Data processing method and system for cross-sectional images of analytical materials

Abstract

This invention provides a data processing method and system for cross-sectional images of analytical materials that can accurately remove unwanted scratches caused by material cutting present in the cross-sectional images of the analytical materials. [Solution] In a data processing method for a cross-section image of an analytical material that uses Fourier transform and inverse Fourier transform as data processing to remove knife marks N (unwanted scratches) caused by material cutting present in the original image D1 of the cross-section Sa of the analytical material, a two-dimensional Fourier transform is applied to the original image D1 to create a spatial frequency spectrum D2, an extracted spatial frequency spectrum D3a is created by extracting the knife mark component Fn from the spatial frequency spectrum D2, a two-dimensional inverse Fourier transform is applied to the extracted spatial frequency spectrum D3a to create a scratch image D4a, and a data processing device 2 is performed to subtract the component of the scratch image D4a from the original image D1 to obtain a processed image D5 from which the knife marks N have been removed.

Description

Technical Field

[0001] The present invention relates to a data processing method and system for a cross-sectional image of an analysis material, and more particularly, to a data processing method and system for a cross-sectional image of an analysis material that can accurately remove unnecessary scratches caused by material cutting present in the cross-sectional image of the analysis material.

Background Art

[0002] When analyzing the internal structure of a rubber material or the like, for example, observing a cross-sectional image of the material is performed. Unnecessary scratches caused by material cutting exist in this cross-sectional image. These unnecessary scratches become noise when observing the cross-sectional image to accurately grasp the internal structure.

[0003] As described in Patent Document 1, generally, for noise removal in image data, noise removal filters such as Gaussian filters and median filters are used (see paragraph 0025). However, in data processing using these noise removal filters, the above-mentioned unnecessary scratches (noise) cannot be accurately removed. Therefore, there is room for improvement in accurately removing this unnecessary scratch (noise) in the cross-sectional image.

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0005] An object of the present invention is to provide a data processing method and system for a cross-sectional image of an analysis material that can accurately remove unnecessary scratches caused by material cutting present in the cross-sectional image of the analysis material.

Means for Solving the Problems

[0006] A first data processing method for a cross-section image of an analytical material that achieves the above objective is a data processing method for a cross-section image of an analytical material that uses Fourier transform and inverse Fourier transform as data processing to remove unwanted scratches caused by material cutting that are present in the original image of the cross-section of the analytical material, characterized in that a two-dimensional Fourier transform is applied to the original image to create a spatial frequency spectrum, an extracted spatial frequency spectrum is created from the spatial frequency spectrum in which the unwanted scratch components are extracted, a two-dimensional inverse Fourier transform is applied to the extracted spatial frequency spectrum to create a scratch image that can be considered to have only the unwanted scratch components, a data processing device performs to subtract the components of the scratch image from the original image, and a processed image from which the unwanted scratches have been removed is obtained.

[0007] The second data processing method for a cross-section image of an analytical material according to the present invention is a data processing method for a cross-section image of an analytical material that uses Fourier transform and inverse Fourier transform as data processing to remove unwanted scratches caused by material cutting present in the original image of the cross-section of the analytical material, characterized in that a unidirectional Fourier transform is applied to the target image to create a frequency spectrum, then a deselected frequency spectrum is created by removing predetermined low-frequency components from the frequency spectrum, then the unidirectional inverse Fourier transform is applied to the deselected frequency spectrum to create an inverse transformed image, and then a predetermined blurring process is applied to the inverse transformed image to create a blurred image, and this series of processing steps is repeated a predetermined number of times by a computing device, using the original image as the initial target image and the blurred image created in the previous series of processing steps as the target image for subsequent steps, and in the preceding and succeeding series of processing steps, the unidirectional direction is alternately changed between the horizontal and vertical directions, and the inverse transformed image created in the last series of processing steps is obtained as a processed image from which the unwanted scratches have been removed from the original image.

[0008] The third data processing method for a cross-section image of an analytical material according to the present invention is a data processing method for a cross-section image of an analytical material that uses Fourier transform and inverse Fourier transform as data processing to remove unwanted scratches caused by material cutting present in the original image of the cross-section of the analytical material, characterized in that a predetermined blurring process is applied to the target image to create a blurred image, then a unidirectional Fourier transform is applied to the blurred image to create a frequency spectrum, then a deselected frequency spectrum is created by removing predetermined low-frequency components from the frequency spectrum, and then the unidirectional inverse Fourier transform is applied to the deselected frequency spectrum to create an inverse transformed image, and this series of processing steps is repeated a predetermined number of times by a computing device, using the original image as the initial target image and the inverse transformed image created in the previous series of processing steps as the target image for subsequent steps, and in the preceding and succeeding series of processing steps, the unidirectional direction is alternately changed between the horizontal and vertical directions, and the inverse transformed image created in the last series of processing steps is obtained as a processed image from which the unwanted scratches have been removed from the original image.

[0009] The first data processing system for a cross-section image of an analytical material according to the present invention is a data processing system for a cross-section image of an analytical material comprising a computing device that performs Fourier transform and inverse Fourier transform as data processing to remove unwanted scratches caused by material cutting present in the original image of the cross-section of the analytical material, and an output device, wherein the computing device has a calculation unit, a storage unit, and an input unit, the original image is input to the storage unit through the input unit, the calculation unit performs a two-dimensional Fourier transform on the original image to create a spatial frequency spectrum, an extracted spatial frequency spectrum is created by extracting the component of the unwanted scratches from the spatial frequency spectrum, a two-dimensional inverse Fourier transform is performed on the extracted spatial frequency spectrum to create a scratch image that can be considered to have only the component of the unwanted scratches, data processing is performed to subtract the component of the scratch image from the original image, and a processed image from which the unwanted scratches have been removed is output to the output device.

[0010] The second invention of the present invention is a data processing system for a cross-section image of an analytical material, comprising a computing device that performs Fourier transform and inverse Fourier transform as data processing to remove unwanted scratches caused by material cutting present in the original image of the cross-section of the analytical material, and an output device, wherein the computing device has a computing unit, a storage unit, and an input unit, the original image is input to the storage unit through the input unit, a one-way Fourier transform is applied to the target image to create a frequency spectrum, then a deselected frequency spectrum is created by removing predetermined low-frequency components from the frequency spectrum, and then the deselected frequency spectrum is subjected to the A series of processing steps is performed by the calculation unit a predetermined number of times, in which a one-way inverse Fourier transform is applied to create an inversely transformed image, and then a predetermined blurring process is applied to the inversely transformed image to create a blurred image. In the first step, the original image is used as the target image, and in subsequent steps, the blurred image created in the previous processing step is used as the target image. In the preceding and succeeding processing steps, the one-way direction alternates between the horizontal and vertical directions, and the inversely transformed image created in the last processing step is output to the output device as a processed image from which the unwanted scratches have been removed from the original image.

[0011] The third data processing system for images of cross-sections of analytical materials according to the present invention is a data processing system for images of cross-sections of analytical materials comprising a computing device that performs Fourier transform and inverse Fourier transform as data processing to remove unwanted scratches caused by material cutting present in the original image of the cross-section of the analytical material, and an output device, wherein the computing device has a computing unit, a storage unit, and an input unit, the original image is input to the storage unit through the input unit, a predetermined blurring process is applied to the target image to create a blurred image, then a one-way Fourier transform is applied to the blurred image to create a frequency spectrum, and then a predetermined low-frequency component is removed from the frequency spectrum A series of processing steps is performed by the calculation unit a predetermined number of times, wherein the original image is used as the target image for the first step, and the inverse Fourier transform created in the previous step is used as the target image for subsequent steps, and the unidirectional direction alternates between horizontal and vertical in the preceding and succeeding steps, and the inverse transform created in the last step is output to the output device as a processed image from which the unwanted scratches have been removed from the original image. [Effects of the Invention]

[0012] According to the present invention, by using the Fourier transform and the inverse Fourier transform as the data processing, the unwanted scratches in the original image and the other parts can be distinguished by the degree of difference in their respective frequency components. As a result, a processed image can be obtained from which the unwanted scratches have been removed from the original image.

[0013] In the first data processing method and system for cross-sectional images of analytical materials of the present invention, it is utilized that the periodicity of the unwanted scratch component is stronger than the periodicity of the other components in the spatial frequency spectrum obtained using a two-dimensional Fourier transform. The scratch image is obtained by retaining the unwanted scratch component with stronger periodicity in the spatial frequency spectrum. By subtracting the component of the scratch image from the original image, the processed image can be obtained in which the unwanted scratches in the original image have been accurately removed.

[0014] In the second and third data processing methods and systems for cross-sectional images of analytical materials of the present invention, it is utilized that in the frequency spectrum obtained using a unidirectional Fourier transform, the unwanted defect component appears as a predetermined low-frequency component. By repeating the series of processing steps of unidirectional Fourier transform, removal of the predetermined low-frequency component, and unidirectional inverse Fourier transform, the pixel value of each pixel decreases (approaches black), and the difference between the pixel value of each pixel constituting the unwanted defect and the pixel value of each pixel constituting the other parts increases. As a result, in the inverse-transformed image, the unwanted defect is buried in the background and disappears. Therefore, as the final inverse-transformed image, the processed image can be obtained in which the unwanted defect in the original image has been accurately removed.

[0015] As described above, since the unwanted scratches (noise) in the original image are removed from the processed image, the internal structure of the analytical material can be understood more accurately in accordance with its actual state. Furthermore, the effort required to appropriately select the cutting tool and cutting conditions used for cutting the material when acquiring the original image in order to avoid the presence of unwanted scratches, and the effort required to search for areas within the cut surface where no unwanted scratches appear, can be greatly reduced. This makes it easier to understand the internal structure of the analytical material. [Brief explanation of the drawing]

[0016] [Figure 1] This is an explanatory diagram illustrating an embodiment of a data processing system for cross-sectional images of a first analytical material. [Figure 2] It is an explanatory diagram illustrating the original image. [Figure 3] It is a flowchart illustrating the procedure of the data processing method for the cross-sectional image of the first analysis material. [Figure 4] It is an explanatory diagram illustrating the spatial frequency spectrum. [Figure 5] It is an explanatory diagram illustrating the extracted spatial frequency spectrum. [Figure 6] It is an explanatory diagram illustrating another extracted spatial frequency spectrum. [Figure 7] It is an explanatory diagram illustrating the defect image. [Figure 8] It is an explanatory diagram illustrating another defect image. [Figure 9] It is an explanatory diagram illustrating the processed image in the first embodiment. [Figure 10] It is a flowchart illustrating the procedure of the data processing method for the cross-sectional image of the second analysis material. [Figure 11] It is an explanatory diagram illustrating the frequency spectrum in the horizontal direction. [Figure 12] It is an explanatory diagram illustrating the frequency spectrum in the vertical direction. [Figure 13] It is an explanatory diagram illustrating the intensity distribution in the frequency spectrum of FIG. 11. [Figure 14] It is an explanatory diagram illustrating the frequency spectrum after removal based on the frequency spectrum of FIG. 11. [Figure 15] It is an explanatory diagram illustrating the frequency spectrum after removal based on the frequency spectrum of FIG. 12. [Figure 16] It is an explanatory diagram illustrating the image after inverse transformation. [Figure 17] It is an explanatory diagram illustrating the blurred image. [Figure 18] It is an explanatory diagram illustrating the frequency spectrum after removal in the horizontal direction. [Figure 19] It is an explanatory diagram illustrating the frequency spectrum after removal in the vertical direction. [Figure 20] It is an explanatory diagram illustrating the processed image in the second embodiment. [Figure 21]This flowchart illustrates the procedure for processing data from cross-sectional images of the third analytical material. [Figure 22] This is an explanatory diagram illustrating the original images used in Examples 1 and 2. [Figure 23] This is an explanatory diagram illustrating the image after processing in Example 1. [Figure 24] This is an explanatory diagram illustrating the post-processing image of Example 2. [Figure 25] This is an explanatory diagram illustrating the original image used in Example 3. [Figure 26] This is an explanatory diagram illustrating an extracted image based on the processed image from Example 3. [Figure 27] This graph shows the relationship between the number of repetitions of the series of processing steps in Example 3 and the rate of decrease in pixel value. [Modes for carrying out the invention]

[0017] The data processing method and system for cross-sectional images of analytical materials according to the first embodiment of the present invention will be described below based on the embodiments shown in the figure.

[0018] The data processing system 1 illustrated in Figure 1 comprises a computing device 2 and an output device 3. This data processing system 1 is used to remove unwanted marks (hereinafter referred to as knife marks N) caused by material cutting present in the original image D1, which is a cross-sectional image of a sample S taken from a desired analytical material. Fourier transform and inverse Fourier transform are used as data processing to remove these knife marks N. The original image D1 is acquired by a known imaging device C or the like and input to the computing device 2.

[0019] For example, various known vulcanized or unvulcanized rubbers containing at least fillers can be used as analytical materials. Vulcanized and unvulcanized rubbers generally contain one or more types of polymers and additives such as fillers, vulcanization accelerators, antioxidants, and anti-aging agents. Various known fillers such as carbon black, silica, and calcium carbonate can be used as fillers. In this embodiment, vulcanized rubber containing carbon black as a filler is used. For example, resins or metals may also be used as analytical materials.

[0020] Sample S is collected from the analytical material using a cutting tool such as a knife or microtome. The cross-section Sa of sample S reveals particles of compounding components, such as carbon black or antioxidants. Therefore, it is preferable to use a sample S that exhibits a typical distribution of the compounding component being observed. For example, when using vulcanized rubber containing carbon black as the analytical material and observing the carbon black, multiple samples S are collected from the vulcanized rubber, and a sample S is selected from among these samples S that shows a typical distribution of carbon black on its cross-section Sa.

[0021] Various known imaging devices are used in imaging device C, depending on the analytical material and the object to be observed. Examples of imaging devices C include optical microscopes with cameras, focused ion beam (FIB) systems, electron microscopes (TEM, SEM), and atomic force microscopes (AFM).

[0022] The arithmetic unit 2 receives and stores various data, and performs data processing using this data. Various known computers can be used as the arithmetic unit 2. The arithmetic unit 2 has an arithmetic unit (CPU) 4, a main memory unit (memory) 5, an auxiliary storage unit (HDD, etc.) 6, and an input unit (various interfaces) 7. The auxiliary storage unit 6 corresponds to the storage unit of the present invention. The input unit 7 can be any interface that can input the original image D1. The input unit 7 is connected to a data input device such as a scanner or camera device that digitizes and captures the original image D1, an imaging device C, and an external storage device that reads a storage medium such as a USB memory or CD-ROM containing the original image D1.

[0023] Output device 3 is connected to arithmetic unit 2 and outputs the results of data processing by arithmetic unit 2. Output device 3 can be a well-known display or printer.

[0024] Figure 2 schematically shows the original image D1. The original image D1 is acquired by the imaging device C and stored in the auxiliary storage unit 6 of the computing device 2. In this original image D1, the black dots represent carbon black particles P, the black diagonal lines represent knife marks N, and the remaining areas represent rubber components. The X and Y directions in Figure 2 represent the horizontal and vertical directions in the original image D1, respectively, and are orthogonal to each other.

[0025] Knife marks N are formed on the cut surface Sa when a sample S is taken from the analytical material (material cutting) using a cutting tool such as a knife or microtome, mainly by the cutting edge of the cutting tool. Knife marks N are linear in shape, extending in the direction of cutting by the cutting tool, and in Figure 2 they extend diagonally from the upper right to the lower left. In actual images of the cut surface of analytical materials, the characteristics of knife marks N, such as the direction of extension, width (width dimension in the direction perpendicular to the direction of extension), brightness (pixel value of each pixel constituting the knife mark N), and spacing between knife marks N, differ slightly from one knife mark N to another, but in Figure 2 they are conveniently depicted as being roughly the same.

[0026] The state of knife marks N in the original image D1 differs slightly depending not only on the type of cutting tool and the cutting conditions when the sample S was taken, but also on the internal structure of the analytical material (the distribution of particles). For example, carbon black particles P are harder and more difficult to cut than other parts (e.g., polymers), so the knife marks N differ subtly in areas where these particles P are dense and areas where they are sparse. In other words, even if samples S are taken from the same type of vulcanized rubber using the same type of cutting tool and cutting conditions, if the distribution of particles P at each cut surface Sa is different, the state of knife marks N in the original image D1 will also be different. Therefore, although knife marks N are a highly regular type of noise that forms a linear shape extending in the cutting direction, their state in the original image D1 differs due to various factors such as the type of cutting tool, the cutting conditions when the sample S was taken, and the internal structure of the analytical material (the size and distribution of particles P). Consequently, knife marks N cannot be accurately removed by noise reduction filters such as Gaussian filters and median filters commonly used in image processing.

[0027] Next, we will explain the data processing method for the cross-sectional image of the first analytical material.

[0028] As illustrated in Figure 3, in the procedure for processing the data of the cross-sectional image of the first analytical material, the original image D1 is input to the arithmetic unit 2 (S110). Next, the arithmetic unit 2 sequentially creates the spatial frequency spectrum D2 obtained by applying a two-dimensional Fourier transform to the original image D1, the extracted spatial frequency spectrum D3 (D3a, D3b) obtained by extracting the knife mark component Fn from the spatial frequency spectrum D2, and the damaged image D4 obtained by applying a two-dimensional inverse Fourier transform to the extracted spatial frequency spectrum D3 (S120~S140). Next, the components of the damaged image D4 are subtracted from the original image D1 to obtain the processed image D5 from which the knife mark N has been removed (S150). Finally, this processed image D5 is output to the output device 3. The output processed image D5 can be used, for example, to quantify the internal structure of the analytical material. The details of each step (S110~S150) are described below.

[0029] In step S110, the original image D1 is input to the arithmetic unit 2. The original image D1 is input to the auxiliary storage unit 6 of the arithmetic unit 2 via the input unit 7 from data input devices such as scanners and cameras including the imaging device C, or from external storage devices such as USB memory or CD-ROMs.

[0030] In step S120, the arithmetic unit 4 performs data processing to create a spatial frequency spectrum D2 by applying a two-dimensional Fourier transform (2D FFT) to the original image D1. The created spatial frequency spectrum D2 is stored in the auxiliary storage unit 6 of the arithmetic unit 2. Various known Fast Fourier Transform (FFT) algorithms can be used in this step S120. A two-dimensional Fourier transform is performed on the original image D1 in either the horizontal or vertical direction, and then the transformed data is subjected to another Fourier transform in either the horizontal or vertical direction.

[0031] The spatial frequency spectrum D2 illustrated in Figure 4 was created using a two-dimensional fast Fourier transform based on the original image D1 illustrated in Figure 2, and is stored in the auxiliary memory unit 6. In Figure 4, the intensity of the spectrum increases in the order of the light gray mesh area (minimum), the light gray mesh area, the area surrounded by the light gray mesh area, and the dark gray area. Also, in the spatial frequency spectrum D2, the frequency decreases as you approach the center and increases as you move away from the center towards the edge. In the original image D1 illustrated in Figure 2, a periodic structure of knife marks N is seen in a diagonal direction from the upper left to the lower right, so in the transformed image D2 illustrated in Figure 4, the frequency corresponding to that period appears as a darker colored area (dark gray). That is, in the transformed image D2, it can be seen that the periodicity of the knife marks N is stronger than the periodicity of the particle P in the original image D1.

[0032] Prior to performing step S120, it is preferable to apply a predetermined denoising process and / or a predetermined enhancement process to the original image D1, and then apply a two-dimensional Fourier transform to the original image D1 after these processes have been performed. For the predetermined denoising process, various known denoising filters such as Gaussian filters and median filters can be used. This predetermined denoising process is advantageous for enhancing the knife marks N in the original image D1 by treating objects other than the knife marks N in the original image D1, such as carbon black particles P, as noise and removing that noise. For the predetermined enhancement process, known edge enhancement filters such as Laplacian filters and known dilation processes can be used. This predetermined enhancement process is advantageous for enhancing the knife marks N in the original image D1 by making them sharper.

[0033] In step S130, data processing is performed by the calculation unit 4 to create extracted spatial frequency spectra D3 (D3a, D3b, described later) in which the knife mark component Fn is extracted from the spatial frequency spectrum D2. The knife mark component Fn is the frequency component that shows the knife mark N in the spatial frequency spectrum D2. In step S130 of this embodiment, various known sparse modeling methods such as L1 regularization, L2 regularization, and TV regularization are used.

[0034] The periodicity of the knife-mark component Fn in the spatial frequency spectrum D2 is stronger than that of the other components. Therefore, in sparse modeling, the knife-mark component Fn, which has stronger periodicity, is treated as a characteristic object image in the spatial frequency spectrum D2. In other words, in sparse modeling, frequency components other than the knife-mark component Fn are considered noise, and the knife-mark component Fn is extracted by removing these frequency components.

[0035] Figure 5 shows the extracted spatial frequency spectrum D3a obtained by applying sparse modeling using L1 normalization to the spatial frequency spectrum D2. L1 normalization yields a solution (extracted spatial frequency spectrum D3a) in which most of the pixels other than the knife mark component Fn in the spatial frequency spectrum D2 are zero (black). Therefore, in this extracted spatial frequency spectrum D3a, the knife mark component Fn is extracted as a characteristic object image, and most of the components other than this characteristic object are zero, i.e., the background.

[0036] Figure 6 shows the extracted spatial frequency spectrum D3b obtained by applying sparse modeling using TV regularization to the spatial frequency spectrum D2. TV regularization yields a solution (extracted spatial frequency spectrum D3b) in which the difference between adjacent images in the spatial frequency spectrum D2 is small. In this extracted spatial frequency spectrum D3b, the difference between pixels constituting components other than the knife mark component Fn is approximately zero, i.e., they are the background, and the knife mark component Fn is extracted as a characteristic object image.

[0037] Prior to performing step S130, it is preferable to apply a predetermined noise reduction process to the spatial frequency spectrum D2 and then apply sparse modeling to the spatial frequency spectrum D2 after the predetermined noise reduction process has been applied. Various known noise reduction filters, such as Gaussian filters and median filters, can be used for this predetermined noise reduction process. In this predetermined noise reduction process, frequency components other than the knife mark component Fn in the spatial frequency spectrum D2 are considered as noise, and this noise is removed. As a result, the knife mark component Fn in the spatial frequency spectrum D2 is further emphasized, which is advantageous for accurately extracting the knife mark component Fn using sparse modeling.

[0038] In step S130, instead of sparse modeling, a predictive model constructed using a known supervised machine learning method such as a convolutional neural network (CNN) or a recurrent neural network (RNN) may be used. To construct this predictive model, a dataset is used as training data, which consists of a large number of spatial frequency spectra of cross-sectional images of the same type of material as the material being analyzed, and spatial frequency spectra of images containing only the knife marks present in those cross-sectional images. That is, in the predictive model, components other than the knife mark component Fn in the spatial frequency spectrum D2 are treated as noise, and the pixel values ​​of each pixel constituting the knife mark component Fn are analyzed and processed, with the knife mark component Fn being treated as the target for reconstruction. Therefore, this predictive model creates an extracted spatial spectrum D3 in which the location and shape of the knife mark component Fn in the input spatial frequency spectrum D2 are extracted.

[0039] In step S140, the arithmetic unit 4 performs data processing to create a scratch image D4 (scratch images D4a and D4b, described later) by applying a two-dimensional inverse Fourier transform (2D IFFT) to the extracted spatial frequency spectrum D3. The created scratch image D4 is stored in the auxiliary storage unit 6 of the arithmetic unit 2. In this step S140, various known Fast Fourier Transform (FFT) algorithms are used, similar to step S120.

[0040] Figure 7 shows the damaged image D4a obtained by applying a two-dimensional inverse Fourier transform to the extracted spatial frequency spectrum D3a exemplified in Figure 5 above. Figure 8 shows the damaged image D4b obtained by applying a two-dimensional inverse Fourier transform to the extracted spatial frequency spectrum D3b exemplified in Figure 6 above. These damaged images D4a and D4b can be considered to have only knife marks N as components, since the particles P in the original image D1 have been largely removed as noise.

[0041] In step S150, the calculation unit 4 performs data processing to subtract the component of the damaged image D4 from the original image D1, and the processed image D5 is obtained. The obtained processed image D5 is stored in the auxiliary storage unit 6 of the calculation device 2 and output to the output device 3.

[0042] In the processed image D5 illustrated in Figure 9, the knife marks N have been removed from the original image D1 illustrated in Figure 2. In Figure 9, the black dots represent carbon black particles P, and the other areas represent rubber components. In this processed image D5, the knife marks N that were present in the original image D1 have been largely removed, so the shape and location of each carbon black particle P are clearer. The degree to which the knife marks N are removed in this processed image D5 is sufficient so that the particles P present in the original image D1 can be clearly distinguished; it is not necessary for all of the knife marks N present in the original image D1 to be removed.

[0043] As described above, according to the first embodiment, by using the Fourier transform and inverse Fourier transform as data processing, the knife marks N in the original image D1 and the other carbon black particles P can be distinguished by the degree of difference in their respective frequency components. As a result, a processed image D5 can be obtained in which the knife marks N have been removed from the original image D1.

[0044] In this first embodiment, the fact that the periodicity of the knife mark component Fn is stronger than that of the other components in the spatial frequency spectrum D2 obtained using a two-dimensional Fourier transform is utilized. By retaining the knife mark component Fn, which has a stronger periodicity in the spatial frequency spectrum D2, a damaged image D4 is obtained. By subtracting the components of the damaged image D4 from the original image D1, a processed image D5 can be obtained in which the knife marks N in the original image D1 are accurately removed.

[0045] The resulting processed image D5 is suitable for observing the internal structure of the analytical material because the knife marks N have been accurately removed. By using this processed image D5, the internal structure of the analytical material can be understood more faithfully to its actual state. Furthermore, according to this first embodiment, it is possible to eliminate the need for complicated work such as setting detailed cutting conditions for the analytical material or extracting areas where knife marks N are not present from the cross-sectional image of the analytical material in order to obtain a cross-sectional image from which the knife marks N have been removed. Therefore, it is advantageous for accurately and efficiently understanding the internal structure of the analytical material.

[0046] The internal structure of the analytical material may be quantified using the processed image D5 exemplified in Figure 9 above, but it is preferable to perform binarization on the processed image D5 using the calculation unit 4. By performing binarization on the processed image D5 in this way, the boundary between the particles P and the rest of the image becomes clearer, which is advantageous for accurately quantifying the size and distribution of the particles P.

[0047] Next, embodiments of the data processing method and system for cross-sectional images of analytical materials according to the second embodiment of the present invention will be described.

[0048] The second embodiment differs from the first embodiment in its data processing method, but the configuration of the data processing system 1 is the same. In the data processing method of the second embodiment, a series of processing steps utilizing a one-way Fourier transform and a one-way inverse Fourier transform are repeated a predetermined number of times (m times). In the preceding and succeeding series of processing steps, the one-way direction of the Fourier transform and inverse Fourier transform is alternately alternating between the horizontal and vertical directions. In the series of processing steps, the original image D1 is used as the target image for the first time (k=1), and the blurred image D9 created in the previous series of processing steps is used as the target image for subsequent times (k≧2).

[0049] An embodiment of the data processing method for the cross-sectional image of the second analytical material is carried out according to the procedure illustrated in Figure 10. In Figure 10, each step enclosed by "loop1" (S210A, S220, S230, S240A) represents a series of processing steps, and this series of processing steps is repeated m times. In Figure 10, "k" indicates the number of times the series of processing steps is repeated, and "m" indicates a predetermined number of times.

[0050] In the second data processing method illustrated in Figure 10, when the original image D1 is input (S110), the calculation unit 4 performs a series of processing steps (S210A, S220, S230, S240A) to sequentially create the frequency spectrum D6A (D6B), the removed frequency spectrum D7A (D7B), the inversely transformed image D8, and the blurred image D9, repeating this process m times. Finally, the inversely transformed image D8 from the last series of processing steps (k=m) is output as the processed image D10 (S250). The details of each step S210A, S220, S230, S240A, and S250 are described below.

[0051] In step S210A, the arithmetic unit 4 performs data processing to generate a frequency spectrum D6A (D6B) by applying a one-way Fourier transform (FFT) to the target image. For the first time (k=1), the original image D1 is used as the target image. For subsequent target images (k≧2), the blurred image D9 created in the previous series of processing steps is used. The generated frequency spectrum D6A (D6B) is stored in the auxiliary storage unit 6 of the arithmetic unit 2. Various known Fast Fourier Transform (FFT) algorithms are used in this step S210A.

[0052] The frequency spectrum D6A shown in Figure 11 was created by applying a Fast Fourier Transform in the X direction to the original image D1 shown in Figure 2. In Figure 11, the vertical axis represents the spectral intensity [m / sec] and the horizontal axis represents the X-axis coordinate. The frequency spectrum D6B shown in Figure 12 was created by applying a Fast Fourier Transform in the Y direction to the original image D1 shown in Figure 2. In Figure 12, the vertical axis represents the Y-axis coordinate and the horizontal axis represents the spectral intensity [m / sec].

[0053] In step S220, the calculation unit 4 performs data processing to create a deselected frequency spectrum D7A (D7B) from the frequency spectrum D6A (D6B) by removing predetermined low-frequency components. In step S220, for example, a known high-pass filter is used. The cutoff frequency of this high-pass filter can be varied each time the series of processing steps are repeated, as long as it is set to be able to remove low-frequency components from the input frequency spectrum D6A (D6B). As the series of processing steps are repeated, the low-frequency components are removed, so the cutoff frequency of the high-pass filter gradually decreases.

[0054] In the frequency spectra D6A and D6B illustrated in Figures 11 and 12 above, it can be seen that the intensity of the knife mark component Fn is greater than the intensity of the particle component Fp, and the period of the knife mark component Fn is lower than the period of the particle component Fp. Therefore, in frequency spectra D6A and D6B, this knife mark component Fn can be considered to be a low-frequency component. A low-frequency component refers to a component belonging to the low-frequency band in the intensity distribution obtained by decomposing the signal intensity into frequency components.

[0055] Figure 13 shows a portion of the intensity distribution obtained by decomposing the signal intensity in frequency spectrum D6A into its frequency components. This intensity distribution shows that the knife-mark component Fn is a low-frequency component. Low-frequency components refer to components in the frequency band that fall within an acceptable range relative to the lowest frequency in the intensity distribution for each frequency spectrum D6A and D6B. For example, in Figure 13, the bar graph shaded with diagonal lines represents the low-frequency components that fall within an acceptable range relative to this standard. The acceptable range is sufficient if the knife-mark component Fn is included within the low-frequency components, for example, around 100% to 130%.

[0056] The decompressed frequency spectrum D7A, illustrated in Figure 14, is obtained by applying a high-pass filter to the frequency spectrum D6A, illustrated in Figure 11, to remove low-frequency components. The decompressed frequency spectrum D7B, illustrated in Figure 15, is obtained by applying a high-pass filter to the frequency spectrum D6B, illustrated in Figure 12, to remove low-frequency components.

[0057] In step S230, the arithmetic unit 4 performs data processing to create an inverse Fourier transform (IFFT) in one direction on the removed frequency spectrum D7A (D7B) to create an inversely transformed image D8. The created inversely transformed image D8 is stored in the auxiliary storage unit 6 of the arithmetic unit 2. In this step S230, various known Fast Fourier Transform (FFT) algorithms are used, similar to step S220A described above, and the inverse Fourier transform is performed in the same direction as in step S210A. For example, if a Fourier transform in the X direction was performed in step S210A, an inverse Fourier transform in the X direction is performed in step S230.

[0058] The inverse-transformed image D8, illustrated in Figure 16, was created by applying an inverse fast Fourier transform in the Y direction to the removed frequency spectrum D7B, illustrated in Figure 15. In the inverse-transformed image D8, the pixel values ​​of each pixel remaining after removing the pixels constituting particle P are smaller (darker) compared to the original image D1. Furthermore, the width of the knife mark N is smaller in the inverse-transformed image D8. On the other hand, there is generally no change in the individual pixels constituting particle P in the inverse-transformed image D8.

[0059] In step S240A, the calculation unit 4 performs data processing to create a blurred image D9 by applying a blurring process to the inversely transformed image D8. The created blurred image D9 is stored in the auxiliary storage unit 6 of the calculation device 2. In this step S240A, various known blurring processes such as Gaussian blurring are used. The degree of blurring in this process should be as large as possible without changing the shape of the particles P. For example, in Gaussian blurring, if the size (particle size) of the particles P in the original image D1 is about 5 pixels, the standard deviation is set to about 3 to 5 pixels.

[0060] The blurred image D9 illustrated in Figure 17 is generated by applying Gaussian blur to the inverse transformed image D8 illustrated in Figure 16. Compared to the inverse transformed image D8, the blurred image D9 is generally blurred, and the width of the knife marks N is larger. On the other hand, the shape of the particles P remains largely unchanged. Thus, the degree of blurring due to the blurring process is greater in the knife marks N than in the particles P. In other words, the shape of the particles P does not change much before and after the blurring process, but the width dimension of the knife marks N after the blurring process is larger than the width dimension before the blurring process. In the process of repeating the series of processing steps, when the knife mark component Fn is reduced to the same level as the particle component Fp, it becomes difficult to reduce the knife mark component Fn by removing low-frequency components. Therefore, by blurring the knife marks N and increasing their width dimension through the blurring process, it becomes possible to maintain the degree of difference between the knife mark component Fn and the particle component Fp. This allows the series of processing steps to be repeated until the knife marks N are largely removed and the particles P become clear.

[0061] The predetermined number of repetitions (m times) should be sufficient to allow the knife marks N in the inversely transformed image D8 to be considered largely removed (i.e., the knife marks N are obscured by the background and disappear). Since it is desirable for the series of processing steps to be repeated the same number of times in both the horizontal and vertical directions, any even number should be selected. The predetermined number of repetitions is determined by visually checking the degree of knife mark N removal in the inversely transformed image D8 created each time the series of processing steps are repeated, until an inversely transformed image D8 is obtained in which the knife marks N can be considered largely removed.

[0062] The predetermined number of repetitions may be set using an input device such as a keyboard or mouse during the preparation stage before the series of processing steps are repeated. Since similar source images D1 will have roughly the same number of repetitions, the predetermined number of repetitions should be kept track of for each state of source image D1. Then, an appropriate number of repetitions is selected from the predetermined number of repetitions that have been kept track of in advance, based on the state of source image D1 to be processed. For example, the larger the dimensions of source image D1, the more repetitions of the series of processing steps required to remove the knife mark N. The smaller the dimensions of source image D1, the fewer repetitions are required. Also, the larger the width dimension of the knife mark N in source image D1 (the length dimension in the direction perpendicular to the extension direction of the knife mark N), the more repetitions of the series of processing steps are required, and the smaller the width dimension of the knife mark N in source image D1, the fewer repetitions are required. Therefore, the predetermined number of repetitions should be set based on the dimensions of source image D1 and / or the width dimension of the knife mark N in source image D1. Furthermore, if the predetermined number of repetitions is set during the preparation phase, and the degree of removal of knife marks N is small after the series of processing steps has been repeated the predetermined number of times, a new predetermined number of repetitions should be set, and the series of processing steps should be repeated again for the newly set number of times.

[0063] The degree to which the knife mark N has been removed can be visually confirmed, but it is preferable to compare the pixel values ​​of the original image D1 with the pixel values ​​of the inversely transformed image D8, as exemplified in Figure 17 below. For this comparison, the reduction rate of the pixel values ​​in the inversely transformed image D8 relative to the pixel values ​​in the original image D1 is used. The reduction rate of the pixel value is calculated as {(representative value of the pixel value of the target object in the original image D1 - representative value of the pixel value of the target object in the inversely transformed image D8) / representative value of the pixel value of the target object in the original image D1} × 100 (%). For example, if the reduction rate of the representative value of each pixel constituting the knife mark N in the inversely transformed image D8 is less than 20%, the knife mark N has been buried in the background and disappeared, so it can be considered that the knife mark N has been largely removed. Furthermore, if the rate of decrease of the representative pixel value of each pixel constituting the particle P in the inversely transformed image D8 differs from the rate of decrease of the representative pixel value of each pixel constituting the knife mark N by more than 10%, then the particle P can be considered to be clearer than the knife mark N. Therefore, the predetermined number of times can also be set by comparing the pixel values ​​of the original image D1 with the pixel values ​​of the inversely transformed image D8. It is preferable that each time the inversely transformed image D8 is created (each time the series of processing steps is repeated), the calculation unit 4 compares the respective pixel values ​​of the original image D1 and the inversely transformed image D8 and performs data processing to determine whether or not to terminate the series of processing steps using the rate of decrease of the pixel values. Preferably, in this data processing, it is preferable to determine to terminate the series of processing steps if the rate of decrease of the representative pixel value of each pixel constituting the knife mark N becomes less than 20%, and the rate of decrease of the representative pixel value of each pixel constituting the particle P differs from the rate of decrease of the representative pixel value of each pixel constituting the knife mark N by more than 10%.

[0064] In step S250, the calculation unit 4 acquires the inversely transformed image D8 from the last series of processes (k=m) as the processed image D10. The obtained processed image D10 is stored in the auxiliary storage unit 6 of the calculation device 2 and output to the output device 3.

[0065] The removed frequency spectrum D7A, illustrated in Figure 18, was created in the final processing sequence (k=m-1). The removed frequency spectrum D7B, illustrated in Figure 19, was created in the final processing sequence (k=m). In these removed frequency spectra D7A and D7B, the intensity of the knife mark component Fn is lower than the intensity of the particle component Fp.

[0066] The processed image D10 illustrated in Figure 20 is the inverse transformed image D8 obtained by applying an inverse Fourier transform in the Y direction to the removed frequency spectrum D7B illustrated in Figure 19 above. In this processed image D10, the knife marks N have been removed from the original image D1 illustrated in Figure 2 above. In Figure 20, the white dots represent carbon black particles P, and the other black areas represent rubber components and knife marks N. That is, in this processed image D10, through the repetition of a series of processing processes, the pixel value of each pixel constituting particles P has become larger than the pixel value of each pixel constituting other components (including knife marks N), and the knife marks N have been buried and disappeared as part of the background. In this processed image D10, the knife marks N that were present in the original image D1 have been largely removed, so the shape and location of each carbon black particle P are clearer. The degree to which knife marks N are removed in the processed image D10 is sufficient if the particles P present in the original image D1 can still be clearly distinguished; it is not necessary for all knife marks N present in the original image D1 to be removed.

[0067] Next, embodiments of a data processing method and system for cross-sectional images of a third analytical material will be described.

[0068] The third embodiment differs from the first embodiment in its data processing method, but the configuration of the data processing system 1 is the same. The procedure of the data processing method in the third embodiment differs from that of the second embodiment in the order of the steps for creating the blurred image D9. Therefore, in the series of processing steps of the third embodiment, the original image D1 is used as the target image for the first time (k=1), and the converted image D8 created in the previous series of processing steps is used as the target image for subsequent times (k≧2).

[0069] An embodiment of the data processing method for the cross-sectional image of the third analytical material is carried out according to the procedure illustrated in Figure 21. In Figure 21, each step enclosed in "loop2" (S240B, S210B, S220, S230) represents a series of processing steps, and this series of processing steps is repeated m times. In the third embodiment, the step of creating a blurred image D9 (S240B) is carried out as the first step in the series of processing steps. Therefore, in the third embodiment, a one-way Fourier transform is applied to the blurred image D9 to create a frequency spectrum D6A (D6B) (S210B). In the third embodiment, the other steps are the same as in the second embodiment and are therefore omitted from description. Also, each image created in the process of the third embodiment is the same as in the second embodiment and is therefore omitted from description.

[0070] As described above, according to the second and third embodiments, similar to the first embodiment, by using the Fourier transform and inverse Fourier transform as data processing, the knife marks N in the original image D1 and the other carbon black particles P can be distinguished by the degree of difference in their respective frequency components. This makes it possible to obtain a processed image D5 from which the knife marks N have been removed from the original image D1.

[0071] In the second and third embodiments, it is utilized that the knife mark component Fn appears as a predetermined low-frequency component in the frequency spectrum D6A (D6B) obtained using a unidirectional Fourier transform. By repeating a series of processing steps (loop 1, 2) of a unidirectional Fourier transform, removal of the predetermined low-frequency component, and unidirectional inverse Fourier transform, the pixel value of each pixel decreases (approaches black), and the difference between the pixel value of each pixel constituting the knife mark N and the pixel value of each pixel constituting the particle P increases. As a result, in the inverse-transformed image D8, the knife mark N is buried in the background and disappears. Therefore, as the final inverse-transformed image D8, a processed image D10 can be obtained in which the knife mark N in the original image D1 has been accurately removed.

[0072] The processed image D10 is suitable for observing the internal structure of the analytical material because the knife marks N from the original image D1 have been removed. Therefore, by using this processed image D10, the internal structure of the analytical material can be understood more accurately in accordance with its actual state. Furthermore, the second and third embodiments, like the first embodiment, eliminate the need for the cumbersome work required to obtain a cross-sectional image from which the knife marks N have been removed. This is advantageous for accurately and efficiently understanding the internal structure of the analytical material.

[0073] While it is possible to quantify the internal structure of the analytical material using the processed image D10 exemplified in Figure 20 above, it is preferable to apply binarization processing to the processed image D10 using the calculation unit 4. By applying binarization processing to the processed image D10 in this way, the boundary between the particles P and the rest of the image becomes clearer, which is advantageous for accurately quantifying the size and distribution of the particles P.

[0074] Furthermore, in the processed image D10, the knife marks N present in the original image D1 have been removed, and the area other than the particles P is present as the background. Therefore, based on this processed image D10, the region occupied by carbon black particles P in the original image D1 can be extracted with high accuracy. The internal structure of the analytical material may be quantified using the image from which the region occupied by carbon black particles P in the original image D1 has been extracted.

[0075] The embodiments described above are not limited to vulcanized rubber as the analytical material, but can also be applied to unvulcanized rubber, resins, metals, etc. Furthermore, the internal structure that can be understood using the obtained post-processing images D5 and D10 is not limited to the distribution state of carbon black, but may also be the distribution state of other compounding components that appear as particles in the original image D1. [Examples]

[0076] Examples 1 to 3 were carried out using samples A and B taken from the same analytical material. In Example 1, the original image D1A of sample A, illustrated in Figure 22, was used, and the first embodiment illustrated in Figure 3, in which L1 normalization was used as sparse modeling, was carried out to obtain the processed image D5A, illustrated in Figure 23. In Example 2, the original image D1A of sample A, illustrated in Figure 22, was used, and the first embodiment illustrated in Figure 3, in which TV regularization was used as sparse modeling, was carried out to obtain the processed image D5B, illustrated in Figure 24. In Example 3, the original image D1B of sample B, illustrated in Figure 25, was used, and the second embodiment illustrated in Figure 10, in which the predetermined number of repetitions was set to 20, was carried out to obtain the extracted image D11, illustrated in Figure 26.

[0077] The analytical material used was vulcanized rubber with a carbon black content of 30 parts by mass per 100 parts by mass of polymer. Samples A and B, with a thickness of no more than 1 mm, were taken from the analytical material sample, which was within a few centimeters in both length and width, using a razor. The imaging device C was an optical microscope with a camera and a magnification of 100x.

[0078] As illustrated in Figures 23 and 24, in the processed images D5A and D5B, respectively, the knife marks N present in the original image D1A have been removed, and the size and distribution of particles P are more clearly visible. In processed image D5A, the knife marks N are not completely removed, but the pixel values ​​of each pixel constituting particle P are generally maintained at approximately the same level as in the original image D1A. In processed image D5B, the knife marks N are largely removed, but the pixel values ​​of each pixel constituting particle P are slightly smaller compared to the original image D1A. Therefore, when selecting sparse modeling, it is best to choose an appropriate method depending on the state of the knife marks N and the size and distribution of the particles P being observed.

[0079] The extracted image D11 shown in Figure 26 is based on an image obtained by applying a binarization process to the processed image D10, which was acquired by repeating a series of processing steps 20 times. The region occupied by carbon black particles P in the original image D1 is extracted from this image. The region enclosed by the white line in Figure 26 indicates the region occupied by carbon black particles P. In this extracted image D11, the region occupied by particles P is clearly visible, which is advantageous for understanding the size and distribution of particles P.

[0080] In the process of obtaining the processed image D10, the number of iterations k of the series of processing steps was counted, and for each iteration k, the representative pixel value of each pixel constituting the knife mark N in the inversely transformed image D8 was compared with the representative pixel value of each pixel constituting the particle P.

[0081] Figure 27 shows a comparison of the representative pixel values ​​of each pixel constituting the knife marks N and the representative pixel values ​​of each pixel constituting the particles P in the inverse-transformed image D8 for each number of iterations k of the processing process. In Figure 27, the horizontal axis represents the number of iterations k, and the vertical axis represents the rate of decrease of the pixel values ​​of each pixel constituting the target object (knife marks N, particles P). It can be seen that the difference between the rate of decrease of knife marks N and the rate of decrease of particles P increases as the number of iterations k increases. When the number of iterations k reached 20, the rate of decrease of knife marks N was less than 20%, and the difference between the rate of decrease of knife marks N and the rate of decrease of particles P was about 10%. Therefore, it can be seen that the knife marks N present in the original image D1B have been removed with high accuracy in the processed image D10.

[0082] The present invention is not limited to any particular embodiment, and various modifications and changes are possible within the scope of the gist of the invention.

[0083] This disclosure encompasses the following inventions: Invention 1: A data processing method for a cross-section image of an analytical material, which uses Fourier transform and inverse Fourier transform as data processing to remove unwanted scratches caused by material cutting present in the original image of the cross-section of the analytical material, A data processing method for a cross-section image of an analytical material, comprising: applying a two-dimensional Fourier transform to the original image to create a spatial frequency spectrum; creating an extracted spatial frequency spectrum from which the unwanted scratch components are extracted; applying a two-dimensional inverse Fourier transform to the extracted spatial frequency spectrum to create a scratch image that can be considered to have only the unwanted scratch components; performing data processing by a computing device to subtract the scratch image components from the original image; and obtaining a processed image from which the unwanted scratches have been removed from the original image. Invention 2: A data processing method for a cross-sectional image of an analytical material according to Invention 1, wherein sparse modeling is applied to the spatial frequency spectrum to create the extracted spatial frequency spectrum. Invention 3: A data processing method for a cross-sectional image of an analytical material according to invention 1 or 2, wherein a predetermined noise reduction process is applied to the spatial frequency spectrum. Invention 4: A data processing method for a cross-sectional image of an analytical material according to any one of inventions 1 to 3, wherein a predetermined noise reduction process and / or a predetermined enhancement process are applied to the original image. Invention 5: A data processing method for a cross-section image of an analytical material, which uses Fourier transform and inverse Fourier transform as data processing to remove unwanted scratches caused by material cutting present in the original image of the cross-section of the analytical material, A series of processing steps to create a frequency spectrum by applying a one-way Fourier transform to the target image, then creating a deselected frequency spectrum by removing predetermined low-frequency components from the frequency spectrum, then applying the one-way inverse Fourier transform to the deselected frequency spectrum to create an inverse transformed image, and then applying a predetermined blurring process to the inverse transformed image to create a blurred image, The original image is used as the target image for the first time, and the blurred image created in the previous series of processing steps is used as the target image for subsequent times, and the processing unit repeats this a predetermined number of times, and in the preceding and succeeding series of processing steps, the one direction is alternately changed between the horizontal and vertical directions. A data processing method for cross-sectional images of an analytical material, wherein the inversely transformed image created in the final series of processing steps is obtained as a processed image from which the unwanted scratches have been removed from the original image. Invention 6: A data processing method for a cross-section image of an analytical material, which uses Fourier transform and inverse Fourier transform as data processing to remove unwanted scratches caused by material cutting present in the original image of the cross-section of the analytical material, A series of processing steps to create a blurred image by applying a predetermined blurring process to the target image, then create a frequency spectrum by applying a one-way Fourier transform to the blurred image, then create a deselected frequency spectrum by removing predetermined low-frequency components from the frequency spectrum, and then create an inverse transformed image by applying the one-way inverse Fourier transform to the deselected frequency spectrum, The original image is used as the target image for the first time, and the inversely transformed image created in the previous series of processing steps is used as the target image for subsequent times, and the calculation unit repeats this a predetermined number of times, and in the preceding and succeeding series of processing steps, the one direction is alternately changed between the horizontal and vertical directions. A data processing method for cross-sectional images of an analytical material, wherein the inversely transformed image created in the final series of processing steps is obtained as a processed image from which the unwanted scratches have been removed from the original image. Invention 7: A data processing method for a cross-sectional image of an analytical material according to invention 5 or 6, wherein the predetermined number of times is set based on the dimensions of the original image and / or the width dimension of the unwanted scratches in the original image. Invention 8: A data processing method for a cross-sectional image of an analytical material according to invention 5 or 6, wherein the predetermined number of times is set based on a comparison of the pixel values ​​in the original image and the pixel values ​​in the inversely transformed image. Invention 9: A data processing method for a cross-sectional image of an analytical material according to any one of inventions 1 to 8, wherein the processed image is subjected to binarization processing by the computing device. Invention 10: A method for processing data of a cross-sectional image of an analytical material according to any one of Inventions 1 to 8, wherein the analytical material is vulcanized rubber or unvulcanized rubber containing at least a filler. Invention 11: A data processing system for images of the cross-section of an analytical material, comprising a computing device that performs Fourier transform and inverse Fourier transform as data processing to remove unwanted scratches caused by material cutting present in the original image of the cross-section of the analytical material, and an output device, The aforementioned arithmetic device has an arithmetic unit, a storage unit, and an input unit. The original image is input to the storage unit through the input unit, the calculation unit performs a two-dimensional Fourier transform on the original image to create a spatial frequency spectrum, an extracted spatial frequency spectrum is created from the spatial frequency spectrum by extracting the unwanted scratch components, a two-dimensional inverse Fourier transform is performed on the extracted spatial frequency spectrum to create a scratched image that can be considered to have only the unwanted scratch components, and data processing is performed to subtract the components of the scratched image from the original image. A data processing system for cross-sectional images of analytical materials, wherein the processed image, from which the unwanted scratches have been removed from the original image, is output to the output device. Invention 12: A data processing system for images of the cross-section of an analytical material, comprising a computing device that performs Fourier transform and inverse Fourier transform as data processing to remove unwanted scratches caused by material cutting present in the original image of the cross-section of the analytical material, and an output device, The aforementioned arithmetic device has an arithmetic unit, a storage unit, and an input unit. The original image is input to the storage unit through the input unit. A series of processing steps is performed, in which a unidirectional Fourier transform is applied to the target image to create a frequency spectrum, then a deselected frequency spectrum is created by removing predetermined low-frequency components from the frequency spectrum, then the unidirectional inverse Fourier transform is applied to the deselected frequency spectrum to create an inverse transformed image, and then a predetermined blurring process is applied to the inverse transformed image to create the blurred image. The original image is used as the target image for the first time, and the blurred image created in the previous series of processing steps is used as the target image for subsequent times, and the calculation unit repeats this a predetermined number of times, and in the preceding and succeeding series of processing steps, the one direction alternates between the horizontal and vertical directions. A data processing system for cross-sectional images of analytical materials, wherein the inverse transformed image created in the final series of processing steps is output to the output device as a processed image from which the unwanted scratches have been removed from the original image. Invention 13: A data processing system for images of the cross-section of an analytical material, comprising a computing device that performs Fourier transform and inverse Fourier transform as data processing to remove unwanted scratches caused by material cutting present in the original image of the cross-section of the analytical material, and an output device, The aforementioned arithmetic device has an arithmetic unit, a storage unit, and an input unit. The original image is input to the storage unit through the input unit. A series of processing steps is performed in which a predetermined blurring process is applied to the target image to create a blurred image, then a one-way Fourier transform is applied to the blurred image to create a frequency spectrum, then a de-removed frequency spectrum is created by removing predetermined low-frequency components from the frequency spectrum, and then the one-way inverse Fourier transform is applied to the de-removed frequency spectrum to create an inverse transformed image. The original image is used as the target image for the first time, and the inversely transformed image created in the previous series of processing steps is used as the target image for subsequent times, and the calculation unit repeats this a predetermined number of times, and in the preceding and succeeding series of processing steps, the one direction alternates between the horizontal and vertical directions. A data processing system for cross-sectional images of analytical materials, wherein the inverse transformed image created in the final series of processing steps is output to the output device as a processed image from which the unwanted scratches have been removed from the original image. [Explanation of symbols]

[0084] 1. Data Processing System 2 Arithmetic unit 3. Output device 4 Arithmetic section 5 Main memory 6 Auxiliary storage section (memory section) 7 Input section C Imaging device D1, D1A, D1B Original Images D2 spatial frequency spectrum D3a, D3b Extracted spatial frequency spectra D4a, D4b scratch images D5, D5A, D5B processed images D6A, D6B frequency spectrum Frequency spectrum after D7A and D7B removal D8 inverse transformation image D9 blurred image D10 Processed Image D11 Extracted Image

Claims

1. A data processing method for a cross-section image of an analytical material, which uses Fourier transform and inverse Fourier transform as data processing to remove unwanted scratches caused by material cutting present in the original image of the cross-section of the analytical material, A data processing method for a cross-section image of an analytical material, comprising: applying a two-dimensional Fourier transform to the original image to create a spatial frequency spectrum; creating an extracted spatial frequency spectrum from which the unwanted scratch components are extracted; applying a two-dimensional inverse Fourier transform to the extracted spatial frequency spectrum to create a scratch image that can be considered to have only the unwanted scratch components; performing data processing by a computing device to subtract the scratch image components from the original image; and obtaining a processed image from which the unwanted scratches have been removed.

2. The data processing method for a cross-sectional image of an analytical material according to claim 1, wherein sparse modeling is applied to the spatial frequency spectrum to create the extracted spatial frequency spectrum.

3. The data processing method for a cross-sectional image of an analytical material according to claim 1, wherein a predetermined noise reduction process is applied to the spatial frequency spectrum.

4. A data processing method for a cross-sectional image of an analytical material according to claim 1, wherein a predetermined noise reduction process and / or a predetermined enhancement process are applied to the original image.

5. A data processing method for a cross-section image of an analytical material, which uses Fourier transform and inverse Fourier transform as data processing to remove unwanted scratches caused by material cutting present in the original image of the cross-section of the analytical material, A series of processing steps to create a frequency spectrum by applying a one-way Fourier transform to the target image, then creating a deselected frequency spectrum by removing predetermined low-frequency components from the frequency spectrum, then applying the one-way inverse Fourier transform to the deselected frequency spectrum to create an inverse transformed image, and then applying a predetermined blurring process to the inverse transformed image to create a blurred image, The original image is used as the target image for the first time, and the blurred image created in the previous series of processing steps is used as the target image for subsequent times, and the processing unit repeats this a predetermined number of times, and in the preceding and succeeding series of processing steps, the one direction is alternately changed between the horizontal and vertical directions. A data processing method for cross-sectional images of an analytical material, wherein the inversely transformed image created in the final series of processing steps is obtained as a processed image from which the unwanted scratches have been removed from the original image.

6. A data processing method for a cross-section image of an analytical material, which uses Fourier transform and inverse Fourier transform as data processing to remove unwanted scratches caused by material cutting present in the original image of the cross-section of the analytical material, A series of processing steps to create a blurred image by applying a predetermined blurring process to the target image, then create a frequency spectrum by applying a one-way Fourier transform to the blurred image, then create a deselected frequency spectrum by removing predetermined low-frequency components from the frequency spectrum, and then create an inverse transformed image by applying the one-way inverse Fourier transform to the deselected frequency spectrum, The original image is used as the target image for the first time, and the inversely transformed image created in the previous series of processing steps is used as the target image for subsequent times, and the calculation unit repeats this a predetermined number of times, and in the preceding and succeeding series of processing steps, the one direction is alternately changed between the horizontal and vertical directions. A data processing method for cross-sectional images of an analytical material, wherein the inversely transformed image created in the final series of processing steps is obtained as a processed image from which the unwanted scratches have been removed from the original image.

7. The data processing method for a cross-sectional image of an analytical material according to claim 5 or 6, wherein the predetermined number of times is set based on the dimensions of the original image and / or the width dimension of the unwanted scratches in the original image.

8. The data processing method for a cross-sectional image of an analytical material according to claim 5 or 6, wherein the predetermined number of times is set based on a comparison of the pixel values ​​in the original image and the pixel values ​​in the inversely transformed image.

9. A data processing method for a cross-sectional image of an analytical material according to any one of claims 1 to 8, wherein the processed image is subjected to binarization processing by the computing device.

10. A method for processing data of a cross-sectional image of an analytical material according to any one of claims 1 to 8, wherein the analytical material is vulcanized rubber or unvulcanized rubber containing at least a filler.

11. A data processing system for images of the cross-section of an analytical material, comprising a computing device that performs Fourier transform and inverse Fourier transform as data processing to remove unwanted scratches caused by material cutting present in the original image of the cross-section of the analytical material, and an output device, The aforementioned arithmetic device has an arithmetic unit, a storage unit, and an input unit. The original image is input to the storage unit through the input unit, the calculation unit performs a two-dimensional Fourier transform on the original image to create a spatial frequency spectrum, an extracted spatial frequency spectrum is created from the spatial frequency spectrum by extracting the unwanted scratch components, a two-dimensional inverse Fourier transform is performed on the extracted spatial frequency spectrum to create a scratched image that can be considered to have only the unwanted scratch components, and data processing is performed to subtract the components of the scratched image from the original image. A data processing system for cross-sectional images of analytical materials, wherein the processed image, from which the unwanted scratches have been removed from the original image, is output to the output device.

12. A data processing system for images of the cross-section of an analytical material, comprising a computing device that performs Fourier transform and inverse Fourier transform as data processing to remove unwanted scratches caused by material cutting present in the original image of the cross-section of the analytical material, and an output device, The aforementioned arithmetic device has an arithmetic unit, a storage unit, and an input unit. The original image is input to the storage unit through the input unit. A series of processing steps is performed, in which a unidirectional Fourier transform is applied to the target image to create a frequency spectrum, then a deselected frequency spectrum is created by removing predetermined low-frequency components from the frequency spectrum, then the unidirectional inverse Fourier transform is applied to the deselected frequency spectrum to create an inverse transformed image, and then a predetermined blurring process is applied to the inverse transformed image to create the blurred image. The original image is used as the target image for the first time, and the blurred image created in the previous series of processing steps is used as the target image for subsequent times, and the calculation unit repeats this a predetermined number of times, and in the preceding and succeeding series of processing steps, the one direction alternates between the horizontal and vertical directions. A data processing system for cross-sectional images of analytical materials, wherein the inverse transformed image created in the final series of processing steps is output to the output device as a processed image from which the unwanted scratches have been removed from the original image.

13. A data processing system for images of the cross-section of an analytical material, comprising a computing device that performs Fourier transform and inverse Fourier transform as data processing to remove unwanted scratches caused by material cutting present in the original image of the cross-section of the analytical material, and an output device, The aforementioned arithmetic device has an arithmetic unit, a storage unit, and an input unit. The original image is input to the storage unit through the input unit. A series of processing steps is performed in which a predetermined blurring process is applied to the target image to create a blurred image, then a one-way Fourier transform is applied to the blurred image to create a frequency spectrum, then a de-removed frequency spectrum is created by removing predetermined low-frequency components from the frequency spectrum, and then the one-way inverse Fourier transform is applied to the de-removed frequency spectrum to create an inverse transformed image. The original image is used as the target image for the first time, and the inversely transformed image created in the previous series of processing steps is used as the target image for subsequent times, and the calculation unit repeats this a predetermined number of times, and in the preceding and succeeding series of processing steps, the one direction alternates between the horizontal and vertical directions. A data processing system for cross-sectional images of analytical materials, wherein the inverse transformed image created in the final series of processing steps is output to the output device as a processed image from which the unwanted scratches have been removed from the original image.

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