JP2005285085A - Data analysis method, device, and program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a data analysis method, device, and program for causing the regression of a group of discrete data to a Fourier series with a high accuracy of approximation or for facilitating data analysis to create a denser and smoother three-dimensional topographic image from given numerical values of altitude. <P>SOLUTION: A group of data for regression are created from both a group of discrete data and a group of data symmetrical to the final data of the group of discrete data and are caused to regress to a Fourier series, the group of discrete data being obtained from luminance values on a predetermined measuring line on an image. The number of terms of the Fourier series is a predetermined one smaller than the number of data of the group of data. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention analyzes a set of discrete data obtained from image data or the like and extracts desired features, or data analysis for generating three-dimensional image data based on given discrete data The present invention relates to a method, a data analysis apparatus, and a data analysis program.

For example, in order to obtain necessary information from a plurality of data obtained by measurement, that is, a data group, the obtained data group is analyzed.
Measurements that require data analysis include, for example, measurement of isochromatic lines and isoclinic lines in photoelastic experiments.
The photoelasticity experiment is a color-matching line or isoclinic line that appears when the optical properties of the translucent elastic body change temporarily and exhibit birefringence when an external force is applied to the translucent elastic body. This is an experiment for examining the stress generated in a translucent elastic body and a similar structure based on the stripe pattern.
In order to specify the positions of the equal color lines and the equal inclination lines, it is necessary to analyze image data obtained by photographing the equal color lines and the equal inclination lines appearing in the translucent elastic body.

Various methods of automatically analyzing image data of isochromic lines and isoclinic lines have been proposed since it takes time and errors are likely to occur when humans perform measurement and analysis of the isochromatic lines and isoclinic lines. It has been.
Non-Patent Document 1 introduces various analysis methods such as a phase shift method and a spectrum analysis method.

  However, the method described in Non-Patent Document 1 has various inconveniences such as complicated procedures, easy errors, and difficulty in automation depending on the type.

  In addition, it is necessary not only for the field of photoelasticity but also for image analysis and measurement analysis in a wide range of fields including engineering and medicine to analyze data with high accuracy automatically with simple procedures. It is said that.

  Computer graphics (CG) such as three-dimensional terrain images are produced by inputting altitude value data at a number of discrete positions on a plane coordinate to a computer and performing appropriate texture pasting processing on the computer. However, in order to produce a precise and smooth image that can give a natural impression, it is necessary to prepare an enormous amount of elevation value data.

  Currently, the Geographical Survey Institute has released a 50m mesh numerical map with a scale of 1/25000. Furthermore, on June 1, 2003, a 5m mesh with a scale of 1/2500 for some areas. A numerical map is newly released. If the scale is reduced to some extent, it is possible to generate a smooth and realistic 3D terrain image using such numerical map data. For example, a model of residential land construction or a neighborhood area When a 3D terrain image of a larger scale used as a floor plan is generated, even if data of a numerical map of 5 m mesh is used, only a 3D terrain image that is rough and unrealistic can be produced. could not.

In the case of a game using a 3D terrain image such as a driving course of a driving game, altitude value data at a large number of discrete positions in the virtual space of the driving course is prepared, and based on this, 3D terrain data is prepared. Making images is done. And in order to be able to experience a more realistic driving feeling, etc., it is necessary to make the three-dimensional terrain image of the driving course smoother and more realistic, and for that purpose, the amount of elevation value data must be reduced. It is necessary to increase it. On the other hand, new and upgraded products are frequently produced for this type of product, and each time a new 3D terrain image of the driving course is required, so much effort is required to generate elevation data for the driving course. Was spent.
Eisaku Umezaki, “Current status of photoelasticity experiment automation”, Proceedings of the Japan Society for Experimental Force, P.121-124, No.1, 2001 Japanese Patent Laid-Open No. 10-154138

  An object of the present invention is to solve the above-mentioned problems, and to perform data approximation that can automatically approximate and analyze a data group that is a set of discrete data, and to improve the approximation accuracy It is an object to provide a method, an apparatus, or a program.

  In addition, the present invention provides a data analysis method, apparatus, program, or given data that can generate a 3D image such as a precise and smooth 3D terrain image rich in reality by a simple operation. It is an object of the present invention to provide a data analysis method, apparatus, or program capable of refining numerical map data and generating a more detailed and smooth three-dimensional terrain image that is more realistic.

  The present invention solves the above problems, and is a data analysis method for performing a predetermined process on a data to be analyzed which is a set of discrete data by a processing device and performing regression to a Fourier series, A symmetric data group is added to the first data group, which is a set of discrete data, to the last data of the first data group, and the number of data is a natural number times the number of data in the first data group. Generating a second data group, and regressing the second data group to a Fourier series by setting a Fourier series term number to a predetermined number smaller than the data number of the first data group; Is a data analysis method characterized by causing the processing device to execute.

The analysis target data in the present invention is a set of data obtained by sampling the values of the dependent variables whose values change with respect to the explanatory variables for the discrete explanatory variables. For example, the discrete positions (explanatory variables) on the image. This corresponds to the luminance value (dependent variable) at. Here, the term “discrete” includes a case of being discrete at an unequal interval (unequally spaced) as a case of being discrete at an equal interval.
The present invention obtains an approximate function form of a dependent variable from such discrete analysis target data by regression to Fourier series, and when regression to Fourier series is performed by a normal method, Since the sampled value includes an error, the regression curve has a slight jagged shape, which causes inconveniences such as inability to properly analyze the maximum value, minimum value, and inflection point. While solving the problem by reducing the number of terms in the Fourier series to a predetermined number, the increase in error due to the decrease in the number of terms is solved by increasing the number of data by a predetermined method.

  Here, the first data group in the present invention may be the analysis target data itself or may be obtained by adding data conversion such as linear conversion or logarithmic conversion for scale correction to the analysis target data. Alternatively, a third data group generated by linear interpolation of the analysis target data may be added to the analysis target data.

  The second data group of the present invention is the last data of the first data group (the maximum value of the explanatory variable in the first data group or the sampling value of the dependent variable corresponding to the minimum value). Symmetric (When the first data group is plotted in the orthogonal XY coordinates with the explanatory variable as the X axis and the dependent variable as the Y axis, the sampling value of the dependent variable corresponding to the maximum value or the minimum value of the explanatory variable A data group generated by adding a data group (additional data group) that is point symmetric or line symmetric with respect to a line parallel to the Y axis passing through the sampling value to the first data group. Yes, the number of data is twice that of the first data group.

  Alternatively, a symmetric data group (second additional data group) is generated with respect to the last data of the additional data group generated as described above, and the additional data group and the second additional data group are generated as the first data group. By adding a data group, or considering the second data group as a new first data group, an additional data group that is a symmetric data group with respect to the last data of the new first data group Can be added to this new first data group to generate a second data group having three or four times the number of data in the first data group. It is also possible to generate a data group of an arbitrary natural number such as 5 times or 6 times the number of data of the first data group and use this as the second data group.

  From the viewpoint of improving the accuracy of approximation using the periodicity of the Fourier series, the number of data in the second data group is an even number (especially twice) the number of data in the first data group. Similarly, it is preferable that the additional data group is generated so as to be line-symmetric with respect to the first data group.

  Further, in the present invention, how much it is appropriate to reduce the number of terms of the Fourier series depends on the number of data in the first data group and the content of the analysis to be performed. For example, the first data group When the number of data is in the order of several hundred to several thousand and the maximum value, minimum value, or inflection point of the approximate curve is specified, the data number is 10% or less, particularly 4-6%. It is preferable to set the degree.

  In the present invention, when the luminance value data on the predetermined measurement line of the isochromatic line image or the isoclinic line image in the photoelasticity experiment is the analysis target data, even when the luminance value data includes an error, etc. Approximate curves with sufficient smoothness to identify the position of the maximum and minimum values on the measurement line of the luminance value corresponding to the position of the color line and the isoclinic line can be obtained, and stress analysis can be performed efficiently Can be done.

  Further, in the present invention, when the altitude value data at discrete positions on the numerical map is used as analysis target data, it is smoother and more realistic than a three-dimensional shape created by simply connecting altitude values with straight lines. A 3D terrain image with a feeling can be obtained.

  In addition, for example, the luminance values of the isochromatic line image or the isoclinic line image in the photoelasticity experiment are measured on a plurality of measurement lines, and approximate curves obtained as analysis target data are displayed as three-dimensional landform images. It is also possible to create three-dimensional topographic images of various shapes very easily by changing the shape of the translucent elastic body used in the photoelasticity experiment and the manner in which the stress is applied. Become.

  The present invention can also be implemented as a Fourier analysis device or a Fourier analysis program.

  Embodiments of the present invention will be described below with reference to the accompanying drawings.

  First, as a first embodiment of the present invention, a case will be described in which the present invention is applied to analysis of stress distribution and the like in a photoelastic experiment.

FIG. 1 is a schematic configuration diagram of a photoelasticity experimental apparatus.
As described above, the photoelasticity experiment is a color matching that occurs when an external force is applied to the translucent elastic body, and the optical properties of the translucent elastic body change temporarily to show birefringence. This is an experiment for examining the stress generated in a translucent elastic body and a similar structure based on a stripe pattern of lines and isotropic lines. Therefore, in the photoelasticity experiment, it is necessary to measure the isochromatic line or the isoclinic line.
If the position of the isochromatic line and the isoclinic line appearing on the translucent elastic body can be obtained by measurement, the stress distribution can be obtained from the main stress difference or the main stress direction.

In order to measure the equal color line or the equal inclination line, the photoelasticity experiment apparatus 1 according to the present invention includes an optical system 3, a digital camera 40, a data analysis apparatus 5, and a monitor 60 as shown in FIG. Have.
The digital camera 40 is arranged on the optical axis LX of the optical system 3 so as to be able to receive light passing through the optical axis LX. Further, the data analysis device 5 is connected to the digital camera 40. The data analysis device 5 is further connected to a monitor 60.

As will be described later, the optical system 3 is for generating a uniform color line or a uniform inclination line on a specimen used for a photoelasticity experiment so that the uniform color line or the uniform inclination line can be photographed.
A specimen in which a uniform color line or a uniform inclination line appears is photographed by the digital camera 40. Image data obtained by photographing using the digital camera 40 is input to the data analysis device 5.

The data analysis device 5 is a device for analyzing the image data transmitted from the digital camera 40 and automatically specifying the position of the equal color line or the equal inclination line.
The analysis result by the data analysis device 5 is displayed on the monitor 60 in the form of a graph or the like, for example.

The optical system 3 includes a light source 31, a load table 34, and two polarizing plates 32 and 36 and quarter wavelength plates 33 and 35 each in a set.
These are the light source 31, the first polarizing plate 32, the first quarter wavelength plate 33, the load table 34, and the second quarter wavelength plate from a far position to a near position with respect to the digital camera 40. 35 and the second polarizing plate 36 are arranged on the optical axis LX of the light emitted from the light source 31 in this order.

  The light source 31 is a light source that functions as a surface light source by scattering light. In addition, since the resolving power is increased by using monochromatic light as the light source for the isochromatic line and white light as the light source for the isoclinic line, it becomes possible to read the isochromatic line or the isoclinic line more accurately. Also in the embodiment, a monochromatic light source 31 is used for photographing a uniform color line, and a white light source 31 is used for photographing a uniform inclination line.

Each of the first and second polarizing plates 32 and 36 emits incident light as polarized light whose vibration direction is aligned in a direction parallel to the polarization axis.
The first and second polarizing plates 32 and 36 can be rotated in conjunction with each other about the optical axis LX or can be rotated independently. The direction of each polarization axis of the first and second polarizing plates 32 and 36 is changed by the rotation of the first and second polarizing plates 32 and 36 around the optical axis LX.
In the present embodiment, when only the reference position marker of the second polarizing plate 36 is set to the 0 degree position, the polarization axis of the first polarizing plate 32 and the polarization axis of the second polarizing plate 36 are orthogonal to each other. Become a direction. Further, when only the reference position marker of the second polarizing plate 36 is set to the 90 degree position, the polarization axis of the first polarizing plate 32 and the polarization axis of the second polarizing plate 36 are parallel to each other.

The first and second quarter-wave plates 33 and 35 emit polarized light that crosses the two polarization axes of the first and second quarter-wave plates 33 and 35 while shifting the phase of the polarized light by a quarter wavelength.
The first and second quarter-wave plates 33 and 35 emit the polarized light incident in parallel to one of the two polarization axes as it is without shifting the phase.

The first quarter-wave plate 33 and the second quarter-wave plate 35 can be rotated in conjunction with each other about the optical axis LX. In the present embodiment, when the reference position markers of the first and second quarter-wave plates 33 and 35 are set to the position of 0 degrees, the first and second quarter-wave plates 33 and 35 The direction of one of the polarization axes is parallel to the direction of the polarization axis of the first polarizing plate 32.
When the reference position markers of the first and second quarter-wave plates 33 and 35 are set at 45 degrees, the direction of one polarization axis of the first and second quarter-wave plates 33 and 35 is The first polarizing plate 32 is shifted by 45 degrees from the direction of the polarization axis.

  The load table 34 is for applying a load to a specimen formed of a translucent elastic body. FIG. 2A shows a plan view of the specimen 7 used in the present embodiment, and FIG. 2B shows an elevation view of the load table 34.

As shown in FIG. 2A, a plate having a circular outer shape is used as the specimen 7 in the present embodiment. The radius R1 of the disk-shaped specimen 7 is, for example, R1 = 130 mm.
The thickness of the specimen 7 is 6 mm, for example.

For the specimen 7, for example, a plate made of diallyl phthalate (DAP) is used. Since the DAP plate has translucency and is elastically deformed according to an external force, it can be used as a specimen to which a load is applied in a photoelasticity experiment.
In addition to the DAP plate, a translucent resin such as an epoxy resin can also be used.

The specimen 7 is provided with a circular opening 70. The radius R2 of the opening 70 is, for example, R2 = 13 mm.
The distance L1 from the circumference of the specimen 7 to the circumference of the opening 70 is, for example, L1 = 13 mm.

In addition to the opening 70, the specimen 7 is provided with an attachment hole for attaching the specimen 7 to the load table 34.
In the present embodiment, two circular mounting holes 7a and 7a are provided. The radius R3 of the mounting holes 7a, 7a is, for example, R3 = 4 mm.
The two mounting holes 7 a and 7 a are provided in line symmetry with respect to a straight line connecting the center point of the specimen 7 and the center point of the opening 70.
As shown in FIG. 2A, distances L2 and L3 from the center point of the specimen 7 to the mounting hole 7a are, for example, L2 = 70 mm and L3 = 70 mm.

As shown in FIG. 2B, the load table 34 includes a load arm 34a and a frame 34b.
The specimen 7 is attached to the frame 34b through the attachment holes 7a and 7a. In the present embodiment, for example, in order to measure the isochromatic line and the isoclinic line when the concentrated load acts on the center of the arc boundary of the arched structure, the load 9 of the load arm 34a and the specimen 7 are measured. The specimen 7 is attached to the frame 34b so as to face the opening 70 side.

The load arm 34a is attached to the frame 34b at a fulcrum 34p, and the position of the balance weight WB is adjusted so as to balance the fulcrum 34p when the weight M is not attached. By attaching the weight M to the load arm 34 a with the load arm 34 a in a balanced state, an equal load can be applied to the specimen 7 via the load 9.
As described above, the concentrated load can be applied in the linear direction connecting the center point of the opening 70 and the center point of the specimen 7 at the center of the arc boundary of the arch-shaped structure.

The load applied to the specimen 7 can be resolved, for example, with a uniform color line and an inclined line, and is within the elastic deformation range of the specimen 7, and deformation that affects the stress distribution is applied to the specimen 7. Make it as large as possible within the range that does not occur.
Of the surface of the specimen 7, the surface through which the opening portion 70 penetrates becomes a photographing surface 7 </ b> S for photographing a uniform color line and a uniform inclination line.

The digital camera 40 is a camera having an image sensor such as a charge coupled device (CCD) or a complementary metal oxide semiconductor (CMOS), for example.
It is assumed that the number of pixels of the image sensor has a fine density sufficient for resolving isochromatic lines and isoclinic lines. For example, in the present embodiment, a digital camera 40 having 3.3 million pixels is used.

The photographing surface 7S of the specimen 7 is photographed by the digital camera 40 via the second quarter-wave plate 35 and the second polarizing plate 36.
Image data of the photographing surface 7S photographed by the digital camera 40 is input to the data analysis device 5 described below.

The data analysis device 5 is realized by a computer, for example.
As shown in FIG. 1, the data analysis device 5 includes a CPU (Central Processing Unit) 51, a data driver 53, an image driver 57, and a storage device 55.
One embodiment of the processing apparatus and processing unit in the present invention is a CPU 51.

As shown in FIG. 1, the CPU 51 is connected to a data driver 53, an image driver 57, and a storage device 55, respectively.
The data driver 53 and the storage device 55 are also connected.
The image driver 57 is further connected to the monitor 60.
Furthermore, an operation device such as a keyboard (not shown) for operating the data analysis device 5 may be connected to the CPU 51.

Image data obtained by the digital camera 40 is input to the data analysis device 5 via the data driver 53.
FIG. 1 shows a form in which the digital camera 40 and the data driver 53 are connected. For example, the digital camera 40 and the data driver are stored using a storage means such as a portable semiconductor memory or a disk-shaped storage medium. It is also possible to input image data to the data analysis device 5 without directly connecting to 53.
The data driver 53 outputs the input image data as a file to the storage device 55 for storage.

The storage device 55 is realized by storage means such as a semiconductor memory or a hard disk drive, for example.
The storage device 55 stores the image data file input from the data driver 53 in a freely readable manner.
In addition, the storage device 55 can store a calculation processing result of the CPU 51 described later as data.
Further, the storage device 55 also stores a program for causing the CPU 51 to perform analysis of image data of equal color lines and equal inclination lines, and a program for operating the data analysis device 5.

When performing image analysis, the CPU 51 accesses the storage device 55 and acquires image data.
When the digital camera 40 and the data driver 53 are connected, the CPU 51 captures images using the digital camera 40 via the data driver 53 and transfers image data obtained by the image capture to the data driver 53. It is also possible to adopt a form in which such control is performed.

  The CPU 51 performs predetermined processing on the image data from the storage device 55 and analyzes it to obtain desired information. In the case of the present embodiment, the position of a striped pattern of isochromatic lines or isoclinic lines is specified. The contents of the process performed on the image data by the CPU 51 will be described in detail later.

The CPU 51 outputs analysis result data to the image driver 57.
The analysis result input from the CPU 51 is displayed on the screen of the monitor 60 via the image driver 57.

The monitor 60 is, for example, various display devices such as a CRT (Cathode Ray Tube) and a liquid crystal display panel. On the screen of the monitor 60, an image photographed by the digital camera 40 and an analysis result by the CPU 51 can be displayed.
In addition, a GUI (Graphical User Interface) screen for operating the data analysis device 5 can be displayed on the screen of the monitor 60.

Hereinafter, a photoelasticity experiment using the photoelasticity experiment apparatus 1 and a procedure for analyzing an image of a color matching line or an isoclinic line obtained in the photoelasticity experiment will be described.
FIG. 3 is a diagram for illustrating a region to be subjected to analysis processing in the image data of the imaging surface 7S of the specimen 7 obtained by the photoelasticity experiment.
From the digital camera 40, for example, image data is obtained as a collection of luminance value data in pixels of a predetermined size. FIG. 3 shows which region of the pixel data in the image displayed as a collection of pixels is used for data analysis.

In the case of stress analysis of a structure having an arched portion, such as the specimen 7 having the opening 70 according to the present embodiment, the peripheral portion of the opening 70 is orthogonal to the load application direction and the application direction. The stress distribution is important in the direction in which the arch is formed and in the arc portion forming the arch.
Therefore, for example, as shown by the arrows D1 to D5 in FIG. 3, the cross section on which the imaging surface 7S of the specimen 7 exists is shown as an upper cross section, a lower cross section, a cross section horizontal section, a cross section arc section, and a cross section opening. Divide into parts.
When a concentrated load is applied in the vertical direction from the top TP of the circular arc of the symmetric specimen 7 as in the present embodiment, the stress distribution is axisymmetric with respect to the vertical line passing through the vertex TP. For the horizontal portion, the cross-sectional arc portion, and the cross-sectional opening, it is only necessary to perform analysis on one side.

In FIG. 3, a line provided with a scale represents a measurement line for sampling pixel data at each part in the imaging surface 7S. However, these measurement lines are virtual, and the measurement lines with scales are not actually provided on the imaging surface 7S.
In each measurement line, the directions of the arrows D1 to D5 represent the directions of sampling pixel data. Further, as shown in FIG. 3, the interval between the scales on each measurement line represents the sampling interval when data is sampled along each measurement line. Hereinafter, this sampling interval is represented as dx. The value of the sampling interval dx means how many pixels are sampled.
In addition, the interval between the measurement lines is expressed as an interval dy. The interval dy can be arbitrarily determined. However, since the shear stress at the boundary is 0 in the analysis of the part where the boundary such as the cross-sectional opening or the circular arc part exists, it is necessary to set the interval dy in the stress analysis and sample the data on the plurality of measurement lines. There is no.
In the photoelastic experiment analysis, it is said that when the value of dx / dy is close to 1, an accurate stress value is obtained in terms of numerical integration.
As described above, the data related to the image of the equal color line and the equal inclination line to be analyzed by the CPU 51 is data obtained by sampling the luminance values of the respective pixels of the image data along the measurement line at equal intervals. Therefore, in the following, data to be analyzed by the CPU 51 is referred to as a data group.

FIG. 4 is a flowchart showing a procedure of a data analysis method using the CPU 51 in the data analysis apparatus 5 according to the present embodiment.
In the following, data analysis relating to isochromatic lines or isoclinic lines in a predetermined region of the imaging surface 7S will be described as different analysis examples.
First, analysis of image data relating to color matching lines will be described along the flowchart of FIG.

Analysis example 1
In the analysis, first, an image data group to be subjected to data analysis is extracted from the image data obtained by the digital camera 40, and this is used as the first data group of the present invention (step ST1).
In the analysis example 1, in order to analyze the image data group related to the color matching lines, the digital camera 40 captures the imaging surface 7S on which the color matching lines appear.

In order to photograph the color matching line, in the optical system 3 according to the present embodiment, the reference position markers of both the first and second quarter-wave plates 33 and 35 are aligned at a 45 degree position, The reference position marker of the second polarizing plate 36 is set to the 0 degree position.
In this state, black stripes appearing on the photographing surface 7S as shown in FIG. 5 are called color matching lines. By specifying the position of the color matching line LC, the distribution of the main stress difference of the stress applied to the specimen 7 can be examined.
However, in actuality, the color matching line LC is a stripe having shading, and the density of the color matching line LC increases in a portion where stress is concentrated. Have difficulty. Therefore, in the present embodiment, the image of the color matching line LC is analyzed by the data analysis device 5 so that the position of the color matching line LC can be automatically specified.
In order to automatically specify the position of the color matching line LC, the image of the color matching line LC photographed by the digital camera 40 is converted into, for example, 256-step gray scale data and stored in the storage device 55. Is remembered as

As described above, the color matching lines when the respective polarizing axes of the first and second polarizing plates 32 and 36 are orthogonal to each other with the reference position marker of the second polarizing plate 36 set to the 0 degree position. The image is called a dark-field color-matching line image because the background with respect to the photographing surface 7S becomes dark.
On the other hand, when the reference position marker of the second polarizing plate 36 is set to a position of 90 degrees and the respective polarization axes of the first and second polarizing plates 32 and 36 are made parallel, the color matching line image is as follows. Since the background with respect to the photographing surface 7S becomes bright, it is called a bright field color matching line image. In a bright-field color image, a portion that appeared as a black stripe in a dark-field color image is inverted and brightened, and a bright portion is black and recognized as a color-match image.
In Analysis Example 1, image data of a dark-field color matching line image is used to examine the distribution of main stress differences.

After the image data of the color matching lines LC appearing on the imaging surface 7S is stored in the storage device 55, in step ST1, an image data group of an area to be analyzed is further extracted.
For example, in Analysis Example 1, as shown in FIG. 5, the measurement axis MAL is provided on the cross-sectional side as the above-described measurement line, and the position of the color matching line LC is extracted on the measurement axis MAL by extracting an image data group. Identify.
In order to extract the image data group used for the analysis from the image data of the imaging surface 7S, for example, a measurement axis MAL is formed by drawing a straight line on the image of the imaging surface 7S displayed on the monitor 60 using a GUI. The CPU 51 extracts the luminance value data at each pixel on the measurement axis MAL designated by the GUI at every sampling interval dx.

  As described above, it is possible to obtain a group of discrete image data sampled at equal intervals used for data analysis.

In Analysis Example 1, for example, dx = 0.06 mm. This value is almost the same as the pixel interval of the color matching line image obtained by the digital camera 40. Therefore, at this time, the luminance values of all the pixels on the measurement axis MAL are collected. Under this condition, the number of data of the image data group obtained in Analysis Example 1 was 651, for example.
In Analysis Example 1, the value of the interval dy is, for example, dy = 0.4 mm.
Drawing of a straight line for forming the measurement axis MAL and designation of the sampling intervals dx and dy can be executed using an operation device (not shown) such as a keyboard or a mouse connected to the CPU 51.

FIG. 6A shows a graph GDC1 of the image data group obtained in step ST1. In the graph of FIG. 6A, the horizontal axis represents the distance [mm] from the reference point, and the vertical axis represents the luminance value of each pixel represented by 256 gray scales.
The image data group is discrete data, but in FIG. 6A, individual data are connected by a solid line and shown as a graph GDC1.
Further, positions A, B, and C on the measurement axis MAL indicated by arrows in FIG. 5 correspond to positions A, B, and C in the graph shown in FIG. The position A is a reference point in measurement. The position A is a boundary point with the opening 70 on the measurement axis MAL.

As can be seen from the graph GDC1, the image data group obtained by photographing the photographing surface 7S using the digital camera 40 has a fine value due to the influence of noise due to digitization and noise due to imperfection of the optical system. Increase or decrease.
In order to specify the position of the contour line, it is necessary to specify the maximum and minimum points of the graph GDC1. In order to specify the maximum and minimum points, conventionally, for example, the image data group is regressed to an approximate curve by the least square method. It was. However, in order to finely increase or decrease the image data group due to the influence of noise or the like as described above, in the least square method, the graph obtained by approximation and the graph GDC1 are approximated with high accuracy so that they are substantially the same. It was difficult. Since data that increases or decreases finely at short intervals cannot be effectively approximated, there is a disadvantage that the sampling interval that can be used as an image data group is limited when the least square method is used.

Therefore, in the present embodiment, approximation is performed by regressing the image data group to a Fourier series.
Regressing a discrete data group to a Fourier series is a well-known technique, but is briefly described below.

When the Fourier series is used, a curve of a discrete data group to be reproduced by a regression curve can be expressed by a single expression using a trigonometric function.
If a function x (t) in which N pieces of data are sampled at equal intervals is represented by a Fourier series, A ₀ , A ₁ , A ₂ ,..., A _k and B ₀ , B ₁ , B ₂ ,. _{When k} is a constant that can be appropriately determined, x (t) = A ₀ + A ₁ cost + A ₂ cos 2t +... + A _k coskt +... + B ₀ + B ₁ sint + B ₂ sin 2t +... + B _k sinkt +.
The above formulas can be summarized as the following formula (1).

In equation (1), the sampling interval is Δt, and the duration of the function x (t) is NΔt.
Equation (1) is an infinite series summing from 0 to infinity with respect to k, but when censored up to k = N / 2, it becomes a finite trigonometric series represented by the following equation (2).

When the function represented by the above equation (2) is converted into a function that passes N sample values x _m (m = 0, 1, 2,..., N−1) sampled at the sampling interval Δt, The sample value x _m can be expressed as the following equation (3).

The coefficients A _k and B _k in the above equation (3) can be expressed by the following equations (4) and (5), respectively.

Function represented by the above formula (3) is all accurately pass through the sample values x _m. Therefore, if the above equation (3) is used, an approximate curve can be obtained by regressing the image data group in Analysis Example 1 to a Fourier series.
However, when the function of Expression (3) is used as it is and the regression is performed so that the entire image data group passes, the approximate curve obtained by the regression to the Fourier series is as fine as the graph GDC1 shown in FIG. It becomes a curve that repeats increasing and decreasing.
In this embodiment, in order to prevent the data value after Fourier series approximation from increasing or decreasing finely and to obtain a smooth approximate curve, in this embodiment, the number of terms of the function of equation (3), that is, the coefficient A The number of _k and B _k is set to a predetermined number smaller than the number of data of the image data group obtained in step ST1, and the image data group is regressed to the Fourier series.

The number of terms in the Fourier series is preferably about 10% or less of the number of data in the image data group in the photoelasticity experiment in order to specify the color matching lines and the isoclinic lines.
In Analysis Example 1, the number of terms in the Fourier series p is, for example, p = 35, which is about 5% of the number of data N = 690 obtained in step ST1.
However, if the number of data in the image data group is too small, the number of terms p decreases so that sufficient approximation accuracy cannot be obtained. Therefore, although depending on the required approximation accuracy, in order to increase the number of terms p and ensure a certain degree of approximation accuracy, the number of data of the original image data group is also required to some extent. The approximation accuracy improves as the number of data in the image data group increases.

As the number of terms p decreases, the calculation time of the function of Equation (3) becomes shorter and the obtained approximate curve tends to be smoother.
However, when the number of terms p decreases, the error between the approximate value increases in the rear part of the image data group. Therefore, in order to increase the accuracy of approximation, in this embodiment, an additional data group is added to the image data group, and the number of data to be returned to the Fourier series is increased to a predetermined multiple of the image data group.

In order to increase the number of data to be regressed to the Fourier series, the CPU 51 generates an additional data group to be added to the image data group obtained in step ST1 (step ST2).
Since the Fourier series is a periodic function, in order to improve the accuracy of approximation using this property, the additional data group is composed of image data centered on the last data of the image data group in terms of its size. Data is generated as a data group arranged so as to be symmetric with respect to the data size of each group. In the present embodiment, a graph GDC1 ′ in which individual data of the additional data group is connected by a broken line corresponds to a vertical line passing through the last point of the graph GDC1 of the image data group as shown in FIG. An additional data group is generated so as to be line symmetric with respect to the graph GDC1.
The additional data group may be generated so that the graph GDC1 ′ is symmetric with respect to the graph GDC1 with the last point of the graph GDC1 as the center, but from the viewpoint of improving the approximation accuracy, as shown in FIG. It is preferable that data such that the graph is line symmetric be the additional data group.

As described above, by adding the additional data group arranged so as to be symmetric to the last data of the image data group to the image data group, the number of sample values in Equation (3) is not N but αN. can do. Hereinafter, the αN data group is referred to as a regression data group (step ST3).
One embodiment of the second data group in the present invention corresponds to this regression data group.
Here, the coefficient α is a natural number from the viewpoint of increasing the number of data. In particular, the coefficient α is preferably an even number from the viewpoint of improving the accuracy of approximation using the periodic nature of the Fourier series. This is because if the coefficient α is an even number (for example, 2), all the data of the original image data group is used as data having a symmetric size around the last data of the image data group.
However, from the viewpoint of increasing the number of data, the coefficient α can be a positive decimal number.
In order to set the coefficient α to 2 or more so that the number of data is more than twice the first N data, the regression data group generated based on the first image data group is considered as the first data group, and this What is necessary is just to produce | generate a new data group so that it may become symmetrical centering on the last data of a data group.

The regression data group generated as described above is regressed to a Fourier series using the CPU 51 (step ST4).
In Analysis Example 1, for example, α = 2.
As described above, the number of terms p of the Fourier series to be regressed is set to p = 35, for example. This value is 10% or less of the number of data of the image data group that is the origin of the regression data group.

FIG. 6B shows a graph FGDC1 of the approximate curve obtained by regressing the regression data group to the Fourier series. The horizontal axis in FIG. 6B represents the distance [mm] from the reference position A on the same measurement axis MAL as in FIG. 6A, and the vertical axis represents the magnitude of luminance.
When the regression data group is regressed to the Fourier series, an approximate curve for the entire regression data group can be obtained. However, only the analysis result relating to the image data group on the measurement axis MAL is used for specifying the position of the color matching line. Since it is necessary, FIG. 6B shows only the graph FGDC1 of the approximate curve of the portion related to the original image data group.

As is clear from the graph FGDC1, the value of each data changes smoothly by reducing the number of terms p to some extent and regressing to the Fourier series.
In addition, since the regression is performed using data with an increased number including the additional data group, each data after approximation to the Fourier series changes smoothly, but the error with the original image data group becomes small, The accuracy of approximation is improved. By using the original image data group, it is considered that the accuracy of approximation improves as the generated regression data group becomes periodic data. However, the smoothness and approximation accuracy of the obtained approximate curve change in a complex manner depending on the characteristics of changes in the image data group and the combination of parameters such as the number of terms p and the number of data in the regression data group, and are not decided unconditionally. .

Based on the approximate data obtained by regressing the Fourier series as described above, the CPU 51 specifies the position of the stripe of the color matching line LC (step ST5).
The stripes of the color matching lines LC are 0th order, 1st order, 2nd order,... Integer order values, 0.5th order, 1.5th order, 2.5th order, half order values, and integer order. A numerical value called a fringe order having an intermediate value between the half order and the half order is attached and used for stress analysis.

The position of the stripe of the integer order of stripe order corresponds to the darkest position of each stripe in the image of the contour line of the dark field. In FIG. 5 and FIGS. 6A and 6B, the stripe located at the position C is a zero-order stripe, the stripe at the position B is a primary stripe, and the stripe at the position A is a secondary stripe. .
Further, the position of the half-order fringe order fringe corresponds to the darkest position of each fringe in the bright-field color matching line image. Therefore, the position of the half-order stripe corresponds to the brightest position between two black stripes in the dark-field isochromatic line image. 5 and 6 (a) and 6 (b), the 0.5th order fringe is located between position C and position B, and the 1.5th order fringe is located between position B and position A. Will be located.
Therefore, the integer-order stripe and the half-order stripe of the color matching line correspond to the minimum value and the maximum value of the graph obtained from the image data group in the analysis region in the dark-field color matching line image, respectively.
If approximate data that changes smoothly as shown in the graph FGDC1, the maximum and minimum values can be easily obtained. Therefore, based on the approximate data indicated by the graph FGDC1, integer-order fringes such as a zero-order fringe at the position C, a first-order fringe at the position B, and a second-order fringe at the position A in the graph of FIG. And the position of half-order fringes, such as the 0.5th-order fringe between position C and position B, and the 1.5th-order fringe between position B and position A, are each accurately pointed to Can be determined.

Note that the stress analysis may require an intermediate fringe order intermediate between the integer order and the half order. In order to obtain the intermediate fringe order for the position between the integer-order fringe and the half-order fringe, for example, the Tardy method is used.
Since the Tardy method is a method well known to those skilled in the art in the field of photoelasticity experiments, detailed description is omitted.

According to the above procedure, if an area to be analyzed with respect to the color matching line image is designated by the GUI, the image data group based on the color matching line image is analyzed by the data analyzing device 5 and a plurality of stripes of the color matching line LC Can be automatically identified.
When analyzing another region of the color matching line image, the procedure from step ST1 to step ST5 is repeated, and if not, the analysis is terminated (step ST6).

As described above, the stripe order can be determined by easily specifying the position of the color matching line LC at various positions on the imaging surface 7S of the specimen 7.
From the color matching line LC in which the stripe order and position are specified, the distribution of the main stress difference in the specimen 7 to which stress is applied and the structure represented by the specimen 7 can be obtained.
Since the procedure for obtaining the distribution of the main stress difference from the color matching line LC is well known to those skilled in the art, a detailed description thereof is omitted.

Analysis example 2
Hereinafter, an example of analyzing the image data group in the cross-sectional opening shown in FIG.
The analysis procedure for the image data group is the same as the procedure described with reference to the flowchart shown in FIG.

FIG. 7 is an enlarged view of the vicinity of the opening 70 of the specimen 7. An image data group is extracted on the measurement line MPL shown in FIG.
In Analysis Example 2, similarly to Analysis Example 1, a concentrated load is applied vertically from the vertex TP of the arc of the specimen 7. In this case, since the stress distribution is symmetric about the vertical line passing through the vertex TP, in order to examine the stress distribution in the opening 70, as shown by the measurement line MPL, on one side with respect to the vertical line passing through the vertex TP. It is sufficient to analyze only the color matching lines.

Similar to the case of step ST1 shown in FIG. 4, the measurement line MPL is designated using the GUI, and an image data group is acquired. The sampling interval dx along the measurement line MPL is set to dx = 0.06 mm, for example, as in Analysis Example 1.
As described above, it is not necessary to set the interval dy in the analysis of the cross-sectional opening located at the boundary.

FIG. 8A shows a graph obtained by plotting the obtained image data groups. In FIG. 8A, the horizontal axis represents the distance [mm] along the measurement line MPL from the reference position, and the vertical axis represents the magnitude of luminance represented by the image data group.
In the measurement line MPL, the number 1 side shown in FIG. 7 is used as a reference, and data is sampled toward the number 6 side.

In the analysis example 2, for the analysis of the color matching line LC in the cross-sectional opening, for example, as shown by the numbers 1 to 6 in FIG. Then, each image data group obtained by dividing into six equal parts is set as a first data group of the present invention.
Similar to Analysis Example 1, a regression data group was generated by doubling the number of data for each of the six image data groups. The number of terms in the Fourier series to be regressed was 5% of the number of data in each image data group (rounded up).

FIG. 8B is a graph obtained by connecting six Fourier series approximation curves for each image data group obtained under the above conditions.
In FIG. 8B, intervals (mm) from the reference number 1 side are plotted on the horizontal axis, with sections (1) to (6) corresponding to the regions represented by numbers 1 to 6 in FIG. Further, the vertical axis of FIG. 8B is the same luminance as the vertical axis of FIG.
Circles in the graph of FIG. 8B indicate division points between the image data groups.
As can be seen by comparing FIG. 8A and FIG. 8B, a smooth approximate curve with high approximation accuracy is obtained. Further, the approximate curves are smoothly connected at the dividing points between the image data groups.

In the conventional analysis method using the least square method, the approximate curves obtained individually for each group of image data obtained by division are usually not smoothly connected. Further, in order to smoothly connect the approximate curves, it is necessary to change various parameters such as the number of data, which requires very complicated labor and great labor.
On the other hand, in the present embodiment, as can be seen from the result of the above-described Analysis Example 2, the image data group obtained by dividing the image data group obtained by dividing the image data group individually as in the case where the analysis region is lengthened or curved is used. Also in the case of analyzing by regression, the connection of each data group after approximation becomes good, and the position of the color matching line can be easily specified.
Obtaining a smooth approximation result for the divided image data group is particularly useful in automating the analysis of image data.

Analysis example 3
The analysis examples 1 and 2 were analyzes on the color matching lines. In Analysis Example 3, an analysis for an isotropic line will be described.
However, since Analysis Example 3 is the same as Analysis Example 1 except that an isotropic line is an analysis target, detailed description of approximation to the Fourier series is omitted.

  FIG. 9 is a view showing an example of an isotropic line appearing on the imaging surface 7 </ b> S of the specimen 7, and shows an enlarged cross-sectional lateral portion near the opening 70. The isoclinic lines are identified based on the isoclinic image in which a plurality of black stripes LI appear as shown in FIG.

In order to capture an isotropic line image, in the optical system 3 according to the present embodiment, the reference position markers of both the first and second quarter-wave plates 33 and 35 are adjusted to the 0 degree position. Then, the first and second polarizing plates 32 and 36 are moved in conjunction so that the respective reference position markers are positioned at predetermined angles.
For example, FIG. 9 shows an isoclinic image when the reference position markers of the first and second polarizing plates 32 and 36 are aligned at a position of 74 degrees.
Black stripes whose positions move when the rotation angles of the first and second polarizing plates 32 and 36 are changed are called isotropic lines.

Similar to Analysis Example 1, an image data group that is the basis of analysis is extracted on the measurement axis MAL at the cross section of the cross section. For example, assuming that the sampling interval dx is dx = 0.06 mm, the number of data of the obtained image data group is 690.
In Analysis Example 3, the interval dy is set to dy = 0.4 mm, for example.

FIG. 10A shows a graph GDI obtained by plotting and connecting image data groups related to the isotropic image obtained as described above. In FIG. 10A, the horizontal axis represents the distance [mm] from the reference point, and the vertical axis represents the luminance level of each pixel represented by 256 gray scales.
Positions A, B, and C on the measurement axis MAL indicated by arrows in FIG. 9 correspond to positions A, B, and C in the graph shown in FIG. The position A is a reference point for measurement. The position A is a boundary point with the opening 70 on the measurement axis MAL.

FIG. 10B shows a graph FGDI of an approximate curve obtained by approximating the image data group shown in the graph of FIG. 10A by regressing it into a Fourier series. Similar to FIG. 10A, the horizontal axis in FIG. 10B is the distance [mm] from the reference position, and the vertical axis is the luminance. Positions A, B, and C in FIG. 10B also represent the same positions as positions A, B, and C in FIG.
In the approximation, the number of data in the regression data group is, for example, twice the number of data in the image data group. The number of terms p of the Fourier series is, for example, p = 35.

In a predetermined analysis region, when obtaining a data group sampled at a predetermined constant interval as in Analysis Example 3, the position of the minimum minimum value of the data group is a polarizing plate 32 that has captured an isotropic image, This is the position of the equiclinical line at the rotation angle of 36.
10 (a) and 10 (b), the position indicated by the position C is the position of the isotropic line, and when the regression is performed to the Fourier series as shown by the approximate curve in FIG. 10 (b), the isotropic line is obtained. Can be easily identified.

  FIG. 10B shows the case where the angles of the polarizing plates 32 and 36 are 74 degrees, but the above-mentioned isotropic line positions are set every 1 degree when the angles of the polarizing plates 32 and 36 are 0 to 90 degrees. A specific procedure is executed by the data analysis device 5 to calculate 91 isotropic line position data.

  FIG. 11A shows a graph plotting the obtained 91 isotropic line position data. In FIG. 11A, the horizontal axis represents the distance [mm] from the reference position similar to FIGS. 10A and 10B. In addition, the vertical axis in FIG. 11A represents the angle [degree] at which the polarizing plates 32 and 36 were located when the positions of each isotropic line were specified.

As shown in FIG. 11 (a), the equi-tilt line position data is discontinuous and non-uniform data with respect to the distance from the reference position on the horizontal axis, and therefore data interpolation is performed on the horizontal axis.
In Analysis Example 3, for example, isotropic line position data is interpolated at a low order using the least square method.

FIG. 11B shows a graph of an approximate curve obtained by interpolating isotropic line position data by the least square method. Similarly to FIG. 11A, the horizontal axis in FIG. 11B represents the distance [mm] from the reference position, and the vertical axis represents the angle [degree].
As shown in FIG. 11B, by interpolating data with respect to the distance, it is possible to specify which angle of equal inclination passes through the measurement axis MAL at an arbitrary point on the measurement axis MAL. become.

The measurement of isotropic lines by data analysis using the data analysis device 5 can be applied not only to a straight line such as the measurement axis MAL but also to an analysis region of a curve as in Analysis Example 2.
Since the isotropic line is a line indicating the principal stress direction, if the position of the isotropic line at each angle can be specified in each area in the analysis area as shown in FIG. 11B, stress is applied. The direction of the principal stress in the specimen 7 and the structure represented by the specimen 7 is obtained.

Analysis example 4
In the analysis examples 1 to 3, the example in which the approximation to the Fourier series is performed on the data group of the luminance values sampled at equal distances from the reference position has been described. A case where approximation to a Fourier series is performed on a sampled data group will be described.

  Also in this analysis example 4, data analysis was performed according to the procedure shown in the flowchart of FIG. 4. From the 651 data (hereinafter referred to as the original data group) used as analysis target data in the analysis example 1, Three types of data groups (one missing data group, two missing data groups, three missing data groups) sampled at unequal intervals are created by three methods, and the original data group, one missing data group, Each of the two-out data group and the three-out data group is set as an image data group which is the first data group of the present invention (step ST1).

  FIG. 12 is an explanatory diagram showing a data deletion method performed to create data sampled at unequal intervals.

  As shown in the drawing, 651 data is divided into 20 blocks from the reference point (position A in FIG. 5) as a single data group, and the second, fifth, and ninth in each block are divided. The 1st data group which consists of 488 data was created by deleting the 14th, 14th, and 20th data. Note that the second, fifth, and ninth data were deleted from the last remaining 10 data in the division into blocks.

  In addition, 651 data is divided into 25 blocks from the reference point as a data group to be removed, and the second, third, sixth, seventh, eleventh, twelfth, and seventeenth in each block. By deleting the 18th, 24th and 25th data, a first data group consisting of 386 data was created. Note that the last remaining data in the division into blocks was included in the analysis target data.

  Further, 651 data is divided into 30 blocks each from the reference point as a data group with three pieces removed, and the 2nd to 4th, 7th to 9th, 14th to 16th, 20th in each block. By deleting the ˜22nd and 28th to 30th data, a first data group consisting of 325 data was created. For the 21 data remaining last in the division into blocks, the 2nd to 4th, 7th to 9th, 14th to 16th, and 20th data were deleted.

  FIGS. 13A to 13C show graphs GDC2, GDC3, and GDC4 of the single data group, the two data groups, and the three data groups obtained in this way. These data are discrete data sampled at unequal intervals as described above, but GDC2, GDC3, and GDC4 in FIGS. 13A to 13C are displayed by connecting individual data by solid lines. Yes.

  As shown in FIGS. 13A to 13C, the values of these data groups are finely increased or decreased. In this state, the maximum point and the minimum point indicating the position of the color matching line are specified. Therefore, it is considered to approximate each data group by regressing it into a Fourier series.

In general, when N data sampled at an arbitrary measurement point t _m (x) in the measurement section Tn is x _m (x) (where m = 0, 1,..., N−1), x _m (x) can be approximated by Equation (6).

The coefficients A ₀ , A _k , and B _k in the above formulas (7) to (9) use Simpson's three-point integration or use Simpson's three-point integration and four-point integration together. Thus, it can be obtained for an arbitrary number of data.

Function represented by the above formula (6), all correctly passing each sample value x _m. Therefore, if the above equation (6) is used, not only the data group sampled at equal intervals but also the data group sampled at unequal intervals is used as the first data group, and the approximation curve is regressed to the Fourier series. Can be obtained.

  However, if the function of equation (6) is used as it is and the regression is performed so that the entire image data group is passed, the approximate curve obtained by regressing to the Fourier series is a curve that repeatedly increases and decreases like graphs GDC1 to GDC4. End up.

Therefore, as in the case of Analysis Example 1, in order to prevent the data value after Fourier series approximation from increasing or decreasing finely and to obtain a smooth approximate curve, the number of terms in the function of equation (6) is obtained. That is, the number of coefficients A _k and B _k is set to a predetermined number obtained by reducing the number of data of the image data group obtained in step ST1, and the first data group is regressed to the Fourier series. The number p of Fourier series terms was set to 35 for all data groups of the original data group, the single data group, the two data group, and the three data group. This value is 5% of the number of data of the original data group, 7% of the number of data of the data group of the one-out data group, 9% of the number of data of the two-out data group, and the number of data of the data group of the three-out data group 11%.

  Then, in order to solve the problem of an increase in error in the rear part of each data group due to the reduction in the number of terms p, the vertical axis passing through the last data of each data group, as in Analysis Example 1. An additional data group is created as a data group that is line-symmetric with respect to the original data group (step ST2), and this is added to each first data group, whereby the original data group, the data group without data, and the two data groups A regression data group was generated for each of the extracted data group and the three extracted data groups (step ST3), and regressed to the Fourier series of the number of terms based on equation (6) (step ST4).

  FIGS. 14A to 14D are obtained by regressing a regression data group obtained from the original data group, the one-out data group, the two-out data group, and the three-out data group into a Fourier series, respectively. It is graph SGDC1-SGDC4 of an approximate curve. 14A to 14D, the horizontal axis represents the distance [mm] from the reference position A on the measurement axis MAL, as in FIG. 6A, and the vertical axis represents the luminance. Yes.

  As can be seen from FIG. 14 (a), in the approximate curve SGDC1, the fine increase / decrease of the original data group GDC1 shown in FIG. 6 (a) is deleted and smooth enough to specify the stripe position of the color matching line LC. A curve is obtained, and the approximate curve SGDC1 coincides with the approximate curve FGDC1 in FIG. 6B, and the effectiveness of the regression to the Fourier series using Simpson integration was confirmed.

  Further, as shown in FIG. 14 (b), in SGDC2, the fine increase / decrease of GDC2 in FIG. 13 (a) is deleted, and a smooth curve sufficient for specifying the stripe position of the color matching line LC is obtained. It was.

  Further, in SGDCs 3 and 4 shown in FIGS. 14C and 14D, the fine increase / decrease of GDCs 3 and 4 in FIGS. 13B and 13C is deleted, but the smoothness of the curve is not sufficient. .

  Subsequently, for SGDC1 and SGDC2, the fringe positions of the color matching lines LC were identified by the same method as in Analysis Example 1 (Step ST5), and the fringe positions almost identical to Analysis Example 1 could be identified.

Analysis example 5
In analysis example 5, linear interpolation is performed on the two data groups sampled at unequal intervals created in analysis example 4 and the three data groups sampled to create data groups at equal intervals. The image data group is the first data group of the present invention. As a result, the number of data in each first data group is 652.

Then, the generation of the additional data group (step ST2) and the generation of the data group for regression (step ST3) are performed by the same method as in the analysis example 4, and the regression to the Fourier series using the Simpson integral of Equation (6) is performed. (Step ST4). The number of terms in the Fourier series is 35, which is about 5% of the number of data (652) in each first data group.

  FIGS. 15A and 15B are Fourier series regression curves obtained for the data group without two and the data group without three according to Analysis Example 5, respectively. 15A and 15B, the horizontal axis represents the distance [mm] from the reference position A, and the vertical axis represents the luminance.

  As is clear from the figure, the fine increase / decrease was deleted, and a smooth curve sufficient for specifying the stripe position of the color matching line LC was obtained.

  Subsequently, the fringe position was identified (step ST5) by the same method as in Analysis Example 1, and the fringe position almost identical to Analysis Example 1 could be identified.

Analysis example 6
In the analysis example 6, the Fourier series using the Simpson integration of the equation (6) is applied to the isotropic line position data (data in FIG. 11A) which is the data sampled at unequal intervals obtained in the analysis example 3. Returned to.

  Here, 15 pieces of data (distance of 0 and near 38 mm) in which the distance from the reference position on the horizontal axis hardly changes depending on the angle among the 91 isosceles position data are excluded from the target. The remaining 76 data are set as analysis target data, and 619 data sampled at equal intervals with respect to the distance from the reference position on the horizontal axis are generated by performing linear interpolation in the same manner as in Analysis Example 5. Using this as the first data group, generation of additional data, generation of regression data, and regression to the Fourier series were performed in the same manner as in Analysis Example 5. The number of terms in the Fourier series is 35, which is about 5% of the number of data (619) in the first data group.

The Fourier regression curve thus obtained is shown in FIG. 16A, and the first data group is plotted in FIG. 16B. In FIGS. 16A and 16B, the horizontal axis represents the distance [mm] from the reference position, and the vertical axis represents the angle [degree]. In addition, although the first data group is discrete data, in FIG. 16B, individual data are connected and displayed by a solid line.

  FIG. 16 (a) is a smooth curve that does not show a fine increase and decrease, and the overall shape is an isotropic line of 11 (a) compared to 11 (b) obtained by the least square method. It can be seen that the shape is closer to the position data or the linear interpolation of FIG. 16B.

  As described above, in the present embodiment, based on the discrete image data group sampled at equal intervals or the discrete image data group sampled at unequal intervals, the number of data is the number of image data groups. Data for regression that is a predetermined multiple of the number of data is generated, and the regression data is regressed to a Fourier series in which the number of terms is smaller than the number of data in the image data group to approximate the original image data group. As a result, each data of the data group obtained by the approximation changes smoothly and the accuracy of the approximation is improved.

  Since a smooth and highly accurate approximation result can be obtained in this way, for example, it becomes possible to greatly automate the analysis of image data, such as specifying the positions of isochromatic lines and isoclinic lines. At that time, by reducing the number of terms of the Fourier series to be regressed, the calculation time for the regression can be shortened.

  Although not described, in the above embodiment, even when the sampling interval is set to dx = 0.12 mm and the interval dy is set to dy = 0.4 mm, it is smooth and highly accurate as in Analysis Examples 1 to 3. An approximate curve could be obtained.

  Subsequently, as a second embodiment of the present invention, the present invention is applied to generate terrain elevation data using a color matching line image observed in a photoelasticity experiment, and 3 based on the terrain elevation data. A case where a two-dimensional terrain image is generated will be described.

  In this embodiment, the photoelasticity experimental apparatus of FIG. 1 used in the first embodiment is used.

  FIG. 17A is a plan view of the specimen 107 used in the present embodiment, and FIG. 17B is an elevation view of the load table 134.

  As shown in FIG. 17A, in the present embodiment, a specimen made of a rectangular DAP plate having a length and width of 150 mm × 230 mm and a thickness of 6 mm was used.

  This specimen 107 is intended to generate topographic elevation data of a round road from a substantially rectangular round area having a long side of 130 mm, a short side of 50 mm, and a width of 1 mm indicated by a broken line 171 in the figure. Nine openings 172 are formed in the periphery of the surrounding region 171 so that an appropriate stress mainly including an axial force is generated in the region 171 and a smooth striped pattern of uniform color lines is observed.

  In addition to the opening 172, the specimen 107 is provided with five circular attachment holes 107 a for attaching the specimen 107 to the load table 134.

  As shown in FIG. 17 (b), the load platform 134 is similar to the load platform 34 used in the first embodiment in that the balance weight WB and the weight M are attached to the load arm 134a attached to the frame 134b at the fulcrum 134p. Is attached, and a load is applied to the specimen through the load 109. Further, reference numerals 134c and 134d in the figure denote frames for attaching the specimen 107.

  FIG. 18A shows the second polarization in the optical system 3 of the photoelasticity experimental apparatus in which the reference position markers of both the first and second quarter-wave plates 33 and 35 are aligned at 45 degrees. It is a photographed image of color matching lines appearing on the specimen photographed by the digital camera 40 with the reference position marker of the plate 36 being set to the 0 degree position.

  In the present embodiment, as shown in FIG. 18B, only the surrounding area is extracted from the captured image obtained in this manner by painting the periphery of the surrounding area 171 black, and the right half of the surrounding area is extracted. The luminance value was converted into a numerical value by converting the above image into a gray scale of 256 levels.

  FIG. 19A is an enlarged view of a curved portion of the circular region 171. FIG. 19B shows a luminance value for each pixel for a part of the curved portion. As shown in FIG. 19 (b), the image of this circular area includes 13 pixels in the width direction. The extending direction of the circular area includes 2596 pixels on the inner periphery of the circular area and 2650 pixels on the outer periphery, and generates 13 rows × 2596 to 2650 columns of luminance value data from these pixels. Can do.

  Hereinafter, according to the flowchart shown in FIG. 20, the procedures for generating the topographic elevation data and generating the three-dimensional topographic image in the present embodiment will be described.

  Each of the data groups composed of luminance values of 2596 to 2650 pixels included in the 13 rows of pixels from the inner periphery to the outer periphery of the circular region 171 in FIG. 18B is defined as the first data group of the present invention. (Step ST11).

  Subsequently, an additional data group is created as a data group that is line-symmetric with respect to the last data of each of the 13 first data groups by the same procedure as in Analysis Example 1 of the first embodiment. (Step ST12), this is added to each first data group to generate a data group for regression (step ST13), and this is regressed to a Fourier approximation curve according to equation (3) ( Step ST14). At this time, the number of terms p of the Fourier series was 5% of the number of data in each first data group.

  And the luminance value by the Fourier approximation curve obtained in this way was dxf converted and displayed as a three-dimensional mesh image (step ST15). Here, ArchiCAD7 (Graphic Software) is used to display a three-dimensional mesh image, but other three-dimensional display software may be used.

  FIGS. 21A and 21B are displays of the Fourier approximation curve of the curve portion and the straight line portion thus obtained. FIGS. 21C and 21D show the first curved line part and the first data group of the straight line part as they are dxf-transformed and displayed as a three-dimensional mesh image.

  As is clear from FIG. 21, the display of the Fourier approximation curve (21 (a), (b)) is a smooth display with little unevenness in both the curved portion and the straight portion.

  In addition, in order to obtain a realistic road elevation value from the luminance value obtained by the Fourier approximation curve obtained in this way, linear transformation is performed using an appropriate proportional constant, and similarly created with realistic dimensions. FIG. 22A shows what is displayed together with image data representing the scenery around the road.

  FIG. 22B shows comparison data between the measured value of the first data group in the vicinity of the center in the width direction of the circulation region and the approximate value based on the Fourier approximate curve, and the approximate value / measured value is 1 in the curve portion. .01, 1.00 in the straight line portion, and it can be seen that the Fourier approximation curve accurately reproduces the measured value of the first data group.

  In this way, by using a color-matched line image, an isoclinic line image, or the like in a photoelasticity experiment, topographic elevation data and a topographic three-dimensional display image can be obtained very easily. Further, by changing the shape of the specimen and the manner in which the load is applied, it is possible to obtain terrain altitude data and three-dimensional terrain images that express terrains of various different shapes.

  In addition, the number of terms in the Fourier series is reduced and the number of data is increased by adding an additional data group, so that a smooth and natural three-dimensional topographic image can be obtained with a smaller calculation load.

  Subsequently, as a third embodiment of the present invention, a case where the altitude numerical map is refined by applying the present invention will be described.

  In the present embodiment, the altitude numerical value map is refined by the same procedure as that in the second embodiment shown in the flowchart of FIG.

  The altitude map used as the target is a numerical map of the topographic altitude at a scale of 1/25 in the southeastern part of Saitama Prefecture, published by the Geospatial Information Authority of Japan on June 1, 2003. (Near Miyamoto 2-chome Minuma Hikawa Park / Geographical Survey Institute numerical map number 09kd462) and Toda City data near the flat area (Near Shigese / Geographical Survey Institute numerical map number 09kd654) were used.

  In this numerical map, altitude values of 400 rows (2 km) in the east-west direction and 300 columns (1.5 km) in the north-south direction are recorded in a 5 m mesh. FIG. 23 shows a part of data of Midori Ward.

  First, by linearly interpolating the data of 400 rows × 300 columns, the altitude numerical data of 2000 rows × 1500 columns is generated with 1 m mesh, and the arrangement of 2000 data in the east-west direction of the first column is unified. From the second column to the 1500th column, each of the 2000 data rows is regarded as one data group, and each data group is defined as a first data group of the present invention ( Step S11).

  Subsequently, an additional data group is created as a data group that is line-symmetric with respect to the last data of each first data group by the same procedure as in Analysis Example 1 of the first embodiment (step ST12). This is added to each first data group to generate a regression data group (step ST13), and this is regressed to a Fourier approximation curve according to equation (3) (step ST14). At this time, the number of terms p of the Fourier series was 5% of the number of data in each first data group.

  Then, the approximate value obtained by the Fourier approximation curve obtained in this way is dxf transformed, and the three-dimensional image display software Shade 6, Pro. , (X Tool Co., Ltd.) and displayed as a three-dimensional image (step ST15). Since the dxf conversion data has too much capacity and cannot be read by this software, this data is divided into 16 parts, and after dxf conversion (55.2 MB), it is taken in and combined again and displayed as 4-partition data (1000 x 750). I let you.

  The three-dimensional display of the 1 m mesh of Midori Ward and Toda City obtained in this way is shown in Figs. 24 (a) and 24 (b), and the surface with different shades depending on the altitude value is attached to the mesh. The topographic images are shown in FIGS. 25 (a) and 25 (b), and enlarged displays of the images are shown in FIGS. 26 (a) and 26 (b). As a comparison, altitude values in the altitude numerical maps of Midori Ward and Toda City are converted as they are into dxf, and then Shade 6, Pro. The three-dimensional terrain image obtained by pasting the surface in the same manner as described above in FIGS. 24C and 24D and the enlarged display thereof are shown in FIGS. 25C and 25D. 26 (c) and 26 (d).

  As is apparent from FIGS. 24 to 26, compared to an altitude value displayed as a 5 m mesh, an approximate value obtained by Fourier transform displayed as a 1 m mesh has a smooth curve display with less unevenness, and In addition, a three-dimensional image with a surface attached thereto also has a smooth curved line display with less unevenness than that using an altitude value as it is, and has a smooth curve display with less unevenness. It was possible to generate an image with a sense of reality that could be used as

  In the present embodiment, the example in which the arrangement of the data in the east-west direction (row direction) is analyzed as the first data group has been described. However, 1500 pieces of data in the north-south direction (column direction) are described. The same result can be obtained even if each of the arrangements is analyzed as the first data group, or an approximate curve with each arrangement of data in the row direction (or column direction) as the first data group. The approximate value of the altitude value in the row direction (or column direction) is derived again from the approximate curve, and this approximate value and the array of data in the column direction (or row direction) of the interpolation value are derived. It is also possible to obtain approximate curves using each as the first data group.

  Subsequently, as a fourth embodiment of the present invention, by applying the present invention, quantification of a characteristic portion in an image such as an affected area is performed using an X-ray image captured at a medical institution or the like. The case where it performs is demonstrated.

  FIG. 27 (a) is a photographed image composed of pixels of 220 rows (vertical) × 445 columns (horizontal) in the vertical and horizontal directions of the mammogram as an example of such an X-ray image, and FIG. 27 (b). Dxf-converts the luminance value of each pixel of the photographed image, and the three-dimensional display software Shade 6, Pro. , Are used to display as a three-dimensional image with the vertical and horizontal directions in FIG. 27A and the luminance values of the respective pixels as three orthogonal axes.

  Although a benign calcified portion is photographed with a small white dot at the center left in FIG. 27A, the three-dimensional display in FIG. It is difficult to analyze.

  Therefore, in the present embodiment, the data direction of the luminance values of the pixels of 220 rows × 445 columns obtained from the captured image of FIG. 27A is targeted according to the flowchart shown in FIG. 28 in the row direction (horizontal direction). Approximation was performed by regressing from the column direction (vertical direction) to the Fourier series.

  That is, the arrangement of 445 data in each row from the first row to the 220th row of the photographed image of FIG. 27A is set as the first data group of the present invention (step ST21), and the first implementation is performed. An additional data group is created as a data group that is line-symmetric with respect to the last data of each first data group by the same procedure as in Analysis Example 1 in the form (step ST22). By adding to the data group 1, a regression data group was created (step ST23), and the regression data group was regressed to a Fourier approximation curve according to equation (3) (step ST24). At this time, the number of terms p of the Fourier series is set to 5% of the number of data of each first data group in step ST21.

  Further, in step ST24, 220 luminance value data in each column of the luminance value data of 220 rows × 445 columns generated by deriving the value (luminance value) of each column position in the Fourier approximation curve obtained for each row. Each of these sequences is once again made the first data group of the present invention (step ST25).

  Then, an additional data group is created as a data group that is line symmetric with respect to the last data of each first data group generated in step ST25 (step ST26). By adding to the data group 1, a regression data group was created (step ST27), and the regression data was regressed to a Fourier approximation curve according to equation (3) (step ST28). At this time, the number of terms p of the Fourier series is set to 5% of the number of data of each first data group in step ST25.

  FIG. 29 (a) shows a bitmap display of approximate values obtained by the Fourier approximation curve obtained by the above processing, and this approximate value is converted by dxf, and the three-dimensional display software Shade 6, Pro. FIG. 29B shows a three-dimensional image displayed using,.

  Compared with FIG. 27B, FIG. 29B is a smooth curve from which fine increase / decrease has been deleted. On the other hand, as seen in FIG. There is a possibility that detailed information such as the shape of the calcified portion is lost due to the regression.

  Therefore, for the data group of luminance values that are divided into 5 equal parts between each row and each column of pixels of 220 rows × 445 columns and linearly interpolated between them, the above and Similarly, according to the flowchart shown in FIG. 28, approximation was performed by regressing the Fourier series from the row direction and the column direction.

  FIG. 30A is a bitmap display of the approximate value obtained by this, confirming that detailed information such as the shape of the calcified portion is reproduced, and in the row direction and the column direction. As shown in FIG. 30B, which is a comparison data between the approximate value near the maximum value and the actual measurement value, the approximate value / actual value of the row direction average value is 1.0049, and the approximate value / measurement value of the column direction average value The value was 0.9980, which was confirmed to be an approximate value that accurately reflected the original data. However, the data in FIG. , 3D display could not be performed.

  For this reason, an image portion of 132 rows × 144 columns including a calcified portion is cut out from the photographed image of FIG. 27A (FIG. 31A), and each row and each column of pixels of the image portion have 5 pixels. According to the flowchart shown in FIG. 28, the luminance value data group that is equally divided and linearly interpolated between them to make the data finer to 660 rows × 720 columns is returned to the Fourier series from the row direction and the column direction. An approximation was made.

  The bitmap display of the approximate value of the Fourier approximate curve by the five-part linear interpolation is shown in FIG. 31B, and this approximate value is converted by dxf, and the three-dimensional display software Shade 6, Pro. FIG. 31 (c) shows an image displayed as a three-dimensional image using.

  Similarly, a 96-row × 99-column image portion including a calcified portion is cut out from the photographed image in FIG. 27A (FIG. 32A), and the pixels in each row and each column of the image portion are respectively separated. Returning to the Fourier series from the row direction and the column direction according to the flowchart shown in FIG. 28, for the luminance value data group divided into seven equal parts and linearly interpolated between them to make 672 rows x 693 columns fine. Approximation was performed.

  The bitmap display of the approximate value of the Fourier approximate curve by the seven-part linear interpolation is shown in FIG. 32B, and this approximate value is converted by dxf, and the three-dimensional display software Shade 6, Pro. , Are displayed as a three-dimensional image, and FIG. 33 (d) shows a three-dimensional image with the viewpoint of 45 degrees upward.

  As shown in FIG. 31 (b) and FIG. 32 (b), by using the approximate value obtained by regressing the data obtained by linear interpolation into five or seven equal parts according to the method of the present invention to the Fourier series, It was confirmed that a bitmap image with almost no difference from the X-ray image (FIG. 27A) as an image can be reproduced.

  Further, as shown in FIGS. 31 (c), 32 (c), and (d), approximate values obtained by regressing the data obtained by linearly dividing into five or seven equal parts according to the method of the present invention to the Fourier series. By displaying these three-dimensionally, it is possible to display the features of the changed portions of the luminance value in the image such as the calcified portion in a manner that can be easily visually recognized as convex portions or concave portions in the three-dimensional image.

  Further, as is clear from FIGS. 31 (c), 32 (c), and (d), these convex portions and concave portions have smooth function shapes from which fine increase / decrease has been deleted. It is also possible to automatically derive feature quantities such as height and volume on a computer, and thus screen images for which feature quantities exceeding a predetermined reference value are detected as targets for visual inspection by doctors, etc. The analysis result in this embodiment can also be used for automatic diagnosis of a disease state.

  The present invention can be used for the analysis of image data of isochromatic lines and isoclinic lines in photoelastic experiments.

  The present invention is not limited to image data in a photoelasticity experiment, and can be used for analysis of data of other images. By applying the present invention, for example, in the medical field, an image data such as an X-ray image, a magnetic resonance image, or an ultrasonic image is analyzed to extract a characteristic portion, and a medical condition is automatically diagnosed. Is possible. In addition, for example, in the field of image recognition and image conversion, it is possible to easily extract and use a feature portion from captured image data.

  The present invention is not limited to image data, and can be applied to various data such as discrete measurement data as long as the data is regressed to a Fourier series.

  In addition, according to the present invention, terrain elevation data representing various terrain shapes is generated from the luminance values of each pixel of an image obtained by photographing isochromatic lines and isoclinic lines in a photoelasticity experiment, and three-dimensional data is generated based on the terrain elevation data A topographic image can be generated.

  Further, not only the luminance value but also other types of numerical data such as R value, G value, and B value can be derived from such an image to generate terrain elevation data and a three-dimensional terrain image.

  Moreover, not only the image data obtained by the photoelasticity experiment but also any other type of image data can be used to generate terrain elevation data and a three-dimensional terrain image.

  In addition, according to the present invention, the altitude numerical data can be refined, and a more precise and smooth three-dimensional terrain image can be generated.

  The terrain elevation data thus generated and the three-dimensional terrain image can be used in a wide range of fields such as CG images used in games and video production, floor plans in land development, and three-dimensional guide boards.

It is a schematic block diagram of the photoelasticity experimental apparatus which concerns on one embodiment of this invention. (A) is a top view of the specimen used in one embodiment, and (b) is an elevation view of the load table. It is a figure for showing the field which performs analysis processing among the image data of the photographing surface of the specimen obtained by a photoelasticity experiment. It is a flowchart which shows the procedure of the data analysis method which concerns on one embodiment of this invention. It is a figure which shows an example of the same color line which appears on the imaging surface of a test body. It is a graph of the image data group obtained in the analysis example 1, (a) is a graph of the data group regressed to a Fourier series, (b) is obtained by regressing the data group shown in (a) to a Fourier series. It is a graph of an approximate curve. It is an enlarged view of the opening part vicinity of a test body. It is a graph of the image data group obtained in the analysis example 2, (a) is a graph of the data group regressed to a Fourier series, (b) is obtained by regressing the data group shown in (a) to a Fourier series. It is a graph of an approximate curve. It is the figure which expanded and showed the cross-section horizontal part of the vicinity of an opening part about an example of the equi-gradient line which appears on the imaging surface of a specimen. It is a graph of the image data group obtained in the analysis example 3, (a) is a graph of the data group regressed to a Fourier series, (b) is obtained by regressing the data group shown in (a) to a Fourier series. It is a graph of an approximate curve. (A) is a graph of isotropic line position data obtained in Analysis Example 3, and (b) is a graph of an approximate curve obtained by approximating the isotropic line position data shown in (a) by the least square method. . It is explanatory drawing which shows the method of the data deletion performed in order to produce the data sampled at unequal intervals. It is a graph of the data used in the analysis example 4, (a) is a data group without 1 piece, (b) is a data group without 2 pieces, (c) is a graph of data group without 3 pieces. It is a graph obtained in Analysis Example 4, and (a) to (d) are obtained by regressing the original data group, the one-out data group, the two-out data group, and the three-out data group, respectively, into a Fourier series. It is a graph obtained. It is a graph obtained in the analysis example 5, (a) is a graph obtained about a data group without 2 pieces, (b) is a graph obtained about a data group with 3 pieces removed. It is a graph obtained in the analysis example 6, (a) is a graph obtained by regressing to a Fourier series, (b) is a graph of the data group regressed to a Fourier series. (A) is a top view of the test body used in 2nd Embodiment, (b) is an elevational view of a load stand. It is a figure which shows the example color-matching line which appears on the imaging surface of a test body. (A) is an enlarged view of the curved portion of the circular region, and (b) shows the luminance value for each pixel in a part of the curved portion of the circular region. It is a flowchart which shows the procedure of the data analysis method which concerns on other embodiment of this invention. (A), (b) is a three-dimensional display of the Fourier approximation curve of the Fourier approximation curve obtained in the second embodiment for the curved portion and the straight portion of the round road, respectively. Each of d) is a three-dimensional display of the first curve group and the first data group of the straight line portion. (A) is a combined display of a Fourier approximation curve of a round road and an image showing the surrounding landscape, and (b) is a measured value of the first data group and a Fourier approximation curve near the center in the width direction of the round area. It is the comparison data with the approximate value by. It is explanatory drawing which shows a part of data content of the numerical map of topographic elevation. (A) and (b) are three-dimensional representations of approximate values based on a Fourier approximation curve obtained by the third embodiment of the present invention for Midori Ward and Toda City, and (c), (D) is a three-dimensional display of altitude values of a numerical map with a 5 m mesh. FIGS. 25A to 25D are three-dimensional terrain images obtained by pasting the meshes of FIGS. 24A to 24D with different shades depending on the altitude value. 26A to 26D are enlarged views of FIGS. 25A to 25D. (A) is explanatory drawing which shows the example of the X-ray radiography image by mammography, (b) is the vertical-horizontal direction of the said X-ray radiography image, and each pixel of the luminance value of this X-ray radiography image Is displayed as a three-dimensional image having three orthogonal axes. It is a flowchart which shows the procedure of the data analysis method which concerns on other embodiment of this invention. FIG. 29 (a) is a bitmap display of approximate values of the luminance values of the captured image of FIG. 27 (a) using a Fourier approximate curve, and 29 (b) is a three-dimensional display of the approximate values. FIG. 30A is a bitmap display of approximate values by Fourier approximation curves of luminance value data linearly interpolated in five equal parts, and FIG. 30B shows the vicinity of the maximum values in the row direction and the column direction. It is comparison data of an approximate value and an actual measurement value. FIG. 31A is an image portion cut out from the captured image of FIG. 27A, and FIG. 31B is a bitmap of approximate values obtained by Fourier approximation curves of the quintuple linear interpolation data of the portion. Fig. 31 (c) is a three-dimensional display of this approximate value. FIG. 32A is an image portion cut out from the photographed image of FIG. 27A, and FIG. 32B is a bitmap of approximate values obtained by Fourier approximation curves of seven-part linear interpolation data of the portion. FIGS. 32C and 32D are three-dimensional displays of the approximate values.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 ... Photoelasticity experimental apparatus 3 ... Optical system 5 ... Data analysis apparatus 7, 107 ... Specimen 7S, 107S ... Imaging surface 40 ... Digital camera 51 ... CPU (processing apparatus, processing part)
53 ... Data driver 55 ... Storage device 57 ... Image driver 70, 172 ... Opening LX ... Optical axis MAL ... Measurement axis MPL ... Measurement line

Claims (21)

A data analysis method for performing a predetermined process by a processing device on analysis target data that is a set of discrete data and performing regression to Fourier series,
A symmetric data group is added to the first data group, which is a set of discrete data, to the last data of the first data group, and the number of data is a natural number times the number of data in the first data group. Generating a second data group that is:
Data that causes the processing device to execute a step of setting a Fourier series term number to a predetermined number smaller than the number of data of the first data group and regressing the second data group to the Fourier series. analysis method.   The first data group is generated by adding a third data group generated by linearly interpolating the analysis target data to the analysis target data. Data analysis method.   3. The step of generating the second data group, wherein the number of data in the second data group is an even multiple of the number of data in the first data group. Data analysis method. The data analysis according to any one of claims 1 to 3, wherein the data to be analyzed is image data obtained from an isochromatic line image or an isoclinic line image in a photoelasticity experiment. Method.   The data analysis method according to claim 1, wherein the analysis target data is an altitude value at a discrete position.   The data analysis method according to claim 1, further causing the processing device to further generate a three-dimensional terrain image using an approximate value obtained from the Fourier series. .   The data analysis method according to claim 1, wherein the data to be analyzed is image data obtained from an X-ray image. A data analysis device for performing a predetermined process on analysis target data that is a set of discrete data and performing regression to Fourier series,
A symmetric data group is added to the first data group, which is a set of discrete data, to the last data of the first data group, and the number of data is a natural number times the number of data in the first data group. A second data group is generated, the number of terms in the Fourier series is set to a predetermined number smaller than the number of data in the first data group, and the second data group is returned to the Fourier series. A data analysis apparatus characterized by that.   9. The first data group is generated by adding a third data group generated by linearly interpolating the analysis target data to the analysis target data. Data analysis device.   The control unit, when generating the second data group, makes the number of data of the second data group an even multiple of the number of data of the first data group. The data analysis device described in 1.   The data analysis apparatus according to any one of claims 8 to 10, wherein the analysis target data is image data obtained from an isochromatic line image or an isoclinic line image in a photoelasticity experiment. .   The data analysis apparatus according to claim 8, wherein the analysis target data is an altitude value at a discrete position.   The data analysis apparatus according to any one of claims 8 to 12, wherein the processing unit further generates a three-dimensional terrain image using an approximate value obtained from the Fourier series.   The data analysis apparatus according to any one of claims 8 to 10, wherein the analysis target data is image data obtained from an X-ray image. A data analysis program for causing a computer processing device to execute predetermined processing on analysis target data that is a set of discrete data and performing regression to Fourier series,
A symmetric data group is added to the first data group, which is a set of discrete data, to the last data of the first data group, and the number of data is a natural number times the number of data in the first data group. Generating a second data group that is:
Data that causes the processing device to execute a step of setting a Fourier series term number to a predetermined number smaller than the number of data of the first data group and regressing the second data group to the Fourier series. Analysis program.   16. The first data group is generated by adding a third data group generated by linearly interpolating the analysis target data to the analysis target data. Data analysis program.   17. The step of generating the second data group, wherein the number of data of the second data group is an even multiple of the number of data of the first data group. Data analysis program.   The data analysis program according to any one of claims 15 to 17, wherein the analysis target data is image data obtained from a color matching line image or an isotropic line image in a photoelasticity experiment. .   The data analysis program according to any one of claims 15 to 17, wherein the analysis target data is an altitude value at a discrete position.   20. The data analysis program according to claim 15, further causing the processing device to execute a step of generating a three-dimensional terrain image using an approximate value obtained from the Fourier series. . The data analysis program according to any one of claims 15 to 17, wherein the analysis target data is image data obtained from an X-ray image.

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