JP2011100395A - Discrimination device, discrimination method, and program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To perform learning and discrimination with a less amount of operations in a learning-discrimination system. <P>SOLUTION: In a learning phase, a learning pixel hypersphere mapping unit 110 obtains images imaging only skins and maps them in a color feature space, then maps on a hypersphere surface as unit skin vectors u. A hyperplane setting unit 130 establishes a hyperplane having an average vector m' or m of each of the unit skin vectors u as a normal vector. A learning pixel dimension compression unit 140 projects each of the unit skin vectors u on the hyperplane ϕ and further projects on a base vector of the hyperplane ϕ and designates as projection skin vectors y'. A discrimination boundary setting unit 160 establishes a threshold K of a discrimination boundary for discriminating between the "skins" and "things other than skins". The established hyperplane ϕ, base vector of the hyperplane ϕ, and threshold K of the discrimination boundary are also used in a discrimination phase. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to a learning discriminating system, and more particularly to a discriminating apparatus that performs learning in advance and discriminates whether or not a discrimination target belongs to a set, a processing method therefor, and a program that causes a computer to execute the method.

  In pattern recognition technology, various methods have been proposed depending on how learning data is captured in a feature space. In particular, in the template matching method, a group for each class (category) is expressed by one representative vector (template), and the distance between the input vector and the representative vector of each class and the similarity are evaluated, so that the closest class is determined. Identified. In the learning phase for obtaining a representative vector, an average vector for each class is obtained from the distribution of learning data belonging to each class. Further, in the discrimination phase in which the input is classified, an Euclidean space between the average vector for each class is used (for example, see Non-Patent Document 1).

Hideki Aso, Koji Tsuda, Noboru Murata, “Statistics of Pattern Recognition and Learning”, Iwanami Shoten, April 2003, p. 12-16

  However, in the above-described conventional technology, a large amount of calculation is required in the learning phase and the discrimination phase due to the distribution of data in the feature space, and there is a risk that processing time may be required.

  The present invention has been made in view of such a situation, and an object thereof is to perform learning and discrimination with a small amount of calculation in a learning discrimination system.

  The present invention has been made to solve the above-mentioned problems, and a first aspect of the present invention is that each learning information is mapped to a feature space and then converted into a unit learning vector having a predetermined length. A learning information mapping unit that maps each of the learning information onto a hypersphere, a hyperplane setting unit that sets a hyperplane having an average vector of each unit learning vector as a normal vector, and each of the unit learning vectors And a learning information dimension compression unit that compresses the dimension of the learning information by projecting onto the hyperplane and then projecting onto the basis vector of the hyperplane, and from each distribution of the projection learning vector A discriminant boundary setting unit for setting a discriminant boundary relating to learning information and mapping the discriminant target information into the feature space and converting it into a unit discriminant vector having a predetermined length And a discrimination target information mapping unit that maps the discrimination target information onto a hypersphere, and a projection discrimination target vector that projects the unit discrimination target vector onto the hyperplane and then projects it onto the hyperplane basis vector. A discrimination apparatus comprising: a discrimination target information dimension compressing unit that compresses the dimension of the discrimination target information by using a boundary discrimination unit that discriminates whether or not the projection discrimination target vector is included in the discrimination boundary; It is a program for executing a processing procedure. As a result, the learning information is mapped onto the hypersphere, and the amount of computation in learning and discrimination is reduced.

  In the first aspect, the hyperplane setting unit may set the hyperplane so as to pass through the origin of the feature space. As a result, the specific term becomes zero, and the operation amount is further reduced.

  In the first aspect, the learning information dimension compression unit may generate the basis vector of the hyperplane by principal component analysis for each of the unit learning vectors projected onto the hyperplane. This brings about the effect | action that a base vector is produced | generated through principal component analysis.

  In the first aspect, the discrimination boundary setting unit may set the discrimination boundary based on each Mahalanobis distance of the projection learning vector. As a result, the operation amount is further reduced.

  In the first aspect, the learning information and the discrimination target information may be color information related to an object, and the discrimination boundary may be a boundary for discriminating the object.

  In addition, the second aspect of the present invention maps each of the first learning information into a feature space and then converts the first learning information into a first unit learning vector having a predetermined length, thereby converting the first learning information into the first learning information. A first learning information mapping unit that maps each onto a hypersphere, and a second length having a predetermined length after mapping each of the second learning information contrary to the first learning information to the feature space A second learning information mapping unit that maps each of the second learning information onto a hypersphere by converting to a unit learning vector, and an average vector of each of the first unit learning vectors as a normal vector A hyperplane setting unit that sets a hyperplane, and a first projection learning vector obtained by projecting each of the first unit learning vectors onto the hyperplane and then projecting onto the basis vector of the hyperplane. Compress the dimension of 1 learning information The first learning information dimension compression unit and the second unit learning vector are projected onto the hyperplane and then the second projection learning vector is projected onto the hyperplane basis vector. A second learning information dimension compressing unit that compresses the dimension of the learning information, and a determination boundary that sets a determination boundary relating to the first and second learning information from the respective distributions of the first and second projection learning vectors A setting unit; a discrimination target information mapping unit that maps the discrimination target information onto a hypersphere by mapping the discrimination target information to the feature space and then converting the discrimination target information into a unit discrimination target vector having a predetermined length; and Discrimination target information that compresses the dimension of the discrimination target information by projecting the unit discrimination target vector onto the hyperplane and then projecting it onto the basis vector of the hyperplane. The original compression unit, the projection determination target vector discrimination apparatus and a boundary determination unit for determining whether or not included in the determination boundary for a program for executing the processing methods and procedures. As a result, the two kinds of learning information that are opposite to each other are mapped onto the hypersphere, thereby bringing about an effect of reducing the amount of calculation in learning and discrimination.

  According to the present invention, it is possible to achieve an excellent effect that learning and discrimination with a small amount of calculation can be performed in a learning discrimination system.

It is a figure which shows the example of the application image of embodiment of this invention. It is a figure which shows an example of the learning function structure of the discrimination | determination apparatus in the 1st Embodiment of this invention. It is a figure which shows an example of the skin vector 520 (s) and the skin set 530 in the 1st Embodiment of this invention. It is a figure which shows an example of the unit skin vector 540 (u), the hypersphere 550, and the average vector 560 (m ') in the 1st Embodiment of this invention. It is a figure which shows an example of the unit average vector 561 (m) and the hyperplane 570 ((phi)) in the 1st Embodiment of this invention. Basis vector 580 in the first embodiment of the present invention (e _i), is a diagram showing an example of a projection skin vector 590 (y ') and determine boundaries 600. It is a figure which shows an example of the discrimination | determination function structure of the discrimination | determination apparatus in the 1st Embodiment of this invention. It is a figure which shows an example of the input vector 620 (x) in the 1st Embodiment of this invention. It is a figure which shows an example of the unit input vector 640 (ux) and the hypersphere 650 in the 1st Embodiment of this invention. Hyperplane 670 in the first embodiment of the present invention (phi), is a diagram showing an example of a basis vector 680 (e _i) and projection input vector 690 (z '). It is a figure which shows an example of the process sequence of the learning phase in the 1st Embodiment of this invention. It is a figure which shows an example of the process sequence of the discrimination | determination phase in the 1st Embodiment of this invention. It is a figure which shows an example of the learning function structure of the discrimination | determination apparatus in the 2nd Embodiment of this invention. It is a figure which shows an example of the skin vector 520 (s), the non-skin vector 525 (p), and the skin set 530 in the 2nd Embodiment of this invention. It is a figure which shows an example of the unit skin vector 540 (u), the unit non-skin vector 545 (q), the hypersphere 550, and the average vector 560 (m ') in the 2nd Embodiment of this invention. It is a figure which shows an example of the unit average vector 561 (m) and the hyperplane 570 ((phi)) in the 2nd Embodiment of this invention. Second embodiment of the basis vectors in the form 580 of the present invention (e _i), the projection skin vector 590 (y ') is a diagram showing an example of the projection non-skin vector 595 (r') and determine boundaries 600. It is a figure which shows an example of the process sequence of the learning phase in the 2nd Embodiment of this invention.

Hereinafter, modes for carrying out the present invention (hereinafter referred to as embodiments) will be described. The description will be made in the following order.
1. First embodiment (example using only skin color pixels as learning pixels)
2. Second Embodiment (example using skin color pixels and non-skin color pixels as learning pixels)
3. Modified example

  FIG. 1 is a diagram showing an example of an application image of the embodiment of the present invention. When the subject including the person 11 is imaged by the imaging device 20, if the skin portion of the person 11 can be accurately determined, skin color correction or the like can be accurately performed in post processing by the imaging device 20 or another device. It is assumed that the person 11 has at least a part of skin exposed on the face, hands, arms, legs, and the like.

  However, the subject may include objects other than the person 11. In the example of the figure, a dog 12 and a poster 13 are shown as objects other than the person 11. The dog 12 is shown as an example of an animal having a color close to the skin color. The poster 13 is printed with a human face and skin other than the face. In the embodiment of the present invention, the exposed portion of the skin of the person 11 is determined as “skin”, and other objects such as the dog 12 and the poster 13 are determined as “not skin”.

  Note that the discrimination result may be explicitly presented to the user on the display screen, or may be indirectly presented as additional information for other software processing. In the former case, it is conceivable to highlight the portion determined to be skin on the captured image. In the latter case, it is conceivable to store the coordinate position on the captured image determined as skin in the image file as metadata.

  Here, as color filters arranged on the front surface of the image sensor in the image capturing apparatus 20, six colors of red (R), green (G), blue (B), cyan (C), magenta (M), and yellow (Y) are used. Assume color. Although any one color filter is arranged in one pixel of the image sensor, color information of six colors can be aligned for each pixel by performing demosaic processing. Thus, an arbitrary pixel xi is mapped to coordinates (Ri, Gi, Bi, Ci, Mi, Yi) in the color feature space.

<1. First Embodiment>
The embodiment of the present invention comprises two stages, a learning phase for learning a discrimination boundary of a skin vector and a discrimination phase for discriminating whether or not a discrimination target pixel is skin based on the discrimination boundary.

  Note that the learning phase is executed in advance prior to the discrimination phase. In the learning phase, a normal vector that defines the hyperplane is determined. Further, in this learning phase, the hyperplane base and discrimination boundary are determined. By using these normal vectors, hyperplane bases, and discrimination boundaries, it is discriminated whether or not the discrimination target pixel is skin in the discrimination phase.

[Example of learning function configuration of discrimination device]
FIG. 2 is a diagram illustrating an example of a learning function configuration of the determination device according to the first embodiment of the present invention. This learning function configuration includes a learning pixel hypersphere mapping unit 110, a hyperplane setting unit 130, a learning pixel dimension compression unit 140, and a discrimination boundary setting unit 160.

  The learning pixel hyperspherical mapping unit 110 acquires an image obtained by capturing only the skin, maps the image onto the color feature space, and maps the image onto the hypersphere. The learning pixel hyperspherical mapping unit 110 includes a feature space mapping unit 111 and a unit vector conversion unit 112. The learning pixel hyperspherical mapping unit 110 is an example of a learning information mapping unit described in the claims.

The feature space mapping unit 111 inputs, as learning information, pixels that cause an event of being skin, and, as shown in FIG. 3, coordinates (Ri, Gi, Bi, Ci, Mi, Yi in the color feature space 510). ). In general, a plurality of pixels are input as learning information. Here, each learning information mapped to the feature space is specifically expressed as a skin vector 520 (s). The set of skin vectors 520 (s) is represented as a skin set 530. The skin vector 520 (s) is expressed by the following equation using elements s _{1 to} s ₆ corresponding to six colors.
s = [s ₁ s ₂ s ₃ s ₄ s ₅ s ₆ ] ^T

The unit vector conversion unit 112 converts each set of skin vectors 520 (s) into a unit vector having a size “1”. The skin vector converted by the unit vector converter 112 is represented as a unit skin vector 540 (u) as shown in FIG. This unit skin vector 540 (u) is calculated by the following equation. || s || represents the size of the skin vector 520 (s).
u = s / || s ||

  Since this unit skin vector 540 (u) is a unit vector, it is all mapped onto the hypersphere 550. Here, the unit vector is treated as a size “1” for the sake of convenience, but each of the unit vectors may have a predetermined length equal to each other, and is mapped onto the hypersphere 550 in that case as well.

  The hyperplane setting unit 130 sets a hyperplane having the average vector of each unit skin vector 540 (u) as a normal vector. The hyperplane setting unit 130 includes an average vector generation unit 131, a unit vector conversion unit 132, and a hyperplane generation unit 133.

As shown in FIG. 4, the average vector generation unit 131 generates an average vector 560 (m ′) of each unit skin vector 540 (u). This average vector 560 (m ′) is calculated by the following equation. However, k is the number of elements of the skin set 530.

The unit vector conversion unit 132 converts the average vector 560 (m ′) into a unit vector having a size “1”. The average vector m converted by the unit vector conversion unit 132 is calculated by the following equation.
m = m '/ || m' ||

  As shown in FIG. 5, the hyperplane generating unit 133 generates a hyperplane 570 (φ) having a unit average vector (m) as a normal vector. When this hyperplane 570 (φ) is set so as to pass through the origin of the feature space 510, a specific term becomes zero, so that the calculation can be simplified. Instead of the unit average vector 561 (m), an average vector 560 (m ′) before being converted into a unit vector can be used. Information regarding the hyperplane φ set by the hyperplane generation unit 133 is transmitted to the discrimination function through the signal line 139.

  The learning pixel dimension compression unit 140 projects each of the unit skin vectors 540 (u) onto the hyperplane 570 (φ), and further projects them onto the basis vectors of the hyperplane 570 (φ) to form projection learning vectors. . The learning pixel dimension compression unit 140 compresses dimensions as learning information. The learning pixel dimension compression unit 140 includes a hyperplane projection unit 141, a principal component analysis unit 142, and a base projection unit 143. The learning pixel dimension compression unit 140 is an example of a learning information dimension compression unit described in the claims.

As shown in FIG. 6, the hyperplane projection unit 141 projects each unit skin vector 540 (u) onto the hyperplane 570 (φ). When the unit skin vector 540 (u) as an arbitrary point on the hyperplane is orthogonally projected as the skin vector y on the hyperplane 570 (φ) passing through the arbitrary point Xo, the skin vector y is calculated by the following equation. The
y = u− (m · (u−Xo) / || m || ² ) m
As described above, when hyperplane 570 (φ) is set to pass through the origin of feature space 510, Xo = 0. When the radius of the hyperplane is “1”, || m || = 1. Therefore, the above equation can be simplified as the following equation.
y = u− (m · u) m

Further, the hyperplane projection unit 141 can perform projection different from the normal projection as follows. When the hyperplane passes through an arbitrary point Xo in the space, the skin vector y can be obtained by the following equation.
y = (m · (Xo−u) / (m · u)) u + u
On the other hand, when the hypersphere touches the hypersphere at the point indicated by the average vector m, the skin vector y can be obtained by the following equation.
y = ((|| m || ² −m · u) / (m · u)) u + u

The principal component analysis unit 142 obtains a hyperplane basis vector 580 (e _i (i is an integer from 1 to 5)) as shown in FIG. 6 by subjecting the set of skin vectors y to principal component analysis. is there. Principal component analysis (PCA) is a technique for obtaining principal components from the relationship between variables and compressing the dimensions of the variables. As a result of this principal component analysis, eigenvalues and eigenvectors are obtained. When the eigenvalues are arranged in descending order, the eigenvector corresponding to the one with the largest eigenvalue is the vector with the most variance. Since the second and subsequent eigenvectors have orthogonal characteristics, they can be used as the basis vector 580 (e _i ). This basis vector 580 (e _i ) is transmitted to the discrimination function through the signal line 149.

The base projection unit 143 projects the skin vector y onto each base vector 580 (e _i ) to form a projected skin vector 590 (y ′) as shown in FIG. As a result, the skin vector y expressed in the feature space coordinate system can be expressed as a projected skin vector 590 (y ′) in the coordinate system of the hyperplane φ. This is expressed by the following equation.
y '= e _i · y
y ′ = [y ′ ₁ y ′ ₂ y ′ ₃ y ′ ₄ y ′ ₅ ] ^T

  The origin of the hyperplane φ coordinate may coincide with the origin of the feature space coordinates.

  As shown in FIG. 6, the discrimination boundary setting unit 160 sets a discrimination boundary 600 for discriminating between “skin” and “other than skin”. The discrimination boundary setting unit 160 includes a Mahalanobis distance generation unit 161 and a threshold value determination unit 163.

The Mahalanobis distance generation unit 161 generates a Mahalanobis distance L (y ′) from the origin for each of the projected skin vectors 590 (y ′). The reason why the Mahalanobis distance L (y ′) is adopted is to eliminate the bias in the distribution of the set of projected skin vectors 590 (y ′) and to make the distribution isotropic. The Mahalanobis distance L (y ′) is generated by the following equation. Here, σ _i is a standard deviation in the set of projected skin vectors 590 (y ′).

  The threshold value determination unit 163 determines a threshold value K at the time of discrimination from the distribution of the set of Mahalanobis distances L (y ′). Here, assuming that the skin distribution is a Gaussian distribution, the Mahalanobis distance L (y ′) corresponding to 2σ is set as the threshold value K so as to include 90% of the set of projected skin vectors 590 (y ′). Assume that. The threshold value K is transmitted to the discrimination function through the signal line 169.

[Example of discrimination function configuration of discrimination device]
FIG. 7 is a diagram illustrating an example of a discrimination function configuration of the discrimination device according to the first embodiment of the present invention. This discrimination function configuration includes a discrimination pixel hypersphere mapping unit 210, a discrimination pixel dimension compression unit 240, and a boundary discrimination unit 260.

  The discrimination pixel hyperspherical mapping unit 210 acquires a pixel to be discriminated and maps it onto a color feature space, and then maps it onto the hypersphere. The discrimination pixel hyperspherical mapping unit 210 includes a feature space mapping unit 211 and a unit vector conversion unit 212. The discrimination pixel hyperspherical mapping unit 210 is an example of a discrimination target information mapping unit described in the claims.

The feature space mapping unit 211 inputs a pixel to be discriminated and maps it to coordinates (Ri, Gi, Bi, Ci, Mi, Yi) in the color feature space 610 as shown in FIG. . Here, the mapped vector is represented as an input vector 620 (x). This feature space 610 is the same space as the feature space 510 in the learning function. Note that the input vector 620 (x) is represented by the following equation using elements x _{1 to} x ₆ corresponding to six colors.
x = [x ₁ x ₂ x ₃ x ₄ x ₅ x ₆ ] ^T

The unit vector conversion unit 212 converts the input vector 620 (x) into a unit vector having a size “1”. The input vector converted by the unit vector conversion unit 212 is represented as a unit input vector 640 (ux) as shown in FIG. This unit input vector 640 (ux) is calculated by the following equation.
ux = x / || x ||

  Since this unit input vector 640 (ux) is a unit vector, it is all mapped onto the hypersphere 650. Here, the unit vector is treated as a size “1” for the sake of convenience, but each of the unit vectors only needs to have an equal predetermined length. In this case, the unit vector is mapped onto the hypersphere 650.

  The discriminating pixel dimension compression unit 240 projects the unit input vector 640 (ux) onto the hyperplane 670 (φ), and further projects it onto the base vector of the hyperplane 670 (φ) to obtain a projection input vector. The discrimination pixel dimension compressing unit 240 compresses the discrimination target dimension. The discrimination pixel dimension compression unit 240 includes a hyperplane projection unit 241 and a base projection unit 243. Note that the discrimination pixel dimension compression unit 240 is an example of a discrimination target information dimension compression unit described in the claims.

As shown in FIG. 10, the hyperplane projection unit 241 projects the unit input vector 640 (ux) onto the hyperplane 670 (φ). Hyperplane 670 (φ) is the same as hyperplane 570 (φ) in the learning function, and information about hyperplane 570 (φ) is supplied by signal line 139. An input vector z projected by the hyperplane projection unit 241 is calculated by the following equation.
z = ux− (m · ux) m

The base projection unit 243 projects the input vector z to each base vector 680 (e _i ), and forms a projection input vector 690 (z ′) as shown in FIG. The basis vector 680 (e _i ) is the same as the basis vector 580 (e _i ) in the learning function, and is supplied by the signal line 149. By this projection, the input vector z expressed in the feature space coordinate system can be expressed as a projected input vector 690 (z ′) in the coordinate system of the hyperplane φ. This is expressed by the following equation.
z '= e _i · z
z ′ = [z ′ ₁ z ′ ₂ z ′ ₃ z ′ ₄ z ′ ₅ ] ^T

  The boundary determination unit 260 determines whether it is “skin” or “other than skin”. The boundary determination unit 260 includes a Mahalanobis distance generation unit 261 and a threshold determination unit 263.

  The Mahalanobis distance generation unit 261 generates the Mahalanobis distance L (z ′) from the origin for the projection input vector 690 (z ′). This Mahalanobis distance L (z ′) is calculated by the same formula as the projected skin vector 590 (y ′) in the learning function.

  The threshold discriminating unit 263 discriminates whether it is “skin” or “other than skin” from the relationship between the Mahalanobis distance L (z ′) and the threshold K. Here, the threshold value K is determined by the learning function and is supplied by the signal line 169. If the Mahalanobis distance L (z ′) is less than the threshold value K, the threshold value determining unit 263 determines that the pixel corresponding to the input x is “skin”. On the other hand, when the Mahalanobis distance L (z ′) is greater than or equal to the threshold value K, it is determined that the pixel corresponding to the input x is “other than skin”.

[Example of learning phase procedure]
FIG. 11 is a diagram illustrating an example of a learning phase processing procedure according to the first embodiment of this invention.

  First, when a skin image obtained by photographing only the skin is acquired (step S911), the feature space mapping unit 111 maps the skin image to the feature space 510 as a skin vector 520 (s) (step S912). The unit vector conversion unit 112 converts each set of skin vectors 520 (s) into unit skin vectors 540 (u) (step S913).

  Then, the average vector generation unit 131 generates an average vector 560 (m ′) of each unit skin vector 540 (u) (step S914). The unit vector conversion unit 132 converts the average vector 560 (m ′) to the unit average vector 561 (m) (step S915). The hyperplane is set by the average vector 560 (m ′) or the unit average vector 561 (m). The hyperplane 570 (φ) is set so as to pass through the origin of the feature space 510.

The hyperplane projecting unit 141 projects each of the unit skin vectors 540 (u) onto the hyperplane 570 (φ) to obtain a skin vector y (step S916). The principal component analysis unit 142 generates a hyperplane basis vector 580 (e _i ) by subjecting the set of skin vectors y to principal component analysis (step S917). Then, the base projection unit 143 projects the skin vector y onto each base vector 580 (e _i ) to obtain a projected skin vector 590 (y ′) (step S918).

  Then, the Mahalanobis distance generation unit 161 generates a Mahalanobis distance L (y ′) from the origin for each of the projected skin vectors 590 (y ′) as all teacher data (step S919). Then, the threshold determination unit 163 determines a threshold K for determination from the set distribution of the Mahalanobis distance L (y ′) (step S920).

  In this embodiment, steps S912 and S913 are an example of a learning information mapping procedure described in the claims. Steps S914 and S915 are an example of a hyperplane setting procedure described in the claims. Steps S916 to S918 are an example of a learning information dimension compression procedure described in the claims. Steps S919 and S920 are an example of a discrimination boundary setting procedure described in the claims.

[Example of processing procedure for discrimination phase]
FIG. 12 is a diagram illustrating an example of a determination phase processing procedure according to the first embodiment of this invention.

  First, the discrimination pixel hyperspherical mapping unit 210 maps the pixel to be discriminated as an input vector 620 (x) to the color feature space 610 (step S931). The unit vector conversion unit 212 converts the input vector 620 (x) into the unit input vector 640 (ux) (step S932).

Then, the hyperplane projection unit 241 projects the unit input vector 640 (ux) onto the hyperplane 670 (φ) (step S933). The hyperplane 670 (φ) is the same as the hyperplane 570 (φ) in the learning phase. The base projection unit 243 projects the input vector z onto each base vector 680 (e _i ) to obtain a projection input vector 690 (z ′) (step S934). The basis vector 680 (e _i ) is the same as the basis vector 580 (e _i ) in the learning phase.

  Then, the Mahalanobis distance generation unit 261 generates a Mahalanobis distance L (z ′) from the origin for the projection input vector 690 (z ′) (step S935). Then, the threshold determination unit 263 determines whether it is “skin” or “other than skin” from the relationship between the Mahalanobis distance L (z ′) and the threshold K. That is, if the Mahalanobis distance L (z ′) is less than the threshold value K (step S936), it is determined that the pixel corresponding to the input x is “skin” (step S937). On the other hand, if the Mahalanobis distance L (z ′) is greater than or equal to the threshold value K (step S936), it is determined that the pixel corresponding to the input x is “other than skin” (step S938).

  When a skin region is found from an image, it is possible to identify the skin region in the image by repeatedly executing the above-described one-pixel unit skin determination processing procedure in order of line scan.

  As described above, according to the first embodiment of the present invention, the hyperplane 570 is set after the skin image is mapped to the hypersphere 550 as learning information, and the base vector 580 of the hyperplane 570 is generated. After learning information is mapped to the basis vector 580, a threshold value K for determination is determined from the distribution of the set of Mahalanobis distances. The Mahalanobis distance is also generated for the discrimination target after being mapped to the basis vector 680, and it is discriminated whether it is “skin” or “other than skin” according to the relationship with the threshold value K.

  In this embodiment, steps S931 and S932 are an example of the discrimination target information mapping procedure described in the claims. Steps S933 and S934 are an example of a discrimination target information dimension compression procedure described in the claims. Steps S935 to S938 are an example of a boundary determination procedure described in the claims.

  In the first embodiment, one event is used as learning information. However, in the following second embodiment, an example in which two contradicting events are used as learning information will be described.

<2. Second Embodiment>
[Example of learning function configuration of discrimination device]
FIG. 13 is a diagram illustrating an example of a learning function configuration of the determination device according to the second embodiment of the present invention. In the second embodiment, the learning pixel hyperspherical mapping unit 110 of the first embodiment functions as the event occurrence learning pixel hyperspherical mapping unit 110, and the learning pixel dimension compression unit 140 of the first embodiment. Functions as the event occurrence learning pixel dimension compression unit 140. In addition to the first embodiment, an event non-occurrence learning pixel hypersphere mapping unit 120 and an event non-occurrence learning pixel dimension compression unit 150 are provided.

  The event occurrence learning pixel hyperspherical mapping unit 110 uses, as learning information, a pixel in which an event of “skin” has occurred, and after acquiring an image obtained by capturing only the skin and mapping it to a color feature space It maps onto the hypersphere. Since the function is the same as that of the learning pixel hyperspherical mapping unit 110 of the first embodiment described above, description thereof is omitted here. The event occurrence learning pixel hyperspherical mapping unit 110 is an example of a first learning information mapping unit described in the claims.

  The event non-occurrence learning pixel hyperspherical mapping unit 120 uses, as learning information, a pixel in which an event of “skin” does not occur, acquires an image obtained by capturing images other than the skin, and maps the image to a color feature space. This maps onto the hypersphere. The event non-occurrence learning pixel hyperspherical mapping unit 120 includes a feature space mapping unit 121 and a unit vector conversion unit 122. The event non-occurrence learning pixel hypersphere mapping unit 120 is an example of a second learning information mapping unit described in the claims.

  The feature space mapping unit 121 inputs pixels that do not cause the phenomenon of “skin” as learning information, and, as shown in FIG. 14, coordinates (Ri, Gi, Bi, Ci, Mi in the color feature space 510). , Yi). In general, a plurality of pixels are input as learning information. Each learning information mapped to the feature space for a pixel that does not cause the phenomenon of “skin” is specifically represented as a non-skin vector 525 (p) here.

  The unit vector conversion unit 122 converts each set of non-skin vectors 525 (p) into a unit vector of size “1”. The non-skin vector converted by the unit vector converter 122 is represented as a unit non-skin vector 545 (q) as shown in FIG.

  As shown in FIG. 16, the hyperplane setting unit 130 sets a hyperplane 570 having the average vector of each unit skin vector 540 (u) as a normal vector. Since the function is the same as that of the first embodiment described above, description thereof is omitted here.

  The event occurrence learning pixel dimension compressing unit 140 projects each unit skin vector 540 (u) onto the hyperplane 570 (φ), and further projects it onto the base vector of the hyperplane 570 (φ) to obtain a projection learning vector. It is. Since the function is the same as that of the learning pixel dimension compression unit 140 of the first embodiment described above, description thereof is omitted here. The event occurrence learning pixel dimension compression unit 140 is an example of a first learning information dimension compression unit described in the claims.

  The event non-occurrence learning pixel dimension compression unit 150 projects each of the unit non-skin vectors 545 (q) onto the hyperplane 570 (φ), and further projects them onto the basis vectors of the hyperplane 570 (φ). To do. The event non-occurrence learning pixel dimension compression unit 150 includes a hyperplane projection unit 151 and a base projection unit 153. The event non-occurrence learning pixel dimension compression unit 150 is an example of a second learning information dimension compression unit described in the claims.

As shown in FIG. 17, the hyperplane projecting unit 151 projects each unit non-skin vector 545 (q) onto the hyperplane 570 (φ). The non-skin vector r projected by the hyperplane projection unit 151 is calculated by the following equation.
r = q- (m · q) m

The base projection unit 153 projects the non-skin vector r onto each base vector 580 (e _i ) to form a projected non-skin vector 595 (r ′) as shown in FIG. As a result, the non-skin vector r expressed in the feature space coordinate system can be expressed as a projected non-skin vector 595 (r ′) in the coordinate system of the hyperplane φ. This is expressed by the following equation.
r ′ = e _i · r
r ′ = [r ′ ₁ r ′ ₂ r ′ ₃ r ′ ₄ r ′ ₅ ] ^T

  Note that, as in the first embodiment, the origin of the hyperplane φ coordinate may coincide with the origin of the feature space coordinate.

  The discrimination boundary setting unit 160 sets a discrimination boundary for discriminating between “skin” and “other than skin”. The discrimination boundary setting unit 160 includes Mahalanobis distance generation units 161 and 162 and a threshold value determination unit 164.

  The Mahalanobis distance generation unit 161 generates a Mahalanobis distance L (y ′) from the origin for each of the projected skin vectors 590 (y ′). The Mahalanobis distance generator 162 generates a Mahalanobis distance L (r ′) from the origin for each of the projected non-skin vectors 595 (r ′). The formula for generating the Mahalanobis distance is the same as in the first embodiment.

  The threshold value determination unit 164 determines a threshold value K at the time of discrimination from the distribution of a set of Mahalanobis distances L (y ′) and L (r ′). Hereinafter, a method for determining the threshold value K according to the Bayes determination rule will be described.

When the input imaged at the position of the distance L is skin, the state is ωs. When the input is other than skin, the state is ωn. Determining that the discriminator determines that the input is “skin” is expressed as αs, and determining that the input is “other than skin” is expressed as αn. At this time, the loss is given as follows.
when ωs;
Loss λss = λ (αs | ωs) generated when the discriminator discriminates from αs
Loss λns = λ (αn | ωs) that occurs when the discriminator discriminates from αn
when ωn;
Loss λsn = λ (αs | ωn) generated when the discriminator discriminates from αs
Loss λnn = λ (αn | ωn) that occurs when the discriminator discriminates from αn

Therefore, when the input mapped to the position of the distance L is determined as “skin” or “other than skin”, the respective Bayes risks R (αs | L) and R (αn | L) are given by the following equations.
R (αs | L) = λ (αs | ωs) P (ωs | L)
+ Λ (αs | ωn) P (ωn | L)
R (αn | L) = λ (αn | ωs) P (ωs | L)
+ Λ (αn | ωn) P (ωn | L)

The threshold value K, which is a decision boundary, is equal to L such that R (αs | L) = R (αn | L). Therefore, the threshold value K can be determined as the distance L when the evaluation value of the following evaluation function F (L) becomes zero.
F (L) = λ (αn | ωs) P (ωs | L) + λ (αn | ωn) P (ωn | L)
−λ (αs | ωs) P (ωs | L) −λ (αs | ωn) P (ωn | L)

The above equation can be solved by rewriting the following equation using the Bayes formula.
F ′ (L) = {λ (αn | ωs) −λ (αs | ωs)} P (L | ωs) P (ωs)
− {Λ (αs | ωn) −λ (αn | ωn)} P (L | ωn) P (ωn)
Here, F ′ (L) = F (L) / P (L).

  P (ωs) and P (ωn) are prior probabilities that the inputs are “skin” and “other than skin”, respectively. This value is determined from the usage tendency of the user or P (ωs) = P (ωn).

P (L | ωs) and P (L | ωn) are given by the following equations.
P (L | ωs) = # skin (L) / # skin_total
P (L | ωn) = # non_skin (L) / # non_skin_total
Here, #skin (L) is the number of elements of the skin set existing at the position of Mahalanobis distance L. #Skin_total is the total number of elements in the skin set. #Non_skin (L) is the number of elements of the object set other than the skin existing at the position of the Mahalanobis distance L. #Non_skin_total is the total number of elements of the object set other than the skin.

  In the case of discrimination between skin and an object other than skin, by using a sufficient number of teacher data, the function of F ′ (L) becomes smooth, and L where F ′ (L) = 0 is determined to be one. The threshold value K indicating the decision boundary is the distance L when the evaluation value of the evaluation function F ′ (L) becomes zero.

  Here, since there is one decision boundary, it is assumed that L at which F ′ (L) = 0 is set to one, but it is also possible to prepare a plurality of decision boundaries. For example, each section may be divided into “skin” and “other than skin”. In addition, when a plurality of Ls with F ′ (L) = 0 are obtained in this way, the largest L among them can be used as a decision boundary.

[Example of discrimination function configuration of discrimination device]
The discriminating function configuration of the discriminating device in the second embodiment of the present invention can be the same as that of the first embodiment described with reference to FIG. That is, by using the threshold value K determined by the threshold value determination unit 164 in FIG. 13, it is possible to determine whether it is “skin” or “other than skin” by the determination function configuration in FIG.

[Example of learning phase procedure]
FIG. 18 is a diagram illustrating an example of a learning phase processing procedure according to the second embodiment of the present invention.

  First, when a skin image obtained by photographing only the skin is acquired (step S951), the feature space mapping unit 111 maps the skin image to the feature space 510 as a skin vector 520 (s) (step S952). When a non-skin image obtained by capturing images other than the skin is acquired (step S953), the feature space mapping unit 121 maps the non-skin image to the feature space 510 as a non-skin vector 525 (p) (step S954). Then, the unit vector conversion unit 112 converts each set of skin vectors 520 (s) into unit skin vectors 540 (u) (step S955). The unit vector conversion unit 122 converts each set of non-skin vectors 525 (p) into unit non-skin vectors 545 (q) (step S956).

  Then, the average vector generation unit 131 generates an average vector 560 (m ′) of each unit skin vector 540 (u) (step S957). The unit vector conversion unit 132 converts the average vector 560 (m ′) to the unit average vector 561 (m) (step S958). The hyperplane is set by the average vector 560 (m ′) or the unit average vector 561 (m). The hyperplane 570 (φ) is set so as to pass through the origin of the feature space 510.

  The hyperplane projecting unit 141 projects each of the unit skin vectors 540 (u) onto the hyperplane 570 (φ) to obtain a skin vector y (step S959). Further, the hyperplane projecting unit 151 projects each unit non-skin vector 545 (q) onto the hyperplane 570 (φ) to obtain a non-skin vector r (step S960).

Then, the principal component analysis unit 142 generates a hyperplane basis vector 580 (e _i ) by subjecting the set of skin vectors y to principal component analysis (step S961). The base projection unit 143 projects the skin vector y onto each base vector 580 (e _i ) to obtain a projected skin vector 590 (y ′) (step S962). The base projection unit 153 projects the non-skin vector r onto each base vector 580 (e _i ) to obtain a projected non-skin vector 595 (r ′) (step S963).

  Then, the Mahalanobis distance generation unit 161 generates a Mahalanobis distance L (y ′) from the origin for each of the projected skin vectors 590 (y ′) (step S964). In addition, the Mahalanobis distance generation unit 162 generates a Mahalanobis distance L (r ′) from the origin for each of the projected non-skin vectors 595 (r ′) (step S964). Then, the threshold value determination unit 164 determines a threshold value K for discrimination from the set distribution of the Mahalanobis distances L (y ′) and L (r ′) using the evaluation function F ′ (L) (step S965).

  In this embodiment, steps S952 and S955 are an example of a first learning information mapping procedure described in the claims. Steps S954 and S956 are an example of a second learning information mapping procedure described in the claims. Steps S957 and S958 are an example of a hyperplane setting procedure described in the claims. Steps S959, S961, and S962 are an example of a first learning information dimension compression procedure described in the claims. Steps S960 and S963 are an example of a second learning information dimension compression procedure described in the claims. Steps S964 and S965 are an example of a discrimination boundary setting procedure described in the claims.

[Example of processing procedure for discrimination phase]
As the processing procedure of the discrimination phase in the second embodiment of the present invention, the same procedure as that in the first embodiment described with reference to FIG. 12 can be used. That is, by using the threshold value K determined in step S920 in FIG. 11, it is possible to determine whether it is “skin” or “other than skin” by the processing procedure example in FIG.

  As described above, according to the second embodiment of the present invention, after mapping the skin image and the non-skin image to the hypersphere 550 as learning information, the hyperplane 570 is set, and the basis vector 580 of the hyperplane 570 is generated. Is done. After the learning information is mapped to the basis vector 580, a threshold value K for determination is determined from the distribution of the set of Mahalanobis distances according to the Bayes determination rule. The Mahalanobis distance is also generated for the discrimination target after being mapped to the basis vector 680, and it is discriminated whether it is “skin” or “other than skin” according to the relationship with the threshold value K.

<3. Modification>
In the above-described embodiment, a color feature space based on six color filters of RGBCMY is assumed. However, any natural number can be adopted as the number of colors. The color filter is not limited to the RGBCMY specific color filter, and a color filter having an arbitrary object spectral reflectance can be used.

  In the above-described embodiment, in the determination phase, if the Mahalanobis distance is less than the threshold value K, it is determined to be “skin”, and if it is equal to or greater than the threshold value K, it is determined to be “other than skin”. The relationship between the two is not limited to this. When the Mahalanobis distance is less than or equal to the threshold value K, it may be determined that the skin is “skin”, and when the Mahalanobis distance exceeds the threshold value K, it may be determined that the object is “other than skin”.

  In the above-described embodiment, the example using the Mahalanobis distance of the hyperplane coordinate as the reference for setting the threshold value K has been described. However, the Euclidean distance of the hyperplane coordinate can also be used.

  Further, in the above-described embodiment, the average vector of learning pixels is used when setting the hyperplane. However, in addition to this, a metaheuristic technique that reduces the variance of the skin set 530 can be used. It is also conceivable to set the hyperplane so that the dispersion becomes small. For example, methods such as genetic algorithm (GA) and simulated annealing are assumed.

  If the size (norm) of the pixel to be discriminated is less than a certain value or less than a certain value, the unit vector conversion unit 212 may treat it as a zero vector instead of converting it to a unit vector. Good. The coordinates in the feature space 610 where the pixels to be discriminated are mapped may all be zero or more.

  In the above-described embodiment, the skin image is given as the teacher data. However, the data format does not have to be an image, and there is essentially no difference between the data arrangement.

  In the above-described embodiment, an example of skin discrimination has been described. However, the present invention is not limited to skin discrimination, and can be used for more general discrimination. For example, it is assumed that scene discrimination is performed from an element discrimination element such as sky, soil, and lawn.

  The present invention is not limited to an image processing apparatus, and can be applied to any apparatus having a calculation function. For example, the present invention can be applied to audio data processing.

  As described above, according to the embodiment of the present invention, the learning information and the discrimination target are normalized and handled on the hypersphere, so that robust discrimination can be performed. In addition, by projecting from a hypersphere to a hyperplane, it is possible to express in a hyperplane coordinate system, the dimensions are compressed, and judgment can be simplified. In addition, by allowing the hyperplane to pass through the origin, the specific term becomes zero, and the calculation can be simplified. Further, by using the Mahalanobis distance as a reference in the determination, the super ellipse can be handled as a super circle, and can be expressed in one dimension, and the determination can be simplified.

  The embodiment of the present invention shows an example for embodying the present invention. As clearly shown in the embodiment of the present invention, the matters in the embodiment of the present invention and the claims Each invention-specific matter in the scope has a corresponding relationship. Similarly, the matters specifying the invention in the claims and the matters in the embodiment of the present invention having the same names as the claims have a corresponding relationship. However, the present invention is not limited to the embodiments, and can be embodied by making various modifications to the embodiments without departing from the gist of the present invention.

  The processing procedure described in the embodiment of the present invention may be regarded as a method having a series of these procedures, and a program for causing a computer to execute the series of procedures or a recording medium storing the program May be taken as As this recording medium, for example, a CD (Compact Disc), an MD (MiniDisc), a DVD (Digital Versatile Disk), a memory card, a Blu-ray Disc (registered trademark), or the like can be used.

110 (event occurrence) learning pixel hyperspherical mapping unit 120 (event non-occurrence) learning pixel hyperspherical mapping unit 111, 121 feature space mapping unit 112, 122 unit vector conversion unit 130 hyperplane setting unit 131 average vector generation unit 132 unit vector Conversion unit 133 Hyperplane generation unit 140 (Event occurrence) Learning pixel dimension compression unit 150 (Event non-occurrence) Learning pixel dimension compression unit 141, 151 Hyperplane projection unit 142 Principal component analysis unit 143, 153 Base projection unit 160 Discrimination boundary setting Unit 161, 162 Mahalanobis distance generation unit 163, 164 threshold determination unit 210 discrimination pixel hypersphere mapping unit 211 feature space mapping unit 212 unit vector conversion unit 240 discrimination pixel dimension compression unit 241 hyperplane projection unit 243 base projection unit 260 boundary discrimination unit 261 Mahalanobis distance generation unit 263 Threshold discrimination unit

Claims (10)

A learning information mapping unit that maps each of the learning information onto a hypersphere by mapping each of the learning information to a feature space and then converting the learning information into a unit learning vector having a predetermined length;
A hyperplane setting unit that sets a hyperplane having the average vector of each of the unit learning vectors as a normal vector;
A learning information dimension compressing unit that compresses the dimension of the learning information by projecting each of the unit learning vectors onto the hyperplane and then projecting onto the basis vector of the hyperplane;
A discrimination boundary setting unit that sets a discrimination boundary regarding the learning information from each distribution of the projection learning vectors;
A discrimination target information mapping unit that maps the discrimination target information onto a hypersphere by mapping the discrimination target information to the feature space and then converting the discrimination target information into a unit discrimination target vector having a predetermined length;
A discrimination target information dimension compression unit that compresses the dimension of the discrimination target information by projecting the unit discrimination target vector onto the hyperplane and then projecting the unit discrimination target vector onto the basis vector of the hyperplane;
And a boundary determination unit that determines whether or not the projection determination target vector is included in the determination boundary.   The discrimination apparatus according to claim 1, wherein the hyperplane setting unit sets the hyperplane so as to pass through an origin of the feature space.   The discrimination device according to claim 1, wherein the learning information dimension compression unit generates the basis vector of the hyperplane by principal component analysis for each of the unit learning vectors projected onto the hyperplane.   The discrimination apparatus according to claim 1, wherein the discrimination boundary setting unit sets the discrimination boundary based on each Mahalanobis distance of the projection learning vector.   The determination apparatus according to claim 1, wherein the learning information and the determination target information are color information about an object, and the determination boundary is a boundary for determining the object. First each of the first learning information is mapped onto a hypersphere by mapping each of the first learning information to a feature space and converting the first learning information into a first unit learning vector having a predetermined length. A learning information mapping section;
Each of the second learning information is converted into a second unit learning vector having a predetermined length after mapping each of the second learning information contrary to the first learning information to a feature space. A second learning information mapping unit that maps onto the hypersphere;
A hyperplane setting unit that sets a hyperplane having an average vector of each of the first unit learning vectors as a normal vector;
The first learning information is compressed by projecting each of the first unit learning vectors onto the hyperplane and then projecting the first unit learning vector onto the basis vector of the hyperplane. Learning information dimension compression unit of
The second unit learning vector is projected onto the hyperplane and then the second projection learning vector is projected onto the hyperplane basis vector to compress the dimension of the second learning information. Learning information dimension compression unit of
A determination boundary setting unit that sets a determination boundary related to the first and second learning information from the distribution of each of the first and second projection learning vectors;
A discrimination target information mapping unit that maps the discrimination target information onto a hypersphere by mapping the discrimination target information to the feature space and then converting the discrimination target information into a unit discrimination target vector having a predetermined length;
A discrimination target information dimension compression unit that compresses the dimension of the discrimination target information by projecting the unit discrimination target vector onto the hyperplane and then projecting the unit discrimination target vector onto the basis vector of the hyperplane;
And a boundary determination unit that determines whether or not the projection determination target vector is included in the determination boundary. A learning information mapping procedure for mapping each of the learning information onto a hypersphere by mapping each of the learning information to a feature space and then converting it into a unit learning vector having a predetermined length;
A hyperplane setting procedure for setting a hyperplane having the average vector of each of the unit learning vectors as a normal vector;
A learning information dimension compression procedure for compressing the dimension of the learning information by projecting each of the unit learning vectors onto the hyperplane and then projecting onto the basis vector of the hyperplane;
A determination boundary setting procedure for setting a determination boundary for the learning information from each distribution of the projection learning vectors;
A discrimination target information mapping procedure for mapping the discrimination target information onto a hypersphere by mapping the discrimination target information into the feature space and then converting the discrimination target information into a unit discrimination target vector having a predetermined length;
A discrimination target information dimension compression procedure for compressing the dimension of the discrimination target information by projecting the unit discrimination target vector onto the hyperplane and then projecting it onto the basis vector of the hyperplane,
And a boundary determination procedure for determining whether or not the projection determination target vector is included in the determination boundary. First each of the first learning information is mapped onto a hypersphere by mapping each of the first learning information to a feature space and converting the first learning information into a first unit learning vector having a predetermined length. Learning information mapping procedure;
Each of the second learning information is converted into a second unit learning vector having a predetermined length after mapping each of the second learning information contrary to the first learning information to a feature space. A second learning information mapping procedure for mapping onto the hypersphere;
A hyperplane setting procedure for setting a hyperplane having an average vector of each of the first unit learning vectors as a normal vector;
The first learning information is compressed by projecting each of the first unit learning vectors onto the hyperplane and then projecting the first unit learning vector onto the basis vector of the hyperplane. Learning information dimension compression procedure,
The second unit learning vector is projected onto the hyperplane and then the second projection learning vector is projected onto the hyperplane basis vector to compress the dimension of the second learning information. Learning information dimension compression procedure,
A determination boundary setting procedure for setting a determination boundary regarding the first and second learning information from the distribution of each of the first and second projection learning vectors;
A discrimination target information mapping procedure for mapping the discrimination target information onto a hypersphere by mapping the discrimination target information into the feature space and then converting the discrimination target information into a unit discrimination target vector having a predetermined length;
A discrimination target information dimension compression procedure for compressing the dimension of the discrimination target information by projecting the unit discrimination target vector onto the hyperplane and then projecting it onto the basis vector of the hyperplane,
And a boundary determination procedure for determining whether or not the projection determination target vector is included in the determination boundary. A learning information mapping procedure for mapping each of the learning information onto a hypersphere by mapping each of the learning information to a feature space and then converting it into a unit learning vector having a predetermined length;
A hyperplane setting procedure for setting a hyperplane having the average vector of each of the unit learning vectors as a normal vector;
A learning information dimension compression procedure for compressing the dimension of the learning information by projecting each of the unit learning vectors onto the hyperplane and then projecting onto the basis vector of the hyperplane;
A determination boundary setting procedure for setting a determination boundary for the learning information from each distribution of the projection learning vectors;
A discrimination target information mapping procedure for mapping the discrimination target information onto a hypersphere by mapping the discrimination target information into the feature space and then converting the discrimination target information into a unit discrimination target vector having a predetermined length;
A discrimination target information dimension compression procedure for compressing the dimension of the discrimination target information by projecting the unit discrimination target vector onto the hyperplane and then projecting it onto the basis vector of the hyperplane,
A program for causing a computer to execute a boundary determination procedure for determining whether or not the projection determination target vector is included in the determination boundary. First each of the first learning information is mapped onto a hypersphere by mapping each of the first learning information to a feature space and converting the first learning information into a first unit learning vector having a predetermined length. Learning information mapping procedure;
Each of the second learning information is converted into a second unit learning vector having a predetermined length after mapping each of the second learning information contrary to the first learning information to a feature space. A second learning information mapping procedure for mapping onto the hypersphere;
A hyperplane setting procedure for setting a hyperplane having an average vector of each of the first unit learning vectors as a normal vector;
The first learning information is compressed by projecting each of the first unit learning vectors onto the hyperplane and then projecting the first unit learning vector onto the basis vector of the hyperplane. Learning information dimension compression procedure,
The second unit learning vector is projected onto the hyperplane and then the second projection learning vector is projected onto the hyperplane basis vector to compress the dimension of the second learning information. Learning information dimension compression procedure,
A determination boundary setting procedure for setting a determination boundary regarding the first and second learning information from the distribution of each of the first and second projection learning vectors;
A discrimination target information mapping procedure for mapping the discrimination target information onto a hypersphere by mapping the discrimination target information into the feature space and then converting the discrimination target information into a unit discrimination target vector having a predetermined length;
A discrimination target information dimension compression procedure for compressing the dimension of the discrimination target information by projecting the unit discrimination target vector onto the hyperplane and then projecting it onto the basis vector of the hyperplane,
A program for causing a computer to execute a boundary determination procedure for determining whether or not the projection determination target vector is included in the determination boundary.

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