .

[0027]

The principle of the present invention is to smooth vector data in a polar coordinate format.

That is, for example,

[0029]

[Equation 11]

When given, as a first step

[0031]

(Equation 12)

Is expressed by polar coordinates (r _i θ _i ) in the following equation.

[0033]

(Equation 13)

As a second step, the average value ρ _i of the radial component is calculated using an appropriate positive even number W.

[0035]

[Equation 14]

Is calculated.

The distance between the angle ψ and theta _i as the third stage d _i
(Ψ) is defined by the following equation based on the positional relationship between the angles ψ and θ _i .

[0038]

(Equation 15)

[0039]

(Equation 16)

As the fourth stage, neighboring angle data {θ _{iW / 2} , θ _{iw / 2 + 1} ,..., Θ _{i + w / 2} } of the angle component θ _i determined using an appropriate positive even number W (10) Are sorted as follows.

The _{π ≧ a 0 ≧ a 1 ≧} ... ≧ a p ≧ 0 ≧ a p-1 ≧ ... ≧ a n-1 ≧ -π (11) where n = W + 1 (12) wherein a fifth step (10) It is assumed that the average value ψ _i of the neighborhood data shown in FIG. 2 exists in any of the (n + 1) sections R illustrated in FIG. Here, each section is described by the following equation.

[0042]

[Equation 17]

In the sixth step, the average value ψ _i
Assuming that it exists in _np-1 , and using equations (8) and (9),

[0044]

(Equation 18)

And

[0046]

[Equation 19]

Each

[0048]

(Equation 20)

Calculated by

[0050]

(Equation 21)

When the expression ( 16) is satisfied,

[0052]

(Equation 22)

Assume that the value is valid.

[0054]

(Equation 23)

As a seventh step, assuming that the average value ψ _i exists in the section R _np , the distance d ₀ (ψ _i ) must be calculated by the equation (9-2). After updating ₁ and S ₂ with S ₁ ← S ₁ -2π S ₂ ← S ₂ -4 · π · a ₀ + (2π) ³ (17),

[0056]

(Equation 24)

And

[0058]

(Equation 25)

Is calculated,

[0060]

(Equation 26)

When the expression (18) is satisfied,

[0062]

[Equation 27]

Assume that the value of is valid.

[0064]

[Equation 28]

As an eighth stage, similar processing is performed in the section R
_For each section from _{n-p + 1} to R _n , R _{n-p + 1} , R
repeated in the order of the _{n-p + 2, R n} .

As a ninth stage, the average value ψ _i
Since the distance d _n-1 (ψ _i ) has to be calculated by equation (8-2), assuming that the distance exists at _np-2 , equation (15)
After updating S ₁ and S ₂ shown in ( ₁₎ by S ₁ ← S ₁ -2π S ₂ ← S ₂ -4 · π · an _-1 + (2π) ² (19),

[0067]

(Equation 29)

And

[0069]

[Equation 30]

Is calculated,

[0071]

(Equation 31)

It is assumed that the value of the variance is valid when the expression (20) is satisfied.

[0073]

(Equation 32)

As a tenth step, similar processing is performed in the section R
_For each section from _np-3 to _{R0, Rnp-3} , R
Repeat _np-4 , ..., _R0 in this order.

As an eleventh stage, the above is effective.
Variance with the smallest value

[0076]

[Equation 33]

Average value corresponding to

[0078]

(Equation 34)

Determining the mean value [psi _i of the neighboring angle data by the following equation using the [0079].

[0080]

(Equation 35)

As a twelfth step, ρ _i shown in the equation (7) and
Using ψ _i shown in equation (23) ,

[0082]

[Equation 36]

After smoothing

[0084]

(37)

Is obtained by the following equation.

[0086]

(38)

[0087]

Embodiments of the present invention will be described below in detail.

FIG. 1 is a block diagram showing an embodiment of a vector data smoothing apparatus of the present invention for displaying a contour shape inputted by vector data.

In FIG. 1, vector data storage means 10
Is, for example, on a contour entered using a tablet

[0090]

[Equation 39]

Are stored in the form shown in equation (1) in order along the contour.

The operation of this apparatus starts, for example, when the control means 22 activates the coordinate conversion means 23. The activated coordinate conversion means 23 is stored in the vector data storage means 10 using equation (5).

[0093]

(Equation 40)

The polar coordinate format calculated from

[0095]

[Equation 41]

Are stored in the polar coordinate vector storage means 24, and the processing is terminated.

When the coordinate conversion means 23 ends the processing, the control means 22 activates the neighborhood data extraction means 11. The activated neighborhood data extraction unit 11 uses the positive even number W (25) set in advance to extract the data extracted as the proximity radial data on the i-th vector from the contents stored in the polar coordinate vector storage unit 24. γ _{iW / 2} , γ _{iW / 2 + 1} , ..., γ _{i + w / 2} ｝ (26) and ｛θ _{iW / 2} , θ _{iW / 2 + 1} ,…, θ _{i + w / 2} ｝ (27) Is stored in the proximity radial data storage means 12 and the proximity angle data storage means 13, respectively, and the process is terminated.

When the neighborhood data extracting means 11 completes the processing, the control means 22 activates the radial average value calculating means 14, for example. The activated radial average value calculating means 14 uses the contents stored in the neighboring radial data storage means 12 to obtain the equation (7).
The [rho _i is calculated to end the storing and the processing in the radial average value storing unit 16 by.

When the radial average calculation means 14 finishes the processing, the control means 22 activates the sorting means 15. The activated sorting means 15 stores the data obtained by sorting the contents stored in the neighboring angle data storage means 13 in the ordered angle data storage means 17 in the format shown in Expression (11), and ends the processing.

When the sorting means 15 completes the processing, the control means 22 activates the angle average value calculating means 18. The activated angle average value calculation means 18 operates in the same manner as the procedure described in the sixth to twelfth steps of the principle described above, and operates the average calculated from the contents stored in the ordered angle data storage means 17.
The value ψ _i is stored in the angle average value storage means 19 and the processing is terminated.
I do.

When the angle average value calculating means 18 completes the processing, the control means 22 activates the vector synthesizing means 20.
The activated vector synthesizing means 20 is synthesized by Expression (24) using ρ _i stored in the radial average value storing means 16 and ψ _i stored in the angle average value storing means 19.

[0102]

(Equation 42)

Is output to the display means 21 to end the processing.

When the vector synthesizing means 20 finishes the processing, the control means 22 continues to start the processing group starting from the neighborhood data extracting means 11 in the same manner,

[0105]

[Equation 43]

Of

[0107]

[Equation 44]

When the is output to the display means 21, all the processes are completed.

In the above processing, the display means 21 is constituted by, for example, a CRT and the present display technology, and is inputted.

[0110]

[Equation 45]

A polygonal line drawing having a vertex position is displayed on a CRT. The vector data storage means 10, the polar coordinate vector storage means 24, the proximity radial data storage means 12, the proximity angle data storage means 13, the radial average value storage means 16, the ordered angle data storage means 17, the angle average value storage The means 19 can be composed of, for example, a memory, and the control means 22 can be composed of, for example, a CPU and a memory.

[0112]

According to the present invention described above, for example, vector data distributed on the circumference can be subjected to smoothing while preserving the curvature. Further, the angle average value calculating means 18 described in the present invention can be generally applied to an apparatus using the average value and variance of periodic data.

[Brief description of the drawings]

FIG. 1 is a block diagram showing an embodiment of a vector data smoothing device according to the present invention.

FIG. 2 is a diagram illustrating the principle of the present invention.

FIG. 3 is a diagram for explaining a conventional technique.

FIG. 4 is a diagram for explaining a conventional technique.

[Explanation of symbols]

 6 Radial average value storage means 17 Ordered angle data storage means 18 Angle average value calculation means 19 Angle average value calculation means 20 Vector synthesis means 21 Display means 22 Control means 23 Coordinate conversion means 24 Polar coordinate vector storage means

Claims (2)

(57) [Claims] 1. A mean values for the radial component group vector group present in the vicinity of the target vector and the radial component, said base
Sort the angle components of the vector group, and sort the angle components after sorting.
After dividing the polar coordinates into a plurality of angle sections from the group,
Assuming that an angle average exists in the angle section, the angle component
Calculate the angle average value that is the average value of the group, and calculate the calculated angle
A variance value corresponding to the average value is calculated, and the angle average value and the variance are calculated.
The process of determining whether the value is valid or invalid is performed for each angle section.
After repeating the above, among the plurality of effective variance values,
A vector represented by polar coordinates having an angle average value corresponding to the variance value of (i) as an angle component, as a vector obtained by smoothing the vector of interest. 2. Polar vector storage means for storing vector data in polar coordinate format, and neighborhood data extraction for extracting a radial component group and an angle component group relating to a neighborhood vector group of each output vector data of said polar vector storage means. means, the radial average value calculating means for calculating an average value of said radial component group, and sorting means for sorting the angular component groups, a plurality of each angular interval determined by the output data of said sorting means, sorting From the later angle component group, multiple polar coordinates
After dividing into angle sections, the angle average value is
Assuming that they exist, the angle plane
Calculate the average value and calculate the variance value corresponding to the calculated angle average value.
Calculate and determine whether the angle average value and variance value are valid or invalid
Is repeated for each of the angle sections,
Angle corresponding to the smallest of the valid variances of the number
Smoother vector data, characterized by comprising an angle mean value calculating means for calculating an average value.