JP2008271066A - Quantitative evaluation method on shade pattern of paper or sheet-shaped base material - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a quantitative evaluation method of a paper or a sheet-shaped base material applying a shade pattern which increases a correlation with an organoleptic evaluation more by selecting and using a feature quantity of an image expressibly in consonance with organoleptic evaluation results. <P>SOLUTION: An estimation value of an average preference is calculated to a plurality of papers or sheet-shaped base materials from the organoleptic evaluation results by a paired comparison, a difference value is calculated from the calculated estimation value, the feature quantity which has extracted an image feature by using a statistical image processing is converted into a new feature quantity, a linear regression equation is calculated from the difference value of the estimation value of the average preference and a relative value by an Euclidean distance from the feature quantity obtained the statistical image processing, a prediction value of the difference value of the estimation value of the average preference is calculated from the linear regression equation, a coefficient of correlation is calculated from the difference value of the estimation value of the average preference and the prediction value of the difference value of the estimation value of the average preference, an average coefficient of correlation is calculated from a cross examination, the linear regression equation is decided by the calculated average coefficient of correlation, and the shade pattern is evaluated. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a method for quantitative evaluation of a shading pattern applied to paper or a sheet-like substrate, and in particular, a statistically correlated paper or sheet-like substrate with a shading pattern correlated with sensory evaluation. The present invention relates to a quantitative evaluation method using image processing.

  Conventionally, when evaluating a shading pattern applied to a paper or sheet-like base material, it is generally performed by sensory evaluation evaluated by human senses. In other words, the shading pattern was evaluated by sensory evaluation by human eyes.

  As a method of performing sensory evaluation by visual observation, there are a method of evaluating by the evaluator's subjectivity and a method of evaluating by comparing an evaluator with a reference shading pattern that becomes a limit sample or an evaluation sample, and in either method, There was a problem that evaluations differed by different evaluators, and it was difficult for the same evaluator to evaluate with good reproducibility. When evaluating a shading pattern sensuously, visual comparison is made using the human vision, which is the most intelligent and sensitive sensation, so what is seen in the shading pattern depends on the subjectivity of the evaluator. However, there is a problem that the reliability of the quantitative evaluation result based on the sensory evaluation is low rather than the evaluation based on clear numerical values.

  In such a sensory evaluation method, in order to obtain a correct evaluation result, the evaluator needs a certain level of skill, and it takes time to reach a certain level of evaluation skill.

  In addition, when evaluating a shading pattern applied to a large amount of paper or sheet-like base material, the sensory evaluation by the evaluator has a problem that it takes time.

  As a method to obtain results equivalent to visual inspection, the texture of the paper wrinkle appearance is input by inputting texture features such as angular second moment and contrast obtained by image analysis, and quantitative evaluation is performed using a neural network that is a learning algorithm. There is a way to do it.

  Also, after converting the image data into binary or multi-value image data, calculating the fractal dimension from the binary or multi-value image data, quantification based on the fractal feature amount obtained by considering the visual characteristics from the learning algorithm There is a method of performing a physical evaluation, and the calculation of the fractal feature amount is performed using a neural network which is a learning algorithm.

  When evaluating with an algorithm using a pattern matching technique, there is a problem that an error occurs in the evaluation result due to a variation factor due to a change in the shape of the base material, a rotation of the base material, or the like when the evaluation target image is captured. Further, when the evaluation is performed using the learning algorithm, there is a problem that it is necessary to perform correction work of parameter adjustment by sequential learning or erroneous determination.

  In order to solve these problems, the present inventor creates a density histogram from the pixel density of a gray image on a paper or sheet-like substrate, recognizes the created density histogram as a figure, and determines the density histogram recognized as a figure. By calculating the barycentric coordinates of the figure and comparing the barycentric coordinates of the figure with the barycentric coordinates of the paper or sheet-like base material that has been subjected to sensory evaluation in advance, the gray-scale image of the paper or sheet-like base material having a correlation with the sensory evaluation Has been proposed (see, for example, Patent Document 1).

  In addition, in order to enhance the correlation between the quantitative evaluation and the sensory evaluation, a relatively strict sensory evaluation is performed on the grayscale image applied to the paper or sheet-like substrate, and the sensory evaluation result is digitized. A paper or sheet-like substrate obtained by evaluating a grayscale image applied to a paper or sheet-like base material as a transmitted light image, and quantifying with a statistical method using the image processing result of a local area of the captured image. A method for quantitative evaluation of a gray image of a material has been proposed (see, for example, Patent Document 2).

JP 2006-17591 A JP 2006-254330 A

  In the case of a general learning algorithm, learning requires repetitive calculation and requires a large amount of calculation time because many multidimensional feature values are required, and as an accuracy problem, it is an arbitrary image. When an image having a feature amount belonging to a category that has not been learned is recognized, there is often a case in which it is mistakenly output that it is one of the learned categories. Necessary.

  Patent Document 1 is an evaluation method using a centroid method for a grayscale image applied to paper or a sheet-like substrate, and Patent Document 2 is an evaluation method using a statistical method using the image processing result of a local area. There is a certain correlation with sensory evaluation in each evaluation method.

  The present invention proposes a method for evaluating a shading pattern applied to a paper or sheet-like substrate by constructing an algorithm using statistical image processing in order to solve the above-mentioned problems, and sensory evaluation An object is to provide a quantitative evaluation method for the shading pattern of a paper or sheet-like substrate that can further enhance the correlation with the sensory evaluation by selecting and using the feature amount of the image that can be expressed along the result. And

  The quantitative evaluation method for paper or sheet-like substrate of the present invention is a quantitative evaluation method for paper or sheet-like substrate on which a light and shade pattern is applied, and the light and shade applied to a plurality of paper or sheet-like substrates. From the result of the paired comparison method for the pattern, the estimated value in the average preference is calculated, the difference value of the estimated value in the average preference is calculated from the estimated value in the average preference, and a plurality of paper or sheet-like substrates The feature value is extracted from the statistical image processing for the applied shading pattern, and it is linear from the difference value of the estimated value in the average preference degree and the relative value by the Euclidean distance using the feature value obtained from the statistical image processing. A regression equation is calculated, a predicted value of a difference value of the estimated value in the average preference degree is calculated from the linear regression equation, and a difference value between the estimated value of the average preference value and a predicted value of the difference value of the estimated value in the average preference degree is calculated. Calculate the number of relationships, By calculating the average correlation coefficient from the coefficient it is characterized by evaluating the shading pattern.

  In addition, the feature extraction in the quantitative evaluation method of the paper or sheet-like substrate of the present invention is characterized by gray pattern edge extraction using a Gabor function.

  Further, the statistical image processing in the quantitative evaluation method of the paper or sheet-like substrate of the present invention is to extract the edge component of the shade pattern, perform the principal component analysis using the feature amount obtained from the feature extraction, Calculating an orthogonal projection matrix using eigenvectors up to the principal component obtained according to the cumulative contribution rate, and calculating a feature-selected feature obtained by projecting to the subspace using the calculated orthogonal projection matrix and the feature Features.

  The quantitative evaluation method for a paper or sheet-like substrate with a shading pattern according to the present invention includes a dependent variable that is a difference value of an estimated value in an average preference degree from sensory evaluation, and a feature amount from statistical image processing. Calculate the linear regression equation using learning data consisting of independent variables that are relative values based on the Euclidean distance used, and substitute the relative value, which is the test data, into the linear regression equation, and the difference in the estimated value in average preference Calculate the predicted value of the value, calculate the correlation coefficient between the difference value of the estimated value in the average preference degree and the predicted value of the difference value of the estimated value in the average preference degree, and calculate the average correlation coefficient from the cross-validation The method is characterized in that the shading pattern is evaluated by determining a linear regression equation.

  According to the method for quantitative evaluation of shading patterns applied to a paper or sheet-like substrate in the present invention, an algorithm using statistical image processing can be constructed, and the features of an image that can be expressed along the sensory evaluation results By selecting and using the amount, it is possible to further increase the correlation with the sensory evaluation.

Below, the quantitative evaluation method of the shading pattern given to the paper or sheet-like base material by embodiment of this invention is demonstrated using drawing. The present invention is not limited to the best mode for carrying out the invention described below, and various other modes can be implemented within the scope of the technical idea described in the claims.
In the present embodiment, the shading pattern applied to paper or a sheet-like substrate refers to an object that is made of paper fibers and is difficult to objectively evaluate.

In the quantitative evaluation method of the light and shade pattern applied to the paper or sheet-like substrate of the present embodiment, the sample is subjected to sensory evaluation by a human and evaluation by statistical image processing. In the sensory evaluation by a person, the sensory evaluation result by the paired comparison method is digitized. In addition, in the evaluation by statistical image processing, by constructing an algorithm having a correlation with sensory evaluation, a shade pattern is captured as an image, and a numerical result based on the feature amount of the image selected so as to follow the sensory evaluation result and Is used to calculate a linear regression equation.
In the evaluation of an unknown sample, a predicted value is calculated by a linear regression equation determined in advance, and the predicted value is used as a sensory evaluation value, and it is not necessary to actually perform a sensory evaluation.

As the feature extraction method of the shade pattern by the statistical image processing according to the present embodiment, the shade pattern is taken as a transmitted light image, and the edge extraction method of the shade image by the Gabor function is applied.
It is known that the first visual field sense of the brain has a nerve cell that detects the edge of the object, and the Gabor function is a function that approximately represents a response characteristic to a visual stimulus. A Gabor transform image is obtained from a convolution operation using an original image and a Gabor function. The Gabor function is a product of a two-dimensional Gaussian curved surface and a plane wave unilaterally transmitted on a two-dimensional plane.

  Using the Gabor function for the transmitted light image, feature extraction is performed on the edge component of the grayscale image, and the feature value is used to select an image feature that can be expressed according to the sensory evaluation results from a statistical method. Make up quantity.

  The Gabor function ψ is a function composed of a Gaussian function, a sine function, and a cosine function, and is expressed by Equation 1. FIG. 1 shows an outline of the Gabor function defined by Equation 1, which is a Gabor filter in real space.

Here, (x ₀ , y ₀ ) is the center position of the Gaussian distribution, σ is the standard deviation of the Gaussian distribution, ω is the frequency of the sine plane wave, θ is the direction angle of the sine plane wave, and ρ is the phase conversion of the plane wave.

  A Gabor function (Gabor filter) is convoluted with the feature quantity of the original image. That is, the Gabor wavelet transform (Gabor / Wavelet / Transform) is performed on the feature amount. This conversion is a conversion process that makes the features of the image stand out. The Gabor wavelet transform image ο is obtained by a convolution operation between the input image I and the Gabor function ψ.

As a statistical image processing method, a shading pattern applied to a paper or sheet-like substrate is extracted for each of a plurality of directions for a component that matches a shape having a plurality of direction components. In addition, a component that matches a shape having a plurality of frequency components is extracted for each of a plurality of frequencies. Principal component analysis is performed using a plurality of feature quantities extracted, and eigenvalues, eigenvectors, and contribution rates are obtained. By selecting a significant feature based on the result of the principal component analysis, dimensional compression of the feature is achieved. In order to project from the original space to the subspace, an orthogonal projection matrix E is derived using the eigenvectors P _i up to the m-th principal component in accordance with the cumulative contribution rate that is the principal component analysis result.

In addition, in order to extract the unique features of the grayscale image in the feature space and evaluate the difference from other grayscale images, the feature vector obtained by feature extraction is orthographically projected to the subspace, and the residual from the difference of the projection vector with respect to the feature vector is stored. Find the difference vector. Here, sample number i = {1, 2, _... , K}, feature vector X _i , orthogonal projection matrix E, and residual vector R _i .

  Relative evaluation is performed on the plurality of residual vectors generated in the feature space in order to obtain the dissimilarity between the two features. Therefore, in order to evaluate the difference between the two features on a scale, the dissimilarity is defined by a relative value using the Euclidean distance. Here, the two features are the vectors a and b and the Euclidean distance d. Note that h is the number of dimensions of the vector.

For example, when learning and testing are performed on one sample group, the accuracy when the number of samples is small is assumed to be affected by errors, so cross-validation is performed. In the cross-validation, the data set is divided into p blocks, and (p-1) blocks are used as learning data and 1 block is used as test data to obtain accuracy. Block replacement is repeated to obtain p precisions. The average of the accuracy sum is used as the estimated accuracy of the model. The accuracy A _{i is} assumed as follows, and the estimation accuracy EA is as follows.

  Furthermore, as a method of calculating the accuracy, a linear regression equation is obtained from learning data using a least square method. By substituting the relative value that is the test data into the independent variable of the derived linear regression equation, the predicted value of the difference value of the estimated value in the average preference degree that is the dependent variable is obtained. The correlation coefficient between the difference value of the estimated value in the average preference degree, which is test data, and the predicted value of the difference value of the estimated value in the average preference degree is accuracy.

  FIG. 2 shows a linear regression equation calculating means for obtaining a predicted value of a difference value of an estimated value in average preference for a quantitative evaluation method of a shading pattern applied to a paper or sheet-like substrate according to the present embodiment. FIG.

  First, a procedure for visual sensory evaluation will be described. A plurality of subjects perform paired comparisons on a plurality of samples, respectively (step 1). This pair comparison is performed by Scheffe's method (hereinafter also referred to as “Nakaya's modified method”) in which sensory evaluation of paper has a track record and the comparison result is obtained as a numerical value.

  Next, with respect to the paired comparison result of Step 1, one subject is selected, and a uniqueness test is performed in order to test whether or not the sample is uniquely determined, that is, whether or not a correct judgment is made ( Step 2). The test involves all subjects.

  Further, in order to test how much the judgment results of all the subjects are in agreement, a test for coincidence is performed (step 3). This test does not include the evaluation of subjects who had problems with the uniqueness test.

  Next, if there is no problem in the consistency test, since the significance of the subject's judgment is clear, an estimated value for the average preference is obtained from the paired comparison result, and the sensory evaluation result for the sample is digitized (Step 4). If there is a problem in the coincidence test, it indicates that the sensory evaluation results for all the subjects are not significant.

  A sample having the highest numerical value in the sensory evaluation result is determined as a reference sample, and a difference value from other samples is calculated (step 5).

  Next, a procedure for performing evaluation by statistical image processing will be described. A transmitted light image is captured for the sample (step 6), and feature extraction of edge components in the grayscale image using a Gabor function is performed on the captured transmitted light image (step 7).

Next, principal component analysis is performed using the feature amount obtained from the feature extraction. According to the cumulative contribution rate, an orthogonal projection matrix is obtained using eigenvectors up to the principal component to be obtained (step 8).
Principal component analysis is a technique in which high-dimensional feature values are compressed to low dimensions, and is a linear coordinate transformation under conditions that minimize the amount of information lost.
There is a contribution rate as an index indicating how much the reduced information amount absorbs the original information amount, and the loss of information can be determined by the cumulative contribution rate.

  Next, the feature quantity obtained from the feature extraction is orthogonally projected onto the subspace using the orthogonal projection matrix, and the feature quantity based on the residual vector is obtained from the difference of the projection vector with respect to the feature vector (step 9).

  Next, in order to obtain the dissimilarity between the two features with respect to the residual vector generated in the feature space, a relative value using the Euclidean distance which is a distance measure is obtained (step 10).

Next, learning and testing are performed on a data set composed of a difference value of estimated values in the average preference degree by sensory evaluation and a relative value by Euclidean distance by statistical image processing. A linear regression equation is calculated using the learning data.
By substituting the relative value of the test data into the linear regression equation, the predicted value of the difference value of the estimated value in the average preference is obtained. A correlation coefficient between the difference value of the estimated value in the average preference degree of the test data and the predicted value of the difference value of the estimated value in the average preference degree is obtained (step 11).

  Next, cross-validation in which step 11 is repeated is performed (step 12), and an average correlation coefficient is obtained.

  If the correlation reaches a certain level in the previous step, the quantitative evaluation method based on the linear regression equation calculated from the training data can be said to have a correlation with the sensory evaluation, and a linear regression equation that gives good results is selected. (Step 13).

FIG. 3 is a flowchart for calculating a predicted value of the difference value of the estimated values in the average preference degree of the unknown sample by the quantitative evaluation method.
A transmitted light image of an unknown sample is captured (step 14), and feature extraction of the grayscale image is performed on the captured transmitted light image using a Gabor function (step 15). Using the feature quantity obtained from the feature extraction and the orthogonal projection matrix derived in advance, a residual vector is obtained by projecting to the partial space (step 16), and the residual vector of the reference sample and the residual in the unknown sample are obtained. By calculating a relative value representing dissimilarity from the difference vector (step 17), substituting the relative value into an independent variable of a predetermined linear regression equation (step 18), and calculating a predicted value (step 19). It can be said that the predicted value has a correlation with the sensory evaluation result.
Thus, quantitative evaluation that can be correlated with sensory evaluation is possible without performing sensory evaluation by an evaluator.

  (Example) In FIGS. 4 to 7 and Table 1, as an example of the shade pattern applied to the paper or sheet-like substrate, the shade pattern of the face image applied to the paper is shown as an example in the above embodiment. Shows how to evaluate. In addition, these do not limit this invention at all.

As a sample, two sets of 27 sheets of paper with a shading pattern of a face image are prepared as one set.
Using the above-mentioned sample, a paired comparison, which is a visual sensory evaluation, was performed.
Among the two sets of samples, the sample from A to X, A1, and B1 excluding V in one set is specimen 1, and the sample from a to x, a1, and b1 from the other set v is specimen 2 It was.
For the paired comparison method, Scheffe's method was used.
The determination is a three-step evaluation of good (+1), same (0 point), and bad (−1 point) for the definition of the pattern.
The test subjects are 10 expert panels with specialized knowledge and abilities to evaluate.

  When the sensory evaluation was performed, the test of uniqueness was performed for all subjects in order to test whether the sensory evaluation results of the subjects were significant based on variations in the judgment of the subjects. The sensory evaluation results of subjects who failed this test were not adopted.

  Consistency tests were conducted to determine how well the judgments of all the subjects were in agreement, with the subject's judgment that was not a problem in the uniqueness test. Since this test showed significance, the significance of the paired comparison results of all the subjects became clear. If no significance is recognized by this test, the evaluation as all the subjects is not significant, and it does not make sense to calculate an estimated value for the average preference degree to be executed in the next step.

The estimated value in the average preference degree of each sample was calculated from the paired comparison result of each sample, the number of subjects, and the number of samples.
FIG. 4 shows the results of paired comparison of samples by all subjects. For example, when the evaluation is made with the non-evaluation side sample B1 and the evaluation side sample C, all the subjects replied that the sample C is good. From the total points, it can be seen that the sample C is the sample with the highest evaluation.

  The calculation method of the estimated value in the average preference degree of each sample divides the total score of the pair comparison of all subjects in each sample by the value obtained by multiplying by the number of subjects and the number of samples. For example, a total of 203 points of the pair comparison of sample A is divided by a value 270 obtained by multiplying 10 subjects and 27 samples, and divided by 0.75, and this 0.75 is an estimate of the average preference degree of sample A. Value. Thus, the estimated value in the average preference degree of all the samples was calculated.

FIG. 5 shows the estimated value of the average preference of each sample on a number line.
The sensory evaluation result of the sample can be expressed in the range of −1 to 1 on the horizontal axis by using the estimated value in the average degree of preference described above. Sample 1 and sample 2 are evaluated as one sample. This is because one reference sample is limited from 54 samples in advance, and a difference value between the reference sample and another sample is used as a difference value of an estimated value in average preference.

Next, evaluation by statistical image processing is performed.
When the subject evaluates the shading pattern, since the emphasis is on the reproducibility of details in the shading pattern, in order to extract the edge component of the shading pattern, the Gabor function is applied, and the direction component of the shading pattern and Feature extraction of frequency components.

  Next, feature extraction is performed for each pixel on the image using a Gabor function with respect to the transmitted light image of 256 × 256 pixels obtained by capturing the sample as a transmitted light image. The parameters of the Gabor function are mask size 11 × 11 pixels, standard deviation σ 2, sine plane wave frequency ω {0.5, 1.0, 1.5}, and sine plane wave angle direction θ {0. , 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8} and plane wave phase conversion ρ is {0, 1/2}. A 24-dimensional feature was extracted from one image. Increasing the dimensionality of the feature can be achieved by increasing the frequency of the sine plane wave and the angular parameters of the sine plane wave.

  Principal component analysis was performed using 54 samples having 24-dimensional characteristics. Table 1 shows the results of the contribution ratio and the cumulative contribution ratio up to the tenth main component.

According to the above-described experiment, after obtaining an orthogonal projection matrix for projecting to the partial space using the eigenvectors up to the seventh principal component, which has a cumulative contribution rate of 95% with good results, the characteristics of each image Use the vector to find the residual vector. Since it is difficult to extract one effective feature from an image size of 256 × 256 pixels, the image was divided into image sizes of 32 × 32 pixels, and an average value of residual vectors was calculated for each of 64 blocks.
One block has 24-dimensional features.
The sample with the highest sensory evaluation was determined as the reference sample, and in order to evaluate the degree of dissimilarity with other samples, the relative value with the reference sample was determined. In this case, the average value calculated for each block is used to obtain the Euclidean distance for each corresponding block, and the average value is used as a relative value.

  In learning, the difference value of the estimated value in the average preference degree was set as a dependent variable, and the relative value was set as an independent variable, and a linear regression equation was derived from the least square method. In the test, a 24-dimensional feature value based on the Gabor function was calculated and projected onto the subspace using the derived orthogonal projection matrix. Relative values were calculated using the residual vector feature values obtained by projection, and the relative values were substituted into the independent variables of the derived linear regression equation, and the predicted value of the difference value of the estimated value in average preference was calculated. . FIG. 6 shows, as an example, a scatter diagram of a relative value in learning data and a difference value between estimated values in average preference.

  An example of a linear regression equation calculated from learning data is shown.

  The data set was divided into 6 blocks, 5 blocks were learned, and 1 block was used as a test. A linear regression equation was calculated from the learning data, and the relative value of the test data was substituted into the calculated linear regression equation to calculate a predicted value of the difference value of the estimated values in the average preference. Block replacement was repeated 6 times in total, and the correlation coefficient for each block was calculated. Since the average correlation coefficient, which is the average value of the six correlation coefficients, is 0.82, a result with a high correlation was obtained.

  FIG. 7 shows a scatter diagram of the difference value of the estimated value in the average preference degree obtained from the sensory evaluation and the predicted value of the difference value of the estimated value in the average preference degree obtained from the statistical image processing.

  It was confirmed that the evaluation method based on the linear regression equation was a quantitative evaluation method having a high correlation with the sensory evaluation because the above-mentioned average correlation coefficient resulted in a high correlation.

Diagram showing an example of Gabor filter Flow chart for calculating a linear regression equation in the quantitative evaluation method according to the present embodiment Flow chart for calculating the predicted value of the difference between the estimated values for the average preference of unknown samples The figure which shows the evaluation result of the pair comparison with the sample Figure showing the estimated value of the average preference of the sample The figure which shows the scatter diagram of the difference value of the estimated value in the relative value in the data for learning of an Example, and an average preference degree The figure which shows the scatter diagram of the difference value of the estimated value in the average preference degree obtained from sensory evaluation, and the predicted value of the difference value of the estimated value in the average preference degree obtained from statistical image processing

Claims (4)

A method for quantitative evaluation of a paper or sheet-like substrate having a light and shade pattern,
Calculate the average preference value from the results of the paired comparison method for the shade pattern applied to the plurality of paper or sheet-like base materials,
A difference value is calculated from the calculated estimated value,
Extracting feature quantities from statistical image processing for shading patterns applied to a plurality of paper or sheet-like substrates,
Using the extracted feature amount to calculate a relative value by the Euclidean distance,
Calculate a linear regression equation from the difference value of the estimated value of the average preference degree and the relative value by the Euclidean distance,
Calculate a predicted value of the difference value of the estimated value of average preference from the linear regression equation,
By calculating a correlation coefficient from a difference value of the estimated value of the average preference degree and a predicted value of a difference value of the estimated value of the average preference degree, and calculating an average correlation coefficient from the plurality of correlation coefficients, A method for quantitatively evaluating a paper or sheet-like substrate, characterized in that The method for quantitative evaluation of a paper or sheet-like substrate according to claim 1, wherein the feature extraction by the statistical image processing is edge extraction of a light and shade pattern using a Gabor function. The statistical image processing is:
Feature extraction of the edge component of the shading pattern,
Perform a principal component analysis using the feature amount obtained from the feature extraction, calculate an orthogonal projection matrix using an eigenvector up to the principal component obtained according to the cumulative contribution rate,
The paper or sheet-like base material according to claim 1 or 2, wherein a feature-selected feature amount obtained by projecting onto a partial space is calculated using the calculated orthogonal projection matrix and the feature amount. Quantitative evaluation method. A method for quantitative evaluation of a paper or sheet-like substrate having a light and shade pattern,
A dependent variable that is a difference value of the estimated average preference from the sensory evaluation;
An independent variable that is a relative value by the Euclidean distance using the feature amount from the statistical image processing;
Calculate a linear regression equation using learning data consisting of
Substituting a relative value that is test data into the linear regression equation to calculate a predicted value of a difference value of an estimated value of average preference,
Calculating a correlation coefficient between a difference value of the estimated value of the average preference degree and a predicted value of a difference value of the estimated value of the average preference degree, calculating an average correlation coefficient from a cross-validation,
A quantitative evaluation method for a paper or sheet-like substrate characterized by evaluating a shading pattern by determining the linear regression equation.

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