JP2007024502A - Data processing apparatus, method, and program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a data processing apparatus which can filter measured data which represents an unequality in intervals between measurement points. <P>SOLUTION: For a measured data group in which coordinate information of the measurement points distributed discretely and unequally and a measured value at each measurement point are combined, the data processing apparatus 10 for filtering the measured values on the coordinate space of the measurement points. The data processing apparatus comprises a filter coefficient determination means 20 which determines, for one measured value which is filtered, the positional relationship between the measurement point of the one measured value and each measurement point of the measured data group from the coordinate information and calculates each filter coefficient corresponding to each measurement point of the measured data group on the basis of the positional relationship and a processing means 22 which obtains a value which has been filtered for the one measured value on the basis of each measured value of the measured data group and each filter coefficient calculated by the filter coefficient determination means. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a data processing apparatus, and more particularly to an improvement of a filter processing mechanism for unequal interval data.

The surface texture measuring machine such as a three-dimensional measuring machine moves the measuring element for detecting displacement information on the surface of the object to be measured relative to the object to be measured, and the surface of the object to be measured based on the position information of the measuring element. The shape is measured. For example, in roundness measurement, the object to be measured is rotated or the probe is rotated around the object to be measured, and the position information of the probe in the radial direction is acquired at regular sampling time intervals. In this way, a measurement data group is obtained by combining the coordinates of measurement points distributed in a discrete manner (angle coordinates with the center of the object to be measured as an axis) and the measurement values (displacement values in the radial direction) at each measurement point. Become. Various types of filter processing may be performed on such a measurement data group for the purpose of removing disturbance components such as noise (see, for example, Patent Documents 1 and 2).
Japanese Unexamined Patent Publication No. 2000-161983 JP 2004-333293 A

When the above spatial digital filter processing is performed, the measurement points of the measurement data group to be processed must be distributed at equal intervals in the coordinate space. For example, in the above example of roundness measurement, the interval between adjacent measurement points, that is, the difference in angular coordinates between adjacent measurement points needs to be constant for any adjacent measurement point. However, even if the measurement data group is acquired at a constant sampling time interval, the data does not necessarily have data having measurement points at equal intervals. For example, in the case of the roundness measurement described above, the interval (angle) between adjacent measurement points is subject to fluctuations due to fluctuations in the rotational speed of the object to be measured or the measuring element, or a part of the object to be measured is cut. A part of the region is lost due to a notch or a groove, and there is no measurement data in the part (no measurement point exists).
Conventionally, when performing filtering processing on such unequal interval data, the measurement points of the measurement data group are artificially equally spaced in advance by an interpolation method such as linear interpolation or spline interpolation, and the filtering processing is performed on it. I was taking the way. However, unintentional information is added to the measurement data group by this interpolation processing, and there is a big problem in terms of reliability of the processed data.
The present invention has been made in view of the above problems, and an object of the present invention is to provide a data processing apparatus capable of performing filter processing on measurement data at unequal intervals where the intervals between measurement points are not constant. .

  In order to achieve the above object, the data processing apparatus of the present invention is a measurement data group in which coordinate information of measurement points distributed discretely and at irregular intervals and measurement values at each measurement point are combined. A data processing apparatus for performing a filtering process on the measurement value in a coordinate space of a measurement point, and for each measurement value to be filtered, each measurement point of the one measurement value and each of the measurement data group Filter coefficient determining means for calculating each filter coefficient corresponding to each measurement point of the measurement data group based on each position relation, and obtaining each positional relation between the measurement points from the coordinate information; and the measurement data group And processing means for obtaining a filtered value for the one measured value based on each measured value and each filter coefficient calculated by the filter coefficient determining means.

  In the above data processing device, the filter coefficient determining means is configured to determine the measurement point of the one measurement value based on the coordinate information of the measurement point of the one measurement value and the coordinate information of each measurement point of the measurement data group. A distance calculation unit that calculates each distance between each measurement point of the measurement data group, and a coefficient calculation that calculates a filter coefficient corresponding to each measurement point of the measurement data group based on each distance calculated by the distance calculation unit It is suitable to provide a part.

In the data processing apparatus, the processing means corresponds to a coefficient summation unit for obtaining a total value of filter coefficients calculated by the filter coefficient determination means, a measurement value of the measurement data group, and a measurement point of the measurement value. A multiplication value summation unit that multiplies the filter coefficients and sums the multiplications over the respective measurement values of the measurement data group, and a summation value calculated by the multiplication value summation part is calculated by the coefficient summation unit. It is preferable that a division unit that obtains a filtered value for the one measured value by dividing by a total value of filter coefficients is provided.
In the above data processing apparatus, it is preferable that the filter coefficient determination means sets the filter coefficient to 0 when the distance between the measurement points is a predetermined value or more.

  Further, the data processing method of the present invention provides a coordinate space of measurement points with respect to a measurement data group in which coordinate information of measurement points distributed discretely and at irregular intervals and measurement values at each measurement point are paired. A data processing method for performing a filtering process on the measurement value above, wherein for one measurement value to be filtered, between the measurement point of the one measurement value and each measurement point of the measurement data group A filter coefficient determination step for calculating each filter coefficient corresponding to each measurement point of the measurement data group based on each position relation, and each measurement value of the measurement data group; And a processing step of obtaining a filtered value for the one measured value based on each filter coefficient calculated in the filter coefficient determination step.

  Further, the data processing program of the present invention provides a coordinate space of measurement points with respect to a measurement data group in which coordinate information of measurement points distributed discretely and at irregular intervals and measurement values at each measurement point are paired. A data processing apparatus that performs filtering on the measured values is configured by a computer, and for one measured value that is the target of the filtering process, a measurement point of the one measured value and each measured point of the measured data group A filter coefficient determination step for calculating each filter coefficient corresponding to each measurement point of the measurement data group based on each position relation, and each measurement of the measurement data group And a processing step of obtaining a filtered value for the one measured value based on the value and each filter coefficient calculated in the filter coefficient determination step.

  According to the data processing apparatus and method of the present invention, the positional relationship between the measurement point and each measurement point of the measurement data group is obtained for one measurement value to be filtered, and the positional relationship is obtained. Since the filter coefficient is determined based on the filter coefficient, the filter processing is performed while maintaining the position information of the measurement points with respect to the measurement data group in which the measurement point intervals are unequal intervals, that is, the unequal interval data. It became possible.

The data processing apparatus of the present invention provides a measurement data group in which coordinate information of measurement points distributed discretely and at irregular intervals and measurement values on each measurement point are paired on the coordinate space of the measurement points. In the following, a preferred embodiment of the present invention will be described with reference to the drawings.
FIG. 1 is a schematic configuration diagram of a data processing apparatus according to an embodiment of the present invention. The data processing device 10 is configured by a computer or the like, and executes processing of a measurement data group sent from the measurement system 12 as a program. In the present embodiment, description will be made assuming that a three-dimensional measuring machine is used as the measurement system 12. However, the data processing apparatus 10 of the present invention is not limited to the measurement data from the three-dimensional measuring machine, and other surface property measurement. Filter processing can be suitably performed even on nonuniformly spaced measurement data groups measured by the apparatus or other measurement apparatuses.

  The measuring system 12 includes a measuring element 14 that scans the surface of the object to be measured, a moving unit 16 that moves the measuring element 14 three-dimensionally, and a detecting unit 18 that detects position information of the measuring element 14. The moving unit 16 moves the measuring element 14 on the surface of the object to be measured at a predetermined speed, and the detecting unit 18 acquires position information of the measuring element 14 at predetermined sampling time intervals. As a result, a measurement data group is obtained in which the coordinate information of the measurement points distributed discretely and the measurement values at each measurement point are combined. For example, when the measuring element 14 is scanned in the X direction (the position in the Y direction is fixed) and the XY plane cross-sectional shape of the object to be measured is measured, the value of the X coordinate of the measuring element 14 at each sampling point is set to the measurement point. The coordinate information and the value of the Z coordinate are handled as measurement values at each measurement point. Similarly, in the case of roundness measurement by scanning measurement (that is, when the probe 14 is scanned over the circumference of the object to be measured and position information of the probe is detected at a predetermined sampling time interval), at each sampling point The angle position of the measuring element 14 (the least square circle of the object to be measured or an angle with the center of the circle determined by another method as an axis) is treated as coordinate information, and the position information in the radial direction is treated as a measured value. When the probe is scanned in the two-dimensional direction (XY direction) as in the case of measuring the surface roughness, the XY coordinate of the probe at each sampling point is the coordinate information of the measurement point, and at each sampling point. The position of the measuring element in the Z direction may be handled as a measured value.

FIG. 2 is a schematic diagram showing the positional relationship of measurement points when the coordinate space of the measurement points is one-dimensional. In the above example, this corresponds to the case of measuring the XY plane cross-sectional shape of the object to be measured by scanning the measuring element 14 in the X direction or the case of measuring the roundness. Note that the coordinate space is a space provided by coordinate value parameters for designating the position of the measurement point, and the number of coordinate value parameters independent of the dimension of the coordinate space. Assuming that the measured object has no missing part and is ideally controlled so that the moving speed of the probe and the sampling time interval are constant, it is included in the measurement data group as shown in FIG. The measurement points (in the figure, the coordinate values are indicated by P (1) to P (n)) are arranged at equal intervals. That is, the difference ΔX ₁ between the coordinates P (2) and P (1), the difference ΔX ₂ between P (3) and P (2),..., The difference ΔX _m between P (m) and P (m + 1) is Each becomes equal (ΔX ₁ = ΔX ₂ =... = ΔX _m =... = Constant).

However, in actual measurement, the measurement points of the obtained measurement data group are not distributed at regular intervals as described above due to reasons such as fluctuations in the moving speed of the probe and the presence of missing portions of the object to be measured. That is, as shown in FIG. 2B, the difference ΔX ₁ between coordinates P (2) and P (1), the difference ΔX ₂ between P (3) and P (2),..., P (m) and P (m + 1) the difference [Delta] X _m, etc. are not all equal to each other (i.e., at least one, different exists), the measurement points will be distributed at uneven intervals.
Similarly, FIG. 3 shows a schematic diagram showing the positional relationship of measurement points when the coordinate space of the measurement points is two-dimensional. This corresponds to a case where the measuring element is scanned in the XY direction (horizontal direction), position information in the Z direction (height direction) is acquired, and the surface shape of the object to be measured is measured. Assuming an ideal state, as shown in FIG. 3A, the measurement points should be aligned on the lattice points, and the intervals between adjacent measurement points should be equal. However, in actual measurement, as shown in FIG. 3B, the measurement points are not necessarily aligned on the grid points, and the intervals between adjacent measurement points are different.

  Thus, the measurement data group that is generally obtained is one in which measurement points are distributed at unequal intervals. There is a case where it is desired to apply spatial filtering to such a measurement data group for the purpose of noise removal or the like, but the conventional filter processing is based on the assumption that the measurement points of the measurement data group are arranged at equal intervals. .

  Unlike the conventional spatial filter, the data processing apparatus according to the present embodiment enables the filtering process for the unequal interval data as described above. Therefore, the data processing apparatus 10 in FIG. 1 includes a filter coefficient determination unit 20 that determines filter coefficients corresponding to measurement points distributed at unequal intervals, each measurement value of the measurement data group, and each filter coefficient described above. And processing means 22 for performing filtering processing based on the above. Here, it is preferable that the data processing apparatus 10 is configured by a computer and incorporates a program that functions as the filter coefficient determination means 20 and the processing means 22. A measurement data group from the measurement system 12 is stored in the measurement data storage unit 36 of the storage unit 24 of the data processing apparatus 10 in association with each measurement value and coordinate information of the measurement point. Then, at least a measurement value to be subjected to filter processing in the measurement data group is subjected to filter processing on the coordinate space as follows. The value after the filter processing is stored in the processing data storage unit 38 of the storage unit 24 in association with the coordinate information of the measurement point.

The filter coefficient determination unit 20 determines the positional relationship between the measurement point and each measurement point of the measurement data group for one measurement value to be filtered from the coordinate information stored in the measurement data storage unit 36. The filter coefficient corresponding to each measurement point of the measurement data group is calculated based on this positional relationship (see FIG. 4). First, the distance calculation unit 26 of the filter coefficient determination unit 20 reads the coordinate information of each measurement point stored in the measurement data storage unit 36, and the measurement point of one measurement value to be filtered (FIG. 4A). P (i)) and each measurement point of the measurement data group (P (4), P (i-1), P (i), P (i + 1), P (i + 1) in FIG. 4A). ) Etc.) in the coordinate space (X4 _{, i} , Xi _{-1, i} , Xi _{, i} (= 0), Xi _{+ 1, i} , Xi _{+ 2, in FIG. i} )). Note that the above-mentioned “each measurement point of the measurement data group” includes a measurement point of one measurement value to be filtered. Next, in the coefficient calculation unit 28, each filter coefficient corresponding to each measurement point of the measurement data group (K _{4, i} , K _{i−1, i} , K _{i, i} , K _{i + 1, i} , K _{i + 2, i} etc.) is calculated based on each distance calculated by the distance calculation unit 26. Each filter coefficient thus obtained is stored in the coefficient storage unit 40 of the storage unit 24 in association with the corresponding measurement point. Here, the case where only the distance between the measurement points is considered in order to determine the filter coefficient is shown. However, in order to obtain a desired filter characteristic, the direction between the measurement points may be taken into consideration. Good (see FIG. 4B). Furthermore, it is also preferable to set the filter coefficient to 0 when the distance measured from the measurement point of the measurement value to be filtered is a certain value or more. Thereby, calculation time can be shortened.

The processing means 22 obtains a filtered value for the one measured value based on each filter coefficient determined as described above and each measured value of the measurement data group. That is, the coefficient summation unit 30 of the processing means 22 reads out the filter coefficients corresponding to each measurement point of the measurement data group stored in the coefficient storage section 40, obtains the sum, and stores it in the coefficient total value storage section 42 of the storage means 24. Remember. The multiplication value summation unit 32 reads out each filter coefficient from the coefficient storage unit 40 and reads out a measurement value at a measurement point corresponding to each filter coefficient from the measurement data storage unit 36. Then, the read filter coefficient is multiplied by the measured value, and the multiplied result is totaled over each measurement point of the measurement data group. The multiplication total value is stored in the multiplication total value storage unit 44 of the storage unit 24. The division unit 34 reads the coefficient total value and the multiplication total value from the coefficient total value storage unit 42 and the multiplication total value storage unit 44, and divides the multiplication total value by the coefficient total value, thereby filtering the one measurement value. Find the processed value. The obtained filtered value is stored in the processing data storage unit 38 of the storage unit 24 in association with the coordinate information of the measurement point. The above process is performed for all the measurement values to be filtered. In addition, after dividing each filter coefficient by the coefficient total value first, the value after filtering may be obtained by multiplying each measured value by each value and taking the sum.
Further, the data processing apparatus 10 includes a display means 46 constituted by a display and the like, and an input means 48 such as a mouse and a keyboard, and displays measurement data groups before and after the filtering process, and filter conditions. Settings can be made.

FIG. 5 shows the flow of the data processing process. Here, the number of measurement values in the measurement data group is N, the position coordinate of the measurement point is P (m), and the measurement value at the measurement point is D (m) (where m = 1 to N). To do.
In the filter coefficient determination step, the filter coefficient is calculated based on the coordinate information of the measurement points of the measurement data group for one measurement value to be filtered. For example, when the first measurement value D (1) is the target of the filter processing, the position between the measurement point P (1) and each measurement point P (m) (m = 1 to N) of the measurement data group. Find the relationship (distance, etc.). Then, each filter coefficient K _1m is calculated based on the calculated positional relationship. Each filter coefficient K _1m is determined by a function K [P (m), P (1)] having the measurement point P (1) of the measurement value to be filtered and each measurement point P (m) as variables. Become. That is, each filter coefficient K _1m is obtained as a function of the distance and / or direction from the measurement point P (1) to the measurement point P (m). Since the characteristics of the filter processing are determined by the function form of the function K [P (m), P (1)], it is preferable that the function form be selected according to the purpose of data processing. The calculation of the filter coefficient from the positional relationship may be programmed to calculate the above function, or may be stored in the storage means as a table in which the positional relationship and the filter coefficient are associated with each other.

また、各測定値Ｄ（ｍ）に対応したフィルタ係数Ｋ_１ｍを乗算し、これを各測定点に渡って合計した和Ｓ_１を求める。つまり、和Ｓ_１は次の式で表される。

このようにして求めた和Ｓ_１を和ＳＫ_１で除算することで、フィルタ処理後の測定値Ｄ（１）’が次のように求められる。

Next, in the processing step, based on each filter coefficient K _1m calculated above and each measurement value D (m) (m = 1 to N) of the measurement data group, the measurement value D (1) to be filtered is obtained. Filter processing is performed on the image. Therefore, first, the filter coefficient K _1m = K [P (m), P (1)] corresponding to the measurement point position P (m) of each measured value is passed over each measurement point (that is, m is set to m). from 1 to N) the sum SK _1, which is the sum. That is, the sum SK ₁ is expressed by the following equation.

Further, the filter coefficient K _1m corresponding to each measurement value D (m) is multiplied, and a sum S ₁ obtained by summing the filter coefficient K _1m over each measurement point is obtained. That is, the sum S ₁ is expressed by the following equation.

By dividing the sum S ₁ obtained in this way by the sum SK ₁ , the measured value D (1) ′ after filtering is obtained as follows.

  Then, the same processing is performed on the other measurement values D (2), D (3),..., D (N) to perform all (or filter processing) included in the measurement data group. The filtering process is complete for some of the measurements. The filter processing result obtained in this way is output to a display means or the like. In addition, when obtaining the filter coefficient corresponding to each measurement point, it is not always necessary to obtain all the measurement values. For example, the filter coefficient is only obtained at a measurement point within a predetermined distance from the measurement position of the measurement value to be filtered. It may be determined (that is, the filter coefficient at a measurement point equal to or greater than a predetermined distance is set to 0).

  Next, some examples in which simulation is performed using the apparatus according to the above embodiment will be described. Here, it is assumed that the roundness measurement is performed, that is, the case where the filter processing is performed on the measurement data group obtained by measuring the radius of the object to be measured at a plurality of angular positions. The angular positions serving as measurement points are unevenly spaced due to fluctuations in the relative speed of the probe with respect to the object to be measured. Therefore, in order to obtain measurement data (number of data: 200) at unequal intervals, the position coordinates P (n) (n = 1 to 200) of the measurement points are uniformly uniform over the entire circumference from −π to π. It was given by random numbers generated under the condition of distribution. In addition, the measurement value D (n) (n = 1 to 200) at each measurement point was given by a random number generated under the condition that the variance is 1 and the distribution is normal. FIG. 6 shows a graph of unequal interval data generated under the above conditions. FIG. 6A shows a graph of orthogonal coordinate display (the horizontal axis shows the coordinates (angular position) of the measurement point, and the vertical axis shows the measured value (displacement in the radial direction)), and FIG. 6B shows the polar coordinates. The graph of the display is shown. However, in FIG. 6B, an offset having a radius of 10 is added to the measured value D in order to display polar coordinates.

ここで定数filter_Kは、

とした。図７に数４のガウス関数のグラフを示す（ただし、グラフの最大値が１となるように縦軸のスケールを調整した）。上記数４で示したガウス関数をフィルタ係数決定関数として使用しているため、本実施例のフィルタ処理はガウシアンフィルタの特性を持つ。 <Example 1>
As a function for determining a filter coefficient (hereinafter referred to as a filter coefficient determination function), a Gaussian function represented by the following equation using a distance X between measurement points as a variable was used.

Where the constant filter_K is

It was. FIG. 7 shows a graph of the Gaussian function of Equation 4 (however, the vertical scale was adjusted so that the maximum value of the graph was 1). Since the Gaussian function expressed by the above equation 4 is used as the filter coefficient determination function, the filter processing of this embodiment has the characteristics of a Gaussian filter.

ここで、ＳＫ_ｎは

である。 The filter coefficient K _nm is expressed as K _nm = K (|| P (m) −P (n) ||) using K (X) of the above equation 4. However, || P (m) −P (n) || is the distance between P (m) and P (n), that is, min {| P (m) −P (n) |, 2π− | P ( m) −P (n) |}. Here, | · | is an absolute value, and min {·} is a small value of | P (m) −P (n) | and (2π− | P (m) −P (n) |). Represents. Then, the filtered value D (n) ′ at the measurement position P (n) is expressed by the following equation.

Where SK _n is

It is.

  The above filtering process was performed at all measurement points from n = 1 to 200. The results are shown in FIGS. FIG. 8 is a graph represented by orthogonal coordinate display (the horizontal axis is the coordinate (angular position) of the measurement point, the vertical axis is the measured value (displacement in the radial direction)), and FIG. 9 is a graph represented by polar coordinate display. In FIG. 9, an offset with a radius of 10 is added to display polar coordinates. FIGS. 8A and 9A show data before the filtering process, and FIGS. 8B and 9B show data after the filtering process.

ここで、ＡＢＳ（Ｘ）はＸの絶対値を求める関数、また定数filter_Kは

とした。図１０に数８の指数型関数のグラフを示す（ただし、グラフの最大値が１となるように縦軸のスケールを調整した）。実施例２では上記の指数型関数をフィルタ係数決定関数として使用しているので、時定数＝filter_Kのローパスフィルターの特性を持つこととなる。 <Example 2>
Next, filter processing using an exponential function expressed by the following equation as a filter coefficient determination function was performed.

Here, ABS (X) is a function for obtaining the absolute value of X, and the constant filter_K is

It was. FIG. 10 shows a graph of the exponential function of Equation 8 (however, the vertical scale was adjusted so that the maximum value of the graph was 1). In the second embodiment, since the above exponential function is used as the filter coefficient determination function, it has the characteristics of a low-pass filter with a time constant = filter_K.

The filter coefficient K _nm = K (|| P (m) −P (n) ||) is obtained in the same manner as in the first embodiment using K (X) of Equation 8, and the filter coefficient K _nm is used for the implementation. As in Example 1, all the measured values from n = 1 to 200 were filtered. The results are shown in FIGS. 11 is a graph represented by orthogonal coordinate display (the horizontal axis is the coordinate (angular position) of the measurement point, the vertical axis is the measured value (displacement in the radial direction)), and FIG. 12 is a graph represented by the polar coordinate display. In FIG. 12, an offset having a radius of 10 is added for polar coordinate display. Further, FIGS. 11A and 12A are data before filtering, and FIGS. 11B and 12B are data after filtering.

ここで、ＡＢＳ（Ｘ）はＸの絶対値を求める関数、また定数filter_Kは

とした。図１３に数１０の矩形関数のグラフを示す（ただし、縦軸のスケールをグラフの最大値が１となるよう調整した）。実施例３では上記の矩形関数をフィルタ係数決定関数として使用しているので、区間＝２・filter_Kの移動平均フィルタの特性を持つことになる。 <Example 3>
Filter processing was performed using a rectangular function represented by the following equation as a filter coefficient determination function.

Here, ABS (X) is a function for obtaining the absolute value of X, and the constant filter_K is

It was. FIG. 13 shows a graph of the rectangular function of Formula 10 (however, the scale of the vertical axis is adjusted so that the maximum value of the graph is 1). In the third embodiment, the above-described rectangular function is used as the filter coefficient determination function, so that the moving average filter characteristic of section = 2 · filter_K is obtained.

The filter coefficient K _nm = K (|| P (m) −P (n) ||) is obtained using K (X) of Formula 10 in the same manner as in the first embodiment, and this filter coefficient K _nm is used. Filtering was performed on all measured values from n = 1 to 200. The results are shown in FIGS. FIG. 14 is a graph represented by orthogonal coordinate display (the horizontal axis is the coordinate (angular position) of the measurement point, the vertical axis is the measured value (displacement in the radial direction)), and FIG. 15 is a graph represented by polar coordinate display. In FIG. 15, an offset having a radius of 10 is added for polar coordinate display. FIGS. 14A and 15A show the data before the filtering process, and FIGS. 14B and 15B show the data after the filtering process.
As described above, according to the data processing apparatus and method of the present embodiment, with respect to measurement data at unequal intervals, for example, data measured in three-dimensional measuring machine scanning measurement, roundness measurement, shape measurement, etc. Filter processing can be realized while maintaining the position information of the measurement points. Since this method does not add artificial data to the measurement data by the interpolation method as in the prior art, it is expected that more reliable results can be obtained than in the past.

1 is a schematic configuration diagram of a data processing apparatus according to an embodiment of the present invention. Explanatory drawing which showed the example of equidistant data (FIG. 2 (a)) and unequal interval data (FIG.2 (b)) in case the coordinate space of a measurement point is one-dimensional. Explanatory drawing which showed the example of equidistant data (FIG. 3 (a)) and unequal interval data (FIG.3 (b)) in case the coordinate space of a measurement point is two-dimensional Explanatory drawing about calculation of filter coefficient Illustration of data processing process The graph which shows the unequal interval data used in the Example concerning this invention The graph which shows the function (Gauss function) which determines the filter coefficient used in Example 1 The graph which showed the result of the filter process performed in Example 1 by the orthogonal coordinate (FIG. 8 (a) is before filter process, FIG.8 (b) is after filter process) The graph which showed the result of the filter process performed in Example 1 by the polar coordinate (FIG. 9 (a) before filter process, FIG.9 (b) after filter process) The graph which shows the function (exponential type function) which determines the filter coefficient used in Example 2 The graph which showed the result of the filter processing performed in Example 2 by the orthogonal coordinate (FIG. 11 (a) before filter processing, FIG.11 (b) after filter processing) The graph which showed the result of the filter process performed in Example 2 by the polar coordinate (FIG. 12 (a) is before filter process, FIG.12 (b) is after filter process) A graph showing a function (rectangular function) for determining a filter coefficient used in the third embodiment The graph which showed the result of the filter process performed in Example 3 by the orthogonal coordinate (FIG. 14 (a) is before filter process, FIG.14 (b) is after filter process) The graph which showed the result of the filter process performed in Example 3 by the polar coordinate (FIG. 15 (a) is before filter process, FIG.15 (b) is after filter process)

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Filter processing apparatus 12 Measurement system 20 Filter coefficient determination means 22 Processing means

Claims (6)

Filter the measurement values in the coordinate space of the measurement points with respect to the measurement data group in which the coordinate information of the measurement points distributed discretely and at irregular intervals and the measurement values at the measurement points are combined. A data processing device,
For each measurement value to be filtered, each positional relationship between the measurement point of the one measurement value and each measurement point of the measurement data group is obtained from the coordinate information, and based on each positional relationship. Filter coefficient determining means for calculating each filter coefficient corresponding to each measurement point of the measurement data group;
Processing means for obtaining a filtered value for the one measured value based on each measured value of the measurement data group and each filter coefficient calculated by the filter coefficient determining means. Data processing device. The data processing apparatus according to claim 1,
The filter coefficient determining means is configured to determine each measurement point of the one measurement value and each measurement data group based on the coordinate information of the measurement point of the one measurement value and the coordinate information of each measurement point of the measurement data group. A distance calculation unit for obtaining each distance between the points, and a coefficient calculation unit for obtaining a filter coefficient corresponding to each measurement point of the measurement data group based on each distance calculated by the distance calculation unit. Characteristic data processing device. The data processing apparatus according to claim 1 or 2,
The processing means includes a coefficient summation unit for obtaining a total value of filter coefficients calculated by the filter coefficient determination means,
Multiplying the measurement value of the measurement data group by the filter coefficient corresponding to the measurement point of the measurement value, and summing the multiplication over each measurement value of the measurement data group,
A division unit that divides the total value calculated by the multiplication value totaling unit by the total value of the filter coefficients calculated by the coefficient totaling unit to obtain a filtered value for the one measured value, Data processing device. The data processing device according to any one of claims 1 to 3,
The data processing apparatus according to claim 1, wherein the filter coefficient determining means sets the filter coefficient to 0 when the distance between measurement points is equal to or greater than a predetermined value. Filter the measurement values in the coordinate space of the measurement points with respect to the measurement data group in which the coordinate information of the measurement points distributed discretely and at irregular intervals and the measurement values at the measurement points are combined. A data processing method,
For each measurement value to be filtered, each positional relationship between the measurement point of the one measurement value and each measurement point of the measurement data group is obtained from the coordinate information, and based on each positional relationship. And a filter coefficient determination step for calculating each filter coefficient corresponding to each measurement point of the measurement data group,
And a processing step of obtaining a filtered value for the one measurement value based on each measurement value of the measurement data group and each filter coefficient calculated in the filter coefficient determination step. Processing method.   A data processing program for causing a computer to execute the data processing method according to claim 5.

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