JP2008020963A - Pattern recognition device and method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a pattern recognition device for performing accurate pattern recognition by extracting features effective for identification from patterns. <P>SOLUTION: A face image recognition device comprises a face input part, a kernel orthogonal conversion data storage part, a kernel orthogonal conversion part, an input partial space generating part, a dictionary partial space storage part, a partial space similarity calculating part, and a face determining part. The face image recognition device extracts a nonlinear feature from a plurality of input patterns acquired from an identified object, and calculates the similarity between the generated input partial space and a predetermined registered dictionary partial space. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a pattern recognition apparatus and method for improving the accuracy of pattern recognition by extracting non-linear features effective for identification from a pattern.

  There is a mutual subspace method (Patent Document 1) as a pattern recognition method. In the mutual subspace method, the minimum canonical angle between the dictionary subspace, which is the subspace of the dictionary pattern distribution, and the input subspace, which is the subspace of the input pattern distribution to be recognized, is obtained. It determines with belonging to the category corresponding to the dictionary subspace which becomes the minimum. The generation of the partial space may be performed by obtaining a basis vector.

  For example, belonging to a category means that if a human face is recognized using an image, “the person currently receiving recognition is a person registered in the dictionary”. In the mutual subspace method, both the input side and the dictionary side are expressed in the subspace, so the pattern deformation absorption ability is better than the subspace method, but the relationship with other categories is not considered. Therefore, for example, in the case of face recognition, there is a problem that it is easily influenced by illumination conditions.

  For example, a constrained mutual subspace method (Patent Literature 2), a kernel nonlinear constraint mutual subspace method (Patent Literature 3), and an orthogonal mutual subspace method (Patent Literature 4) are proposed as improved methods of the mutual subspace method. Has been.

  In the constrained mutual subspace method, a “constrained subspace” consisting of essential features necessary for identification is prepared in advance, and the subspace method is applied after projecting the subspaces to be compared to the constrained subspace. .

  The kernel nonlinear constraint mutual subspace method uses the kernel nonlinear principal component analysis to map the target pattern into a higher-dimensional nonlinear feature space than the original space, thereby subdividing the pattern distribution of each class into a non-overlapping subspace. It expresses with.

  The orthogonal mutual subspace method is a method in which the mutual subspace method is applied by explicitly orthogonalizing the relationship between the class subspaces using an orthogonalization matrix. The orthogonalization of each class subspace is a method using a transformation similar to the orthogonal matrix used in the orthogonal subspace method, but the learning pattern used to obtain the orthogonal matrix is different.

  In the orthogonal subspace method, an autocorrelation matrix calculated from a learning pattern of each class is used to orthogonalize each class subspace. On the contrary. OMSM uses a projection matrix calculated from the basis vectors that span each class subspace. That is, in the orthogonal subspace method, orthogonalization is performed using all learning patterns, whereas in the orthogonal mutual subspace method, the basis vectors spanning each class subspace are regarded as learning data and orthogonalized.

The orthogonalization matrix O (alphabet “O”) is given by the following equation as a matrix representing a whitening conversion in which the eigenvalues of the sum matrix P of the projection matrix are all 1.

However, the matrix Λ− ^{1 / 2} is a diagonal matrix in which the reciprocals of square roots of eigenvalues of the matrix P are arranged, the matrix H is a matrix in which eigenvectors of the summation matrix P are arranged, and t in the upper right is the transpose. It can be seen from equation (2) that the eigenvalues are all 1 by the transformation using the orthogonalization matrix O. However, the matrix I is a unit matrix.

For the input and dictionary subspace generated from a plurality of patterns, N basis vectors extending the subspace are transformed by the orthogonalization matrix O, and further converted to N vectors after conversion to Gram-Schmidt. Is orthogonalized. Finally, these orthogonalized N vectors are respectively converted into an orthogonal matrix and a dictionary subspace basis vector.
JP-A-11-265542 JP 2000-30065 JP 2003-39192 A JP-A-2005-35300

  However, as described above, there is a limit to the expression capability of each subspace expressed in the linear subspace, and in order to further improve the performance, it is necessary to introduce a nonlinear subspace.

  The present invention proposes a method that enables identification of more complex patterns by applying kernel nonlinear principal component analysis to the orthogonal mutual subspace method.

  In order to solve the above problem, a pattern recognition apparatus according to an embodiment of the present invention uses a plurality of dictionary patterns belonging to each of a plurality of identification objects, and canonical angles between subspaces corresponding to each dictionary pattern. By performing a kernel orthogonalization transformation using the data set for each of the dictionary patterns, and a kernel orthogonalization transformation generating unit for obtaining a data set for calculating a kernel orthogonalization transformation that approximates the orthogonality A dictionary subspace generation unit that generates a dictionary subspace corresponding to each dictionary pattern, and an input subspace generation that generates an input subspace by performing kernel orthogonalization transformation using the data set on the input pattern A similarity calculation unit that calculates a similarity between the input subspace and the dictionary subspace, and a similarity calculated by the similarity calculation unit Using, and a recognition unit for determining the identification object which the input pattern belongs.

  In addition, a pattern recognition method according to an embodiment of the present invention relates to a pattern recognition processing method performed by the above apparatus.

  Moreover, the program regarding one Embodiment of this invention is a program for making a computer perform the pattern recognition process performed by the said apparatus.

  Since the registered dictionary subspace of each category can be identified by a subspace that is not similar in the nonlinear feature space, pattern recognition can be performed with higher accuracy than in the conventional method.

A pattern recognition apparatus according to an embodiment of the present invention will be described. First, a kernel orthogonalization matrix obtained by the pattern recognition apparatus of the present embodiment is obtained, nonlinear feature amounts are extracted, and a transformation matrix _Oφ is obtained by orthogonalizing the dictionary subspaces into mutually dissimilar subspaces. A series of processes in the kernel orthogonal mutual subspace method will be described.

[A kernel nonlinear principal component analysis]
As preparation for realizing the orthogonal mutual subspace method (kernel orthogonal mutual subspace method (KOMSM)) on the nonlinear feature space F, kernel nonlinear principal component analysis will be described. Linear identification by mapping the f-dimensional pattern x = (x ₁ , x ₂ ,..., x _f ) ^T to the nonlinear feature space F of dimension f _φ that is much higher than the original space by the nonlinear linear transformation φ. Transform impossible problems into linearly distinguishable problems.

  Calculate the inner product (φ (x) · φ (y)) of mapping φ (x) and mapping φ (y) to perform principal component analysis and projection to nonlinear subspace for the mapping in space F There is a need to. However, it is difficult to directly calculate this inner product on the space F because the dimension of the target vector is extremely high (impossible in an infinite dimensional space). In FIG. 3, in the original space A, the original patterns x1 and y1 cannot be linearly separated, but the mapped pattern φ (x1) mapped to the high-dimensional space B and the mapped pattern φ (y1) can be linearly separated. Yes. When this is applied to the discrimination between a face pattern and a non-face pattern that is very similar to the face, the face pattern and the non-face pattern can be discriminated by performing nonlinear transformation respectively. However, in the non-linear space B, it is not practical to directly calculate the inner product (φ (x1), φ (y1)) of the mapping pattern φ (x1) and the mapping pattern φ (y1) because the calculation amount is enormous. Absent. In addition, calculation is impossible when the nonlinear space B is infinite.

  However, if the nonlinear transformation φ is defined via the kernel function k (x, y), the inner product (φ (x1), φ (y1)) can be calculated from x1, y1.

This is a calculation technique called “kernel trick”. In order for a specific nonlinear transformation φ to exist, the kernel function k (x, y) needs to satisfy Mercer's condition. For example, the following function exists.

When this Gaussian function is applied, the pattern is mapped to an infinite dimensional space. The principal component analysis on the nonlinear feature space F using the kernel trick is a kernel nonlinear principal component analysis method. The nonlinear principal component analysis for m patterns x _i (i = 1 to m) results in the following eigenvalue problem of an m × m matrix K (kernel matrix) obtained through a kernel function.

The projection component of the mapped vector φ (x) onto the _i- th nonlinear principal component vector ei is calculated by the following equation.

Here, a _ij is the j-th component of the eigenvector a _i corresponding to the i-th largest eigenvalue λ _i of the matrix K. However, a _i is normalized so as to satisfy λ (a _i , a _i ) = 1.0. [B Kernel orthogonalization matrix generation]
Since the generation of the orthogonalization matrix O is executed by an inner product, an orthogonalization matrix can be defined on the nonlinear feature space F, and this is called a kernel orthogonalization matrix _Oφ . Since the inner product of O _φ and the map φ (x) of the arbitrary vector x can be calculated, the orthogonal mutual subspace method can be realized on the nonlinear feature space. This is called the kernel orthogonal mutual subspace method.

The basic flow of generating the kernel orthogonalization matrix _{Oφ is} the same as the generation of the orthogonalization matrix, and the linear class subspace may be replaced with a nonlinear class subspace. Hereinafter, we describe a r pieces of d-dimensional non-linear class subspace _V k (k = _1~r) Procedure for obtaining the _{n k} orthogonal matrix O _phi dimensions from. If a nonlinear class subspace V _{k of} class _k is generated from m learning patterns x _i ^k (i = ₁ to m), d basis vectors e _i ^k (i = 1) spanning the space V _k. -D) is represented by the following equation.

Here, a _ij ^k is a coefficient shown in Expression (6). Similarly, nonlinear class subspaces are generated for other classes. Next, each row vector O _i of the kernel orthogonalization matrix O _φ is obtained from all the basis vectors of the r d-dimensional nonlinear class subspaces, that is, the total (r × d) basis vectors. This is equivalent to performing KL expansion by regarding all base vectors as data. Here, E is a matrix in which all the basis vectors are arranged as columns.

Solve the eigenvalue problem of the matrix Q defined below.

  Here, E [i] means the i-th column component of the matrix E.

The inner product of the i-th basis vector E _i ^k of class k and the j-th basis vector E _j ^{k * of} class k ^* in the above equation is transformed as follows to obtain the kernel function values of x _k and x _{k *} It can actually be calculated as a linear sum of k (x _k , x _{k *} ).

The i-th row vector O _i of the kernel orthogonalization matrix O _φ uses the eigenvector b _i corresponding to the eigenvalue β _i as a weighting coefficient, and the linearity of the basis vector E [j] (j = 1 to r × d) as follows: Expressed in sum.

Here, the vector b _i is normalized so as to satisfy β _i (b _i · b _i ) = 1.0.

Further, if E [j] is the η (j) basis vector of class ζ _j , the above equation can be modified as follows.

This vector O _i cannot actually be calculated, but the inner product with the mapping vector φ (x) can be calculated.

[C Orthogonal transformation of mapping pattern]
A method for generating a dictionary subspace from the learned pattern obtained by orthogonalizing the mapping vector φ (x) using the previously obtained kernel orthogonalization matrix _Oφ will be described.

An orthogonal transformation is performed using a kernel orthogonalization matrix of the mapping vector φ (x). This can be calculated by the following equation using the input vector x and (r × m) total learning vectors xS ^k (S = ^{1 to} m, k = 1 to r).

Therefore, each component of the vector χ (φ (x)) obtained by orthogonally transforming the mapping φ (x) is expressed as follows.

[D Kernel Orthogonal Mutual Subspace Algorithm]
The kernel orthogonal mutual subspace method (KOMSM) can be constructed by applying the mutual subspace method to the orthogonally transformed pattern χ (φ (x)). FIG. 4 shows the flow. The nonlinear mapping φ (x _i ^k ) of all patterns x _i ^k (i = ^{1 to} m) belonging to the class k is transformed using the kernel orthogonalization matrix O _φ (step 401).

A linear class subspace P _k ^Dφ is generated by applying the KL expansion to the set of transformed patterns χ (φ (x ₁ ^k )),..., Χ (φ (x _m ^k )). Specifically, an autocorrelation matrix is obtained from a set of projection patterns, and n of the eigenvectors having the largest eigenvalues are ^{used as} the basis of the n-dimensional linear class k subspace P _k ^Dφ . (Step 402)
Similarly, other class subspaces are obtained. (Step 403)
When performing the identification process, the linear input subspace P _in ^Dφ is ^obtained from the pattern obtained by kernel orthogonal transformation (step 404) of the set of input patterns {x ₁ ⁱⁿ ,..., X _m ⁱⁿ } (step 405).

A canonical angle formed by P _in ^Dφ and each class subspace P _k ^Dφ is _obtained as a similarity (step 406). Among all the similarities, the class of the class subspace corresponding to the highest similarity equal to or higher than the threshold is set as the input pattern distribution class (step 407). In addition to these calculation procedures, the basis vectors (formula (7)) of each nonlinear class subspace are first obtained from the learning pattern, and these basis vectors are orthogonally transformed to obtain the Gram-Schmidt orthogonality. It is also possible to generate a class subspace by applying the optimization. [First embodiment]
The present embodiment relates to an embodiment of a face image recognition apparatus using the kernel orthogonal subspace method described above. The face image recognition apparatus according to the present embodiment performs personal authentication by the kernel orthogonal mutual subspace method when a face image is input. FIG. 1 shows the flow of processing according to this embodiment, and FIG. 2 shows the configuration of the face image recognition apparatus 200 according to this embodiment.

  The face image recognition apparatus 200 includes a face input unit 201, a kernel orthogonalization matrix data storage unit 202, a kernel orthogonalization conversion unit 203, an input subspace generation unit 204, a dictionary subspace storage unit 205, and an intersubspace similarity calculation unit 206. And a face determination unit 207.

  The face input unit 201 captures a face image of a person to be recognized using a camera (step 101), extracts a face area pattern from the image (step 102), and raster scans the face area pattern into a vector. Conversion is performed (step 103). The face area pattern can be determined based on the positional relationship between facial features such as pupils and nostrils, for example. In addition, a pattern to be recognized can always be obtained by acquiring face images continuously in time.

  As described in [B Kernel orthogonalization matrix generation], the kernel orthogonalization matrix data storage unit 202 stores one or a plurality of data sets for calculating a kernel orthogonalization matrix from a plurality of categories of learning sets. Hold the set.

  The kernel orthogonal transformation unit 203 performs nonlinear transformation on each input data for the transformation described above in [C Mapping Pattern Orthogonalization Transformation]. When a predetermined number of vectors have been acquired (step 104), the vector is converted by a kernel orthogonalization matrix (step 105).

  The input subspace generation unit 204 obtains an input subspace by principal component analysis for the converted vector (step 106).

  The dictionary subspace storage unit 205 stores R dictionary subspaces. One dictionary subspace represents individuality depending on how one person looks. The dictionary subspace storage unit 205 stores a dictionary subspace of a person registered in advance.

The inter-subspace similarity calculation unit 206 calculates R similarities between the linearly converted R dictionary subspaces and the input subspace by the mutual subspace method (step 107). An input subspace linearly transformed by the orthogonal matrix in the subspace linear transformation unit 205 is A, and a dictionary subspace transformed in the same manner is B. As described above, the similarity S between A and B is determined in the equation (12) by an angle θ ₁ formed by two subspaces called canonical angles by the mutual subspace method.

The similarity S is determined from an angle 504 formed by the input subspace 502 and the dictionary subspace 503 on the feature space 501 in FIG. In FIG. 5, 505 represents the origin of the feature space.

cos ² θ ₁ is the maximum eigenvalue λ _max among eigenvalues λ of the following matrix X.

Here, Ψ _m and φ _l are _{m of} the subspaces A and B, the l-th orthonormal basis vector, (Ψ _m , φ _l ) is the inner product of Ψ _m and φ _l , and N is the number of base vectors of the subspace. To express.

  The face determination unit 207 has the highest similarity among the R similarities calculated by the inter-subspace similarity calculation unit 206, and when the value is larger than a preset threshold, the dictionary in which the similarity is calculated The person corresponding to the partial space is output as the person to which the input face image belongs. In other cases, a person who is not registered in the dictionary subspace storage unit 205 is output.

[Second Embodiment]
FIG. 7 is a block diagram of a kernel orthogonal transformation unit 700 that performs kernel orthogonal transformation. FIG. 6 is a flowchart of processing performed by the orthogonalization matrix generation unit 700. The kernel orthogonal transformation unit 700 includes a dictionary subspace data storage unit 701 that stores data for generating a dictionary subspace, an input conversion unit 702 that performs the projection calculation of the above equation (18), and an input conversion unit 702. KL expansion calculation unit 703 for calculating eigenvalues and eigenvectors by performing KL expansion on the data generated in (1), and a partial space storage unit 704 for storing the top n eigenvectors.

  Hereinafter, the process of the kernel orthogonal transform unit 700 will be described with reference to FIG.

R pieces of data are extracted from the dictionary subspace data storage unit 701 (step 601).
The input conversion unit 702 performs projection calculation of Expression (18) on the data of the dictionary subspace storage data part 701 and input data, and converts the data into the form of Expression (19) (Step 602).

  The KL expansion calculation unit 703 first performs KL expansion on the data generated by the input conversion unit 702 to obtain eigenvalues and eigenvectors (step 603).

  The upper n eigenvectors are stored in the subspace storage unit 704 (step 604). Next, how to use a plurality of kernel orthogonalization matrices will be described. In order to enhance the generalization ability (discriminating ability for unknown patterns) of the kernel orthogonal mutual subspace method, a method of identifying by combining a plurality of feature quantities is introduced into the kernel orthogonal mutual subspace method.

  A method using a plurality of orthogonal transforms together is called a multi-kernel orthogonal mutual subspace method. For example, in the face image recognition, when performing identification by combining a feature amount obtained from the entire face region and a feature amount obtained from the peripheral region of the eye, only the partial regions are used by using the kernel orthogonalization transform unit 700 described above. Or the above-mentioned kernel orthogonalization transform unit 700 is used to generate orthogonal transformations composed of different R category sets for the same feature quantity, and the orthogonal transformation is performed. This is realized by performing a plurality of similarities to obtain a similarity and integrating the plurality of similarities.

  The flow of this embodiment is shown in FIG. 8, and the configuration of the face image recognition apparatus 900 is shown in FIG. The face image recognition apparatus 900 includes a face input unit 901, an input subspace data generation unit 902, a dictionary subspace data storage unit 903, a kernel orthogonal transformation data storage unit 904, a subspace linear transformation unit 905, and a subspace similarity calculation. A unit 906, a similarity combining unit 907, and a face determination unit 908. The face input unit 901 may have the same configuration as the face input unit 201. The input subspace data generation unit 902 stores data necessary for generating the input subspace. A dictionary subspace data storage unit 903 stores data for generating a dictionary subspace of R categories. The orthogonalization change data storage unit 904 stores data for performing M kernel orthogonalization transforms used for similarity calculation.

In the present embodiment, raster scanning is used when the face input unit 901 converts a pattern into a vector. The subspace nonlinear transform unit 905 performs the R person dictionary subspace stored in the dictionary subspace data storage unit 903 for one set for realizing the kernel orthogonalization transform stored in the orthogonalization transform data unit 904. And the data of the input subspace are converted to obtain each subspace (step 806 in FIG. 8). Note that the calculation of the dictionary subspace may be performed once and retained. The similarity calculation unit 906 between subspaces calculates the similarity between the dictionary subspace and the input subspace converted by one kernel orthogonalization transformation stored in the kernel orthogonalization transformation data storage unit 905 according to the first embodiment. The calculation is performed using the mutual subspace method as in (Step 807 in FIG. 8). Note that the subspace nonlinear transform unit 905 and the subspace similarity calculation unit 906 exist independently by the number M of kernel orthogonalization transformations stored in the kernel orthogonalization transformation data storage unit 904 and perform calculations independently. The similarity combining unit 907 calculates an average, a weighted average, a minimum value, and a maximum from M similarities obtained by using M kernel orthogonal transformations for one dictionary subspace and an input subspace. The final similarity is output by taking a value or the like (step 809 in FIG. 8). The face determination unit 908 has the same function as the face determination unit 207 described above. [Example of change]
The present invention is not limited to the above-described embodiments, and various modifications can be made without departing from the gist thereof. For example, the present invention can use not only a face image but also a character, voice, fingerprint, etc. as a pattern. Moreover, the data as it is may be used according to each medium, and various features can be used as the feature amount obtained by processing the data.

  In addition, a part or all of the configuration / process in each of the above embodiments may be realized by causing a computer to execute a program.

It is a figure which shows the flow of the face image recognition of 1st Example of this invention. 1 is a configuration diagram of a face image recognition device 200. FIG. It is the figure which showed the concept of nonlinear transformation. It is a figure which shows the flow of a kernel orthogonal mutual subspace method. It is the figure which showed the concept of the canonical angle between subspaces. It is a figure which shows the flow of the production | generation of the partial space by which the kernel orthogonalization conversion was carried out. It is a block diagram of the kernel orthogonalization transformation part 700 of a 2nd Example. It is a figure which shows the flow of face image recognition. It is a block diagram of the face image recognition apparatus 900 of 2nd Example.

Explanation of symbols

DESCRIPTION OF SYMBOLS 201 Face input part 202 Kernel orthogonalization matrix data storage part 203 Kernel orthogonalization transformation part 204 Dictionary subspace storage part 205 Subspace linear transformation part 206 Subspace similarity calculation part 207 Face determination part 701 Dictionary subspace data storage part 702 Input transformation unit 703 KL expansion calculation unit 704 Subspace storage unit 901 Face input unit 902 Input subspace data generation unit 903 Dictionary subspace data storage unit 904 Kernel orthogonalization transformation data storage unit 905 Subspace nonlinear transformation unit 906 Similarity between subspaces Degree calculation unit 907 Similarity combination unit 908 Face determination unit

Claims (2)

Kernel orthogonalization for obtaining a data set for calculating a kernel orthogonalization transform that approximates the canonical angles of subspaces corresponding to each dictionary pattern by using a plurality of dictionary patterns belonging to each of a plurality of identification objects A conversion generator;
A dictionary subspace generation unit that generates a dictionary subspace corresponding to each dictionary pattern by performing kernel orthogonalization transformation using the data set for each of the dictionary patterns;
An input subspace generation unit that generates an input subspace by performing kernel orthogonalization transformation using the data set for the input pattern;
A similarity calculator that calculates the similarity between the input subspace and the dictionary subspace;
A recognition unit for obtaining the identification target to which the input pattern belongs, using the similarity calculated by the similarity calculation unit;
A pattern recognition apparatus comprising: Kernel orthogonalization for obtaining a data set for calculating a kernel orthogonalization transform that approximates the canonical angles of subspaces corresponding to each dictionary pattern by using a plurality of dictionary patterns belonging to each of a plurality of identification objects A transformation generation step;
A dictionary subspace generation step for generating a dictionary subspace corresponding to each dictionary pattern by performing kernel orthogonalization transformation using the data set for each of the dictionary patterns;
An input subspace generation step for generating an input subspace by performing kernel orthogonalization transformation using the data set for the input pattern;
A similarity calculator that calculates the similarity between the input subspace and the dictionary subspace;
A recognition step for obtaining the identification target to which the input pattern belongs, using the calculated similarity;
A pattern recognition method comprising: