JP2000207540A - Thinning processing method for data and data processor - Google Patents

Abstract

PROBLEM TO BE SOLVED: To compress sufficient data and to enable high speed processing by thinning original data corresponding to the size of a spatial range having the degree of change greater than a prescribed value. SOLUTION: The surface of a work 2 placed on a measuring table 1 is scanned, the displacement of that surface is contactlessly detected by a displacement detector 3 and a detecting signal is supplied to a measured value sampling part 5. On the basis of the information of a scanning position from the displacement detector 3, that measured value sampling part 5 samples signals from the displacement detector 3 as measured data at fixed intervals in XY direction within a three-dimensional measuring space. These sampled measured data are temporarily stored in a storage device 6 and the stored measured data are supplied to a signal processing part 7. The signal processing part 7 applies thinning processing to the measured data and these thinned data are stored in the storage device 6 and displayed on a display part 8 at high speed.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a data thinning method and a data processing apparatus for thinning data arranged in a two-dimensional or more space while maintaining its characteristics.

[0002]

2. Description of the Related Art When data of a measuring instrument or the like is displayed on a screen, generally, all data cannot be displayed exactly because the display capability of the screen is inferior to the number of data. Further, when a polyhedron is constructed from the obtained data point group, a huge amount of information and calculation time are consumed, and handling of huge data is a serious problem in practical use. In order to solve these problems, it is necessary to appropriately thin out data in some way.

Conventionally, as such data thinning processing, as shown in FIG. 12B, a so-called “comb thinning method” is used to thin out data at regular intervals from original data as shown in FIG. And "compression", as shown in FIG. 3C, dividing data into several blocks, and using characteristic data points (for example, points giving the maximum value / minimum value) in the blocks as representative data of the blocks. The "method" is known.

[0004]

However, among the above-described thinning processing methods, the "comb-thinning method" has a problem that it is difficult to set the thinning interval. That is, if the thinning interval is set so as to sufficiently thin the slowly changing portion, the characteristics of the rapidly changing portion will be lost. The thinning effect cannot be obtained. Similarly, in the “compression method”, it is difficult to determine how to divide a block, and the more time it takes to divide according to the fluctuation of data, the longer the processing time will be. In addition, a method that simplifies the three-dimensional mesh structure with certain rules has been proposed as a method that focuses on accurately expressing the original data, but this method also requires a lot of calculation time. Therefore, there is a problem that it is not suitable for thinning out a large amount of data.

SUMMARY OF THE INVENTION The present invention has been made in view of the above-described problems, and has been developed in view of the data which can realize an intelligent and high-speed decimation process in which a decimation rate is adaptively changed in accordance with a fluctuation state of original data. It is an object to provide a thinning processing method and a data processing device.

[0006]

According to the present invention, there is provided a data thinning processing method for thinning out original data arranged in a two-dimensional or more space.
The original data is divided stepwise from a small spatial range to a large spatial range, and the degree of change of the frequency component corresponding to each spatial range is obtained for each spatial range, and the degree of the change is larger than a predetermined value. It is characterized in that the original data is thinned out according to the size of the range.

[0007] Further, a data processing device according to the present invention comprises:
In a data processing device that performs a thinning process on original data arranged in a two-dimensional or more space, a storage unit that stores the original data, and an interval according to a degree of change from the stored original data. Data processing means for performing a thinning process, wherein the data processing means divides the original data stepwise from a small space range to a large space range, and determines a degree of change of a frequency component corresponding to each space range. The method is characterized in that a process of thinning out the original data is performed according to the size of the spatial range in which the degree of the change is larger than a predetermined value, obtained for each spatial range.

According to the present invention, the frequency components corresponding to each spatial range (spatially and frequency-independent spatial ranges) when the original data is divided stepwise from a small spatial range to a large spatial range. Since the degree of change is obtained for each space range, the degree of change in a small space range increases in a portion where the change is sharp, and the degree of change in a large space range increases in a portion where the change is gentle. Then, since the process of thinning out the original data is performed in accordance with the size of the spatial range in which the degree of change is larger than a predetermined value, the thinning interval becomes small in a portion where the change is sharp, and in a portion where the change is gradual, , The thinning interval increases. For this reason, the thinning-out interval is adaptively changed in accordance with the change state of the original data, and sufficient data compression can be performed without losing a characteristic portion, and high-speed processing can be performed.

[0009] More specifically, the present invention uses a basis function that is spatially and frequency-adapted to each spatial range when the original data is divided stepwise from a small spatial range to a large spatial range. Then, the original data is decomposed into a sequence corresponding to each spatial range, and among the elements of the obtained decomposition sequence, the elements whose absolute values are smaller than a predetermined threshold value are made zero, and then each of the obtained decomposition sequences is By performing weighting according to the degree of overlap of the space range in correspondence with the original data based on the element and executing processing for extracting only the original data having a non-zero weight, higher-speed processing can be performed.

[0010]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Preferred embodiments of the present invention will be described below with reference to the drawings. FIG. 1 is a block diagram showing a main configuration of a surface texture measuring apparatus to which a data thinning processing method according to an embodiment of the present invention is applied. The surface texture measuring device includes a displacement detector 3 that scans the surface of a work 2 placed on a measurement table 1 and detects a displacement of the surface in a non-contact manner. The drive device 4 controls the drive so that the displacement detector 3 scans within a predetermined measurement range of the work 2. The displacement signal output from the displacement detector 3 is a measured value sampling unit 5
Supplied to The measurement value sampling unit 5 receives a predetermined interval, for example, from the displacement detector 3 at regular intervals in the XY directions in the three-dimensional measurement space based on the information on the scanning position of the displacement detector 3 supplied from the driving device 4. Is sampled as measurement data. The sampled measurement data is temporarily stored in the storage device 6. The stored measurement data is supplied to the signal processing unit 7 at an appropriate timing. The signal processing unit 7 performs a thinning process on the original data in order to perform data compression for displaying the measurement data (original data). The data thinned out by the signal processing unit 7 is stored in the storage device 6 and further displayed on the display unit 8 at high speed. The operation unit 9 is used to input parameters required for the thinning process in the signal processing unit 7.

Next, the principle of the thinning process in the surface texture measuring device thus configured will be described. In order to thin out slowly changing portions at large intervals and to cut out strongly changing portions at small intervals, it is necessary to know at what position and at what frequency the data fluctuates.
The simplest way to capture such local fluctuations is to take the difference between two adjacent data. If the absolute value of this difference is large, it means that there is a large variation between data. At this time,
By replacing the two data for obtaining the difference with the average value of the neighboring data, it is possible to obtain a fluctuation component corresponding to the number of data whose average has been obtained. As described above, when the local average of data and its difference are sequentially obtained, it is possible to know which position contains which fluctuation component, and it is possible to determine a thinning interval in accordance with data fluctuation.

FIG. 2 shows a specific example. In the figure, the top row is the original data string, and the level of averaging increases as it goes below the inverted pyramid structure shown below. Numerical values in the second and subsequent frames indicate “average / difference”, and a half of the size of the frame with the largest difference indicated by hatching is used as the thinning interval at that position. Based on the above concept, it is possible to determine the thinning interval according to the degree of data fluctuation. This process is based on Wavele using Har Wavelet.
It has the same meaning as the t-transform, and the Wavelet transform can be used to describe a more general-purpose intelligent thinning process.

In the Wavelet transform, a spatially and frequency-localized M that satisfies the following condition that the average is zero:
Consider other wavelet w (x).

[0014]

(Equation 1)

In order to find a gradual change (low frequency component) from the measurement data z (x), the measurement must be performed over a long distance. In such a case, as shown in FIG. 3, the Mother Wavelet is expanded by a times on the spatial axis to obtain a basis function. Conversely, when a sudden change (high-frequency component) is to be found, the Mother Wavelet must be expanded. It is reduced to 1 / a to be a basis function. Further, in order to find the position where the fluctuation occurs, the basis function is created by translating by b on the spatial axis. The basis function obtained in this way is

[0016]

(Equation 2)

Is given by W using this basis function
The avelet transform is

[0018]

(Equation 3)

And the inner product of the basis function and the original data. As shown in FIG. 4, when a sine wave signal is viewed through windows having different widths, it is well known that as the window becomes narrower, the periodicity of the signal is lost and the frequency distribution becomes wider. Generally, the data is located at some location x along the spatial axis.
Occupies a region of Δx. Then, the Fourier transform occupies a region of Δω around an angular frequency ω along the frequency axis. As can be seen from the description of FIG. 4, if the window is reduced to reduce Δx, the spread of the angular frequency Δω increases, and if Δω is reduced, Δx increases. In this way, the following uncertainty holds between Δx and Δω.

[0020]

(Equation 4)

Due to the uncertainty relation, the signal has a final unit, and a lot of information is duplicated in the continuous Walevelet conversion of the equation (3). If two points (a ₁ , b ₁ ) and (a ₂ , b ₂ ) are included in the same minimum unit, W (a ₁ , b ₁ ) and W (a ₁ , b ₁ )
(a ₂ , b ₂ ) are not independent quantities. Therefore, it suffices to obtain W (a, b) for a set of points (a, b) that do not belong to the same minimum unit. This can be achieved by discretizing the coordinates (a, b) as shown in Expression 5.

[0022]

[Equation 5] (a, b) = (2− ^j , 2− ^j k) (where j and k are integers)

Discrete Wavelet Based on Discretized Coordinates
Transform / inverse transform is defined as in Equation 6.

[0024]

(Equation 6)

In the discrete wavelet transform,

[0026]

(Equation 7)

Then,

[0028]

(Equation 8)

Is obtained. This is because f _j (x) is g _j-1 (x) and f _j (x)
_j-1 (x). In the decomposition process, g _j-1 (x) and f _j-1 (x) are respectively f _j (x)
Are high frequency components and low frequency components. here,

[0030]

(Equation 9)

A scaling function φ (x) that satisfies the two-scale relation defined by By introducing a scaling function φ (x), Mother Wavelet
To

[0032]

(Equation 10)

It can be defined as Where {q _k }
Is a sequence determined by the two-scale relation. function
When f ₁ (x) is represented by a scaling function φ (x),

[0034]

[Equation 11]

## EQU1 ## From these relationships, c _k ^(j-1) , d _k
^(j-1) can be obtained using c _k ^(j).
Is obtained.

[0036]

(Equation 12)

Here, c _k ^(j-1) and d _k ^(j-1) are the outputs of the low-pass filter and the high-pass filter, respectively. Is formed. Where {g _k } and {h _k } are both
This is a decomposition sequence determined by the scale relation.

Conversely, the process of obtaining c _k ^(j) from c _k ^(j-1) and d _k ^(j-1) is called a reconstruction algorithm.
Can be expressed as

[0039]

(Equation 13)

Finally, there remains processing for determining c _k ^(0), which is the start of decomposition, from the signal f (x). However, in practice, there is no problem assuming that the measured data sequence is {c _k ⁽⁰⁾ }. .

The Haar Wavelet is the simplest Mother Wavelet in the form shown in FIG. Haar Wavelet
The decomposition algorithm when using is

[0042]

[Equation 14]

The reconstruction algorithm is given by

[0044]

(Equation 15)

Is given by

FIG. 7 shows the position / frequency space occupied by each element of the decomposition sequence obtained by decomposing the measurement data using the decomposition algorithm of the Wavelet transform. From this figure, it can be seen that each decomposition sequence has information on a specific position and frequency range. Therefore, weighting is performed such that the absolute value of the decomposition sequence is added to the representative position of the data in the range corresponding to each decomposition sequence. Here, since the value of the decomposition sequence corresponds to the amplitude of data fluctuation in the frequency range to which the decomposition sequence belongs, the magnitude of the amplitude to be detected is given as a threshold value λ, and the value of the decomposition sequence below this value is set to zero. In other words, λ
The weight of data characterized by the following amplitude fluctuations becomes zero. Further, if the same processing is performed with the decomposition sequence in a range corresponding to the frequency range of the data fluctuation not to be detected being set to zero, the function of a kind of filter can be added to the thinning processing.

In the thinned data sequence obtained as a result of such processing, a gently fluctuating portion is arranged at large intervals, and a severely fluctuating portion is arranged at small intervals. Also, Wa
Choosing Haar Wavelet as the Mother Wavelet for the velet transform will greatly reduce the amount of computation and allow for very fast processing. Of course, other Waves as Mother Wavelet
Wavelet can also be used, so you can make a selection according to your purpose. Two-dimensional processing can be realized in exactly the same way.

As for the method of adding the data in the range corresponding to each decomposition sequence to the representative position, for example, assuming that the leading data of the spatial range to which the decomposition sequence belongs is the representative position, as shown in FIG. Weight can be obtained.
In this figure, w _k is the weight of the k-th data, and can be obtained by adding the sum of the absolute values of the decomposition sequence indicated by ● in the direction of →.

FIG. 9 shows a simple specific example of the procedure of the intelligent thinning process described above. The measurement data is the same as the data in FIG. 2 described above. Wavelet transform the measured data to obtain a decomposition sequence. Next, the decomposition sequence whose absolute value is equal to or smaller than the threshold λ (here, λ = 0.2) is set to zero. At this time, if necessary, the processing may be performed only in the designated frequency range. Next, the measurement data is weighted using the decomposition sequence. Then, measurement data having a weight other than zero is extracted. As a result of the above processing, the same thinning processing as shown in FIG. 2 is performed.

FIG. 10 is a diagram showing an example in which the above-described intelligent thinning processing is performed on two-dimensional original data. The source data for this example is

[0051]

(Equation 16)

In the figure, (a) shows the original data (the number of data
( _x = 512), and FIG. 7B shows the number of data n _{x with} λ = 0.01.
= Example thinned out to 46, the (c) shows an example in which thinned out until the data number n _x = 17 as lambda = 0.05, respectively. As is apparent from this example, even if the data is thinned out until the number of data becomes 17, the characteristics of the original data are hardly lost.

FIG. 11 is a diagram showing an example in which the above-described intelligent thinning process is performed on three-dimensional original data. The source data for this example is

[0054]

[Equation 17]

In the figure, the upper left is the original data (the number of data n _x
× _ny = 512 × 512), the upper right is a contour map thinned out with λ = 0.001, the lower left is the same mesh structure, the lower right is λ = 0.00
1 data point, the number of data after thinning is 179
3, which is 0.689% of the original data. Thus, even if the above method is extended to three-dimensional data,
A sufficient effect could be confirmed.

[0056]

As described above, according to the present invention,
The thinning interval is adaptively changed in accordance with the fluctuation state of the original data, so that it is possible to sufficiently compress data without losing a characteristic portion and to perform high-speed processing.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a schematic configuration of a surface texture measuring device according to one embodiment of the present invention.

FIG. 2 is a diagram for explaining the principle of thinning processing in the same device.

FIG. 3 is a diagram showing an example of a basis function used for the same processing.

FIG. 4 is a diagram for explaining a relationship between a window of a sine wave function and a spectrum.

FIG. 5 is a diagram showing a filter bank in a decomposition algorithm used in the thinning processing.

FIG. 6 is a diagram showing another example of a basis function used in the same processing.

FIG. 7 is a diagram showing a spatial and frequency arrangement occupied by each element of a decomposition sequence obtained by the same processing.

FIG. 8 is a diagram for explaining a method of calculating data weight from each element of the decomposition sequence.

FIG. 9 is a diagram showing a specific example of the processing.

FIG. 10 is a diagram showing an example in which the same processing is applied to two-dimensional data.

FIG. 11 is a diagram showing an example in which the same processing is applied to three-dimensional data.

FIG. 12 is a diagram for explaining a conventional thinning processing method.

[Explanation of symbols]

1. Measurement table, 2. Workpiece, 3. Displacement detector, 4.
Drive device, 5: measurement value sampling unit, 6: storage device,
7: signal processing unit, 8: display unit, 9: operation unit.

 ────────────────────────────────────────────────── ─── Continued on the front page F term (reference) 5B057 CA12 CA16 CB12 CB16 CD07 CE06 CE09 CE20 CH11 5C076 AA22 AA36 BA03 BA06 BB06 BB13

Claims (4)

[Claims] 1. A data thinning processing method for thinning out original data arranged in a two-dimensional or more space, wherein said original data is divided stepwise from a small space range to a large space range, Determining the degree of change of the corresponding frequency component for each spatial range, and thinning out the original data according to the size of the spatial range in which the degree of change is greater than a predetermined value. Processing method. 2. A data thinning method for thinning out original data arranged in a two-dimensional or more space, wherein each of the spatial ranges when the original data is divided stepwise from a small spatial range to a large spatial range The original data is decomposed into a sequence corresponding to each of the spatial ranges using a basis function spatially and frequency-wise, and an absolute value of each element of the obtained decomposition sequence is smaller than a predetermined threshold value. After reducing the small elements to zero, weighting is performed according to the degree of overlap of the spatial range in correspondence with the original data based on each element of the obtained decomposition sequence, and only the original data having a weight other than zero is extracted. A data thinning processing method characterized by the following. 3. A data processing apparatus for performing a thinning process on original data arranged in a two-dimensional or more space, a storage unit for storing the original data, and a degree of change from the stored original data. Data processing means for performing thinning-out processing at intervals according to the data processing means, wherein the data processing means divides the original data stepwise from a small spatial range to a large spatial range, and a frequency component corresponding to each spatial range. A data processing apparatus for obtaining a degree of change for each spatial range, and executing a process of thinning out the original data according to the size of the spatial range in which the degree of change is larger than a predetermined value. . 4. A data processing apparatus for performing a thinning process on original data arranged in a two-dimensional or more space, a storage unit for storing the original data, and a degree of change from the stored original data. Data processing means for performing decimation processing at intervals according to the data processing means, the data processing means spatially and frequency into each spatial range when the original data is divided stepwise from a small spatial range to a large spatial range The original data is decomposed into a sequence corresponding to each of the spatial ranges using a basis function that is optimally matched, and an element whose absolute value is smaller than a predetermined threshold value among elements of the obtained decomposition sequence is reduced to zero. After doing
Based on each element of the obtained decomposition sequence, weighting is performed in accordance with the degree of overlap of the spatial range in correspondence with the original data, and a process of extracting only non-zero original data is performed. Characteristic data processing device.