KR20110036407A - Method for detrmining distance metric used in fingerprint mathing of fingerprint system by learning - Google Patents

Abstract

PURPOSE: A method for efficiently learning a distance metric through the minimization of a cost function is provided to improve fingerprint recognition performance by learning a distance metric from training data. CONSTITUTION: A training data is composed of the fingerprint of original content and the fingerprint of distorted content. A distance metric is determined through learning in order to improve recognition performance in the use of training data(S200). A parameterized distance metric is generated in a determination procedure of the distance metric. A cost function is generated. The parameter of the distance metric is determined through the minimization of the cost function.

Description

METHODS FOR DETRMINING DISTANCE METRIC USED IN FINGERPRINT MATHING OF FINGERPRINT SYSTEM BY LEARNING}

The present invention relates to content-based content recognition, in particular finger printing, and more particularly, to the improvement of the performance of a fingerprint matching process in a finger printing system.

The demand for protection, management and indexing of digital content is increasing, and interest in fingerprinting is increasing as a feasible solution. Fingerprinting is a technique for identifying unknown content using a short feature vector called a fingerprint. Recently, various audio / video / image fingerprinting techniques have been proposed (Refs. [1]-[7]).

A fingerprinting system for content recognition generally consists of three essential elements: 1) fingerprint extraction, 2) database search, and 3) fingerprint matching (Ref. [4]).

In the fingerprint extraction step, a query fingerprint is extracted from the query content. In the database retrieval phase, a set of candidate fingerprints proximate to the query fingerprint is obtained from the database. In the fingerprint matching step, the distance between the candidate fingerprint and the query fingerprint is calculated based on the distance metric. The fingerprinting system provides metadata regarding the candidate fingerprint that is closest to the query fingerprint.

The fingerprint extraction and matching process has a greater impact on identification performance than the database searching process that determines the computational efficiency of the system. Fingerprinting system may be degraded when the application environment of the system is changed, and a countermeasure is required. In order to improve the recognition performance of the fingerprinting system, a fingerprint extraction process or a registration process must be newly created. Among these, creating a new fingerprint extraction process involves a problem of newly writing a fingerprint DB. However, if only the distance metric used for the fingerprint matching process is newly created, performance can be improved while maintaining the fingerprint extraction process and the fingerprint DB in the existing system. This makes it possible to adapt to the new application environment while maintaining as much of the existing system as possible.

Reference [8]-[10] discusses how distance metrics are learned in the classification and clustering process (the process of determining this matrix when the distance metric is parameterized in matrix form). Recent studies have shown that distance metric learning can improve classification and clustering performance (Ref. [11]). However, the existing distance metric learning method has not been used in a fingerprinting system, and a learning method suitable for a fingerprinting system is needed.

The present invention is to solve the problems of the prior art described above, an object of the present invention is to determine the appropriate distance metric through the learning process of the distance metric in the fingerprinting system, through which the identification of the fingerprint (identification) It is a technical problem to improve performance.

In order to solve the above technical problem, the present invention by using the distance metric learned using the training data (training data) consisting of the original and distorted content, to improve the fingerprint recognition performance of the existing fingerprinting system do. This improves performance while maintaining the fingerprint database and the fingerprint extraction process of the existing fingerprinting system.

Suppose you have training data consisting of original and distorted content. Use training data to learn distance metrics so that improved recognition performance can be achieved. In order for the distance metric to be learned, the distance metric must have a parameterized form. The learning process determines the parameters of the distance metric. A cost function is used for the learning process. The cost function is designed to have a lower value as the recognition performance is improved. The learning process allows one distance metric to be determined by obtaining a parameter of the distance metric that minimizes this cost function.

The fingerprint for the original contents is assumed to be stored in the database, and the fingerprint for the distorted contents is assumed to be a query fingerprint. At this time, in order to improve recognition performance, the distance between the fingerprint of any distorted content and the fingerprint of the original content (corresponding content) of the distorted content should be small, and the fingerprint of any distorted content and its distortion The premise is that the distance between the fingerprints of the original content (non-corresponding content) other than the original content of the specified content must be large. Under this premise, the cost function can take many forms. In the present invention, as an embodiment of this cost function, a cost function having the following two principles is proposed.

(Principle 1)

The distance between the fingerprint of the original content (corresponding content) and the fingerprint of the distorted content must be less than the distance between the fingerprint of the original content and the fingerprint of the other original content (non-corresponding content). .

(Principle 2)

The distance margin between the fingerprint of the distorted content and the fingerprint of the non-corresponding content should be as large as possible (Ref. [10]).

We design a cost function based on these two principles and use them to learn distance metrics. The cost function is minimized if both of the above principles are met. That is, the cost function is designed such that the value of the distorted content increases as the fingerprint of the non-corresponding content is further away from the fingerprint of the corresponding content.

On the other hand, it is preferable that the cost function has the form of a convex function for the convenience of minimizing the cost function. In this case, the minimization of the cost function may be performed by convex optimization.

After all, when the distance metric is parameterized in a specific form, the process of determining the parameter of the distance metric is distance metric learning. The shape of the parameterized distance metric can take a variety of forms, and the present invention uses a general form of Mahalanobis distance as one embodiment of the parameterized distance metric.

After all, when the distance metric is parameterized in a matrix form, the process of determining each parameter value and matrix constituting the matrix is distance metric learning.

Since distance metric learning to be dealt with in the present invention is valid only for a fingerprint having a real value, the following description will assume that the fingerprint has a real value.

More specifically, the present invention provides a fingerprint printing system for recognizing content using matching of fingerprints (x i , j ) of distorted content extracted from distorted content for original content with fingerprint (x i ) of original content. A method of determining the distance metric used in the matching process through learning, comprising: (A) training data consisting of a fingerprint (x i ) of the original content and a fingerprint (x i, j ) of the distorted content; ) (S 100), and (B) determining a distance metric capable of producing improved recognition performance using the training data (S 200).

On the other hand, the step (B), (B-1) generating a parameterized distance metric to determine the distance metric (S 210), and (B-2) the fingerprint of the original content (x i ) and making small the distance between the fingerprint (x i, j of the distortion content) is minimized when the distance is largely created between the fingerprint of the fingerprint (x i) and the other original content (x k) of the original content, Generating a cost function [ε (.)] (S 220), and (B-3) determining a parameter of the distance metric by finding a case where the cost function [ε (.)] Is minimized (S 230). It characterized by including).

In addition, in the step (B-1), the distance metric may be defined as a parameterized form of one matrix A as an embodiment.

[Wherein the function φ (·) is φ (x) = Wx (W is an N × N matrix) and A = W ^T W]

Further, in the step (B-2), the cost function [ε (A)] is preferably defined by the following equation.

는 왜곡 콘텐츠의 핑거프린트(xi ,j)에 가장 근접한 비정합 핑거프린트임][Where, [z] ₊ = max (z, 0), and M represents a margin,

Is an unmatched fingerprint that is closest to the fingerprint (x i , j ) of the distorted content.

Further, in the step (B-2), the cost function [epsilon (A)] is preferably a convex function.

In addition, in the step (B-3), it is preferable to use a projected gradient method to find a case where the cost function [epsilon (A)] is minimized.

The present invention improves fingerprint recognition performance by learning distance metrics from training data consisting of original and distorted content.

In particular, the present invention is a fingerprint (x i) and the fingers of the distortion can be printed (x i, j) fingerprint (x i) of the distance, the original content and the different original content (x k) between the original content of fingers By generating a cost function [epsilon (A)] that is minimized when smaller than the distance between the prints, the distance metric can be effectively learned by minimizing the cost function [epsilon (A)].

In addition, the distance metric according to the present invention has a general shape according to the Mahalanobis distance so that parameterization of the distance metric can be easily and effectively achieved.

In addition, the cost function [ε (A)] according to the present invention has the form of a convex function, thereby minimizing the cost function [ε (A) using a visualized method, for example, using a projected gradient method. To be implemented.

Hereinafter, with reference to the accompanying drawings will be described in detail with respect to the present invention.

In the following description, "learning" refers to a process of determining the matrix when the distance metric is parameterized in a matrix form.

1A and 1B are flowcharts illustrating a process of determining, by learning, a distance metric used in a matching process of a finger printing system according to the present invention.

As shown in FIG. 1A, the method according to the present invention includes a first step S100 of generating training data and a second step S200 of determining a distance metric using learning from the training data. It consists of.

As shown in FIG. 1B, the second step S 200 of determining a distance metric using learning includes generating a parameterized distance metric S 210 and a cost function. Generation step (S 220) and determining (learning) a parameter of the distance metric by finding a case where the cost function is minimized (S 230). Hereinafter, each step will be described in detail.

1. Training data ( Training data ) (S 100)

To learn the distance metric, the fingerprint of the original content (x i ) and the fingerprint of the distorted content (x i , j ) ( i = 1, 2, ..., I and j = 1, 2, ... , A set of training data consisting of J ) is required. The fingerprint (x i , j ) of the distorted content means a fingerprint extracted from the j- th distortion version of the i- th original content. The fingerprint x i is the fingerprint for the i th original content.

In the learning process according to the invention x i Denotes a fingerprint stored in a database, and x i , j denote a query fingerprint.

Further, the fingerprint pair (x i , x i , j ) is a matching fingerprint pair, and the fingerprint pair (x k , x i , j ) ( k ≠ i ) is a non-matching finger. It is a print pair.

The distorted content in the training data is determined in consideration of the distortion that occurs frequently in practical applications. When placed in the new distortion environment of the fingerprinting system, the distortion metric of the fingerprinting system can be adapted to the new distortion environment by using the distortion data suitable for the distortion environment.

2. Through learning Distance  Metric determination ( DETERMINING DISTANCE METRIC USING  LEARNING) (S 200)

2.1. Parameterized Distance  Metric ( DISTANCE MATRIC ) Create (S 210)

Distance metric (DISTANCE MATRIC) is 'denotes a distance between the generally ∥ φ (x) - φ ( x' 2 of the N-dimensional fingerprint x and x) ∥ can be expressed in the form of ^two. Where φ is a mapping function that maps from the N-dimensional real space (R ^N ) to another dimension. This φ function can be used as a parameter of the distance metric. Since the present invention will consider linear projection as an embodiment of the mapping function, it is assumed that the function φ (·) is φ (x) = Wx (W is an N × N matrix). In consideration of this mapping function, the distance metric is defined by Equation 1 below.

(Where A = W ^T W)

In one embodiment, when considering linear projection, a distance metric having a matrix A as a parameter is obtained. The distance metric obtained by the above equation is not limited to a specific form, and can be applied in various forms according to the function φ (·), and thus may have various types of parameters.

The example shown in the above equation can be considered to employ the distance metric in the general form of Mahalanobis distance. Mahalanobis distance is the most widely used distance concept in cluster analysis. It is characterized not only by the distance between two points, but also by the standard deviation and correlation coefficient that characterize the variable. Find the Mahalanobis distance according to the formula p. The distance between q is equal to Equation 1a.

mahalanobis (p, q) = (p-q) ∑ ^-One (p-q) ^T

Where ∑ ^-1 is the inverse of the covariance matrix and T is the transformation matrix.

In the description below, the distance D _A between x and x ' (x, x ') = ∥ φ (x) -φ (x') ∥ ² is defined.

Learning the distance metric means determining the distance metric and, in this embodiment, determining the matrix A. D _A if the matrix A parameterizing the distance metric is a unit matrix (x, x ') matches the Euclidean distance.

2.2. Cost function ( Cost function ) Generate (S 220)

The parameters of the distance metric matrix A are determined by minimizing the cost function. The form of the cost function is not limited to a particular form, the distance between the fingerprint of any distorted content and the fingerprint of the original content (corresponding content) of the distorted content should be small, and the fingerprint of any distorted content And the distance between the fingerprint of the original content (non-corresponding content) other than the original content of the distorted content can be applied in various forms.

Just as an example, D _A (x i , x i , j ) is D _A cost function minimized when (x k , x i , j ) ( k ≠ i ). In order to correctly recognize a distorted version of the query content to original content query fingerprint (x i, j) are to be in closer than x i x k (k ≠ i). A cost function according to the present invention that satisfies this condition may be implemented as in Equation 2 below.

는 쿼리 핑거프린트(xi ,j)에 가장 근접한 비정합 핑거프린트를 나타낸다. 인덱스

는 하기의 수학식 3에 따라 표현할 수 있다.Where [z] ₊ (= max (z, 0)) represents the standard hinge loss function, M represents the margin,

Denotes an unmatched fingerprint that is closest to the query fingerprint (x i , j ). index

Can be expressed according to Equation 3 below.

By including the constant M and the hinge loss function in Equation 2 and minimizing ε (A), D _A (x ξ (i, j) , x i , j ) ≥ M + D _A It is derived to be (x i , x i , j ) (Ref. [10]). Thus, the distance metric is at least M + D _A between the query fingerprint (x i, j ) and the fingerprint of the non-corresponding content. It is learned to be larger than (x i , x i , j ).

2 is a diagram for explaining the meaning of a cost function.

As shown in Fig. 2 (a), x ξ (i, j) is centered on x i , j and the radius is M + D _A (x i, x i, j ) is positioned in the outer sphere has a summand (summand) of _{ε (A) M + D A} (x i, x i, j) - D A (x ξ (i, j) , x i , j ) becomes zero.

However, as shown in Fig. 2 (b), x ξ (i, j) is centered on x i , j and the radius is M + D _A M + D _A if inside the sphere of (x i , x i , j ) (x i , x i , j ) -D _A The cost is added to the cost function by (x ξ (i, j) , x i , j ). Since A can be scaled by M , the generality can be maintained even when M = 1.

2.3. Of cost function Convexity  ( Convexity of the cost function )

The cost function is a convex function for A, so we can find the overall minimum. In order to prove the convexity of the cost function, if E (A) of Equation 2 is described again, Equation 4 is obtained.

Here, K (A, i, j) is defined by the following equation (5).

(Proof of convexity)

The sum of the convex functions is the convex function.

Thus, if [ K (A, i, j)] ₊ is convex, ε (A) is also convex. Also, if the function K (A, i, j) is convex, then [ K (A, i, j)] ₊ is also convex. Since K (A, i, j) is a constant M and the sum of two linear functions, K (A, i, j) is linear with respect to A. Therefore, when K (A, i, j) is convex, ε (A) is also convex.

2.4. optimization ( Optimization )- Distance  Determining the Parameter Matrix (A) of the Metric (S 230)

To find the matrix A, we use the projected gradient method described in Ref. [12].

Since the distance metric must be non-negative and satisfy the triangular inequality, the matrix A is positive semi-definite (Ref. [8]).

Projection gradient is performed in two steps.

First, for unconstrained minimization, the gradient descent method finds the direction in which the gradient is negative at the current position of the function, moves in that direction, takes a new position, and repeats this method. To find the local minimum of the function.

The matrix A is then projected into positive semi-definite space. Projection uses semifinite programming as described in Ref. [12].

If the process of finding the matrix A by the above process is mathematically expressed, the following equation (6) is obtained.

가 된다.Where β is a step size, ∥ · _F is a Frobenius norm. In other words,

Becomes

4. Experimental results ( EXPERIMENTAL RESULTS )

4.1. Experiment set up

In order to show the performance improvement by distance metric learning, the distance metric learning method according to the present invention will be applied to the audio fingerprint system described in Ref. [4].

According to Ref. [4], a 16-dimensional fingerprint is extracted from a frame having a length of 371.5 ms (shift (185.7 ms for the start or end point of each frame)). Euclidean distance was used.

Fingerprint matching was performed using audio clips (27 or 54 frames) of 5 or 10 seconds long, so N = 432 (= 27x16) or N = 864 (= 54x16) (16 dimensions per frame). Since the fingerprint is extracted, the N-dimensional fingerprint is extracted from N / 16 (= 27 or 54) frames.

Since fingerprint matching performance is of primary interest in the present invention, the database search process for the fingerprint system is omitted in this embodiment.

Since N is so large that learning on an N- dimensional ( N x N ) matrix is not easy to calculate, in this experiment, for matrix A _S of M- dimension ( M < N ) instead of matrix A of N- dimension, Let's do the learning.

Matrix A _S Can be obtained by using the M-dimensional fingerprint obtained by dividing the N-dimensional fingerprint by the M-dimensional fingerprint (the 16-dimensional fingerprint is extracted per frame, so the M-dimensional fingerprint is extracted from M / 16 frames). ].

The distance between two N-dimensional fingerprints x and x 'can be obtained from Equation 7 below.

Here, x _s ^(k) and x _s ' ^(k) mean the M-dimensional fingerprint obtained by dividing the N-dimensional fingerprints x and x', respectively. In this embodiment, since M = 48, the summand in Equation 7 means the distance between the fingerprints extracted from 3 (= M / 16 = 48/16) frames.

4.2. Training set ( Training set )

100 different sound sources (songs) were used for distance metric learning. In this embodiment, I = 8000 and J = 4.

Where I is the number of fingerprints (x i ; i = 1, 2, ..., I ) of the original content, and J is the distorted version (x i , ) of the content relative to the fingerprint (x i ) of the original content . j ; i = 1, 2, ..., J ) (see 3.1.)

The audio distortion list used in the present embodiment is described in Ref. [2], and is shown in Table 1 below.

sign Audio distortion Contents L1 EQ1
(Octave band equalization) Adjacent bands in the octave band
(Set by alternating -6 dB and +6 dB) L2 E
(eco) Old generation radio filter replication
(Filter emulation of old time radio) L3 BPF
(Band Pass Filtering) 0.4-4 kHZ Band Band Filter
(0.4-4 kHZ Band Pass Filter) L4 WMA
(WMA encoding) 64 kbps WMA encoding
(64kbps WMA encoding)

For all distortions, 96 kbps MP3 encoding was performed.

4.3. Comparison test

In order to evaluate the performance of the present invention, 100 completely different sound sources (songs) completely distinguished from the above-described training set were used for the comparison test. In addition to the four distortions (EQ1, E, BPF, WMA) described above, three distortions as shown in Table 2 were added to the comparison test, and seven distortions were used.

sign Audio distortion Contents T1 TD
(Time Delay) 92.9 ms shift T2 SR
(Sampling rate change) Downsampling to 16 kHz and
Upsampling to 44.1 kHz T3 EQ2
(1/3 octave band equalization) 30-band pop equalization
(30-band pop equalization)

A test set that combines the three or more distortions is also contemplated.

Each test set includes not only distortion when learning is applied, but also distortion when learning is not applied.

Figure 3 shows the performance and comparative example of the embodiment (distance metric to which the learning is applied, shown as "Learned") according to the present invention. Is a comparison graph showing the performance of using a receiver operating characteristic (ROC) curve.

The ROC graph of FIG. 3 shows the ratio of false positives (FP; false positives actually negative) to the ratio of false negatives (FN; false positives). FP).

That is, in this experiment, the negative error (FN) ratio is defined as the ratio when the matched fingerprint pair is determined to be an unmatched fingerprint pair, and the positive error (FP) ratio is determined as the matched fingerprint pair as the matched fingerprint pair. It is defined as the ratio of cases.

In each experiment, 60,000 matched fingerprint pairs and 100,000,000 unmatched fingerprint pairs were used.

3 (a) to 3 (d) show the performance of the case where only distortion to which learning is applied is present.

3 (e) to 3 (g) show the performances for the case where distortion to which learning is not applied is also included.

3 (h) to 3 (j) show performances when three or more distortions to which learning is applied and distortions to which learning is not applied are combined.

The distortion applied to FIGS. 3 (a) to 3 (j) is shown in Table 3 below.

drawing Applied distortion Figure 3 (a) EQ1 + MP3 3 (b) E + MP3 Figure 3 (c) BPF + MP3 3 (d) WMA + MP3 3 (e) TD + MP3 3 (f) EQ2 + MP3 Fig. 3 (g) SR + MP3 3 (h) WMA + EQ2 + SR + MP3 3 (i) TD + E + BPF + EQ2 + MP3 3 (j) EQ1 + BPF + EQ2 + MP3

As shown in Fig. 3, the performance of an embodiment according to the present invention (distance metric to which learning is applied, shown as "Learned") is compared to that of the comparative example (conventional Euclidean distance and no learning is applied, "Euclidean Shows good performance relative to performance.

That is, under the same conditions, it can be seen that the example (Learned) is disposed on the left-lower side compared to the comparative example (Euclidean), which means that the example has a false positive (FP) ratio and This means that the false negative (FN) rate is low.

In particular, as clearly seen in Figs. 3 (b) and 3 (c), the learning effect of the distance metric according to the present invention is significantly improved for E (eco) and BPF (band band filter) distortion, which is severely distorted. Is showing.

In addition, as shown in FIGS. 3 (i) and 3 (j), even when three or more distortions are combined, the recognition performance is significantly improved when E (eco) and BPF (bandband filter) distortions are included. Shows that

As a result, the embodiment of the present invention to which the learning of the distance metric is applied to all the cases of FIG. 3 has no performance degradation against distortion as compared to the comparative example (Euclidean) to which the learning is not applied.

According to the present invention, a method for improving a fingerprint matching process using learning of a distance metric has been proposed. The learning of the distance metric is performed by minimizing the cost function associated with recognition performance. The cost function is designed to minimize when query content is correctly recognized.

According to an experiment applying the present invention to an audio fingerprinting system, fingerprint performance has been improved by distance metric learning according to the present invention.

Although specific embodiments of the present invention have been described above, the spirit and scope of the present invention are not limited to the specific embodiments, and various modifications and changes can be made without departing from the spirit of the present invention. Those skilled in the art will understand.

Therefore, since the embodiments described above are provided to completely inform the scope of the invention to those skilled in the art, it should be understood that they are exemplary in all respects and not limited. The invention is only defined by the scope of the claims.

<References>

The following references are incorporated as part of this specification.

[1] "Highly robust audio fingerprint system", J. Heistma, etc.

[J. Haitsma and T. Kalker, "A highly robust audio fingerprinting system", Proc . Int . Conf . Music Information Retrieval,, 2002]

[2] "Content-based Identification of Audio Materials Using MPEG-7 Level Technology," E. Alamansh, et al.

[E. Allamanche, J. Herre, O. Helmuth, B. Frba, T Kasten, and M Cremer, "Content-based identification of audio material using MPEG-7 low level description", Proc . Int . Symposium of Music Information Retrieval , 2001]

[3] "Distortion Discrimination Analysis in Audio Fingerprinting", C. Burgess et al.

[C. Burges, J. Plat, and S. Jana, "Distortion discriminant analysis for audio fingerprinting", IEEE Trans . Speech Audio Processing , vol. 11, no. 3, pp. 165-174, May, 2003.]

[4] "Fingerprinting Based on Standardized Subband Moments", J.S. Standing lights

JS Seo, M. Jin, S. Lee, D. Jang, S. Lee, CD Yoo, Audio Fingerprinting Based on Normalized Spectral Subband Moments, IEEE Signal Processing letters , vol. 13, issue 4, pp. 209-212, Apr., 2006.]

[5] "Feature Extraction and Database Strategy for Video Fingerprinting", J. Ostvin et al.

[J. Oostveen, T. Kalker, and J. Haitsma , 'Feature extraction and a database strategy for video fingerprinting ", Proc. Int. Conf. On Visual Information and Information Systems , pp. 117-128, 2002.]

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[S. Lee and CD Yoo, "Robust video fingerprinting for content-Based video identification", IEEE Trans . Circuits and Systems for Video Technology , vol. 18, no. 7, pp. 983-988, July 2008.]

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[8] "Learning Distance Metrics, Clustering with Side Information", E.P. Xing etc.

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[K. Weinberger, J. Blitzer, and L. Saul, 'Distance Metric learning for large margin nearest neighbor classification ", Proc . NIPS 2006.]

[11] 'Learning Distance Metrics: A Overall Overview', L. Yang, etc.

[L. Yang and R. Jin, "Distance Metric learning: A comprehensive survey", Technical report , Department of Computer Science and Engineering, Michigan State University, 2006.]

[12] "Convex Optimization", S. Boyd, etc.

[S. Boyd and L. Vandenberghe, "Convex Optimization", Cambridge University Press , 2004]

1a and 1b are flow charts illustrating the process of the method according to the invention.

2 is a diagram for explaining the meaning of a cost function.

Figure 3 is a comparison graph shown using the Receiver Operating Characteristic (ROC) curve to compare the performance of the embodiment and the performance of the comparative example according to the present invention.

DESCRIPTION OF THE REFERENCE NUMERALS

x i : Fingerprint of the i th original content ( i = 1, 2, ..., I )

x i , j : Fingerprint extracted from the j th distortion version of the i th original content ( j = 1, 2, ..., J)

M : margin

D _A (x, x '): distance between x and x'

: 핑거프린트(xi,j)에 가장 근접한 비정합 핑거프린트

: Mismatched fingerprint closest to fingerprint (x i, j )

Claims (6)

The distance used in the registration process of the fingerprint printing system that recognizes content by matching the fingerprint (x i, j ) of the distorted content extracted from the distorted content of the original content with the fingerprint (x i ) of the original content. As a way to determine metrics by learning, (A) providing training data consisting of a fingerprint (x i ) of the original content and a fingerprint (x i, j ) of the distorted content; (B) determining distance metrics through learning by using the training data to produce improved recognition performance; Method for determining the distance metric used in the matching process of the fingerprint printing system, characterized in that through learning. The distance used in the registration process of the fingerprint printing system that recognizes content by matching the fingerprint (x i, j ) of the distorted content extracted from the distorted content of the original content with the fingerprint (x i ) of the original content. As a way to determine metrics by learning, (A) providing training data consisting of a fingerprint (x i ) of the original content and a fingerprint (x i, j ) of the distorted content; (B) using the training data to determine a distance metric capable of producing improved recognition performance through learning (learning), Step (B) is, (B-1) generating a parameterized distance metric by parameterizing the distance metric (S 210); (B-2) fingerprint (x i) and the making the distance between the smaller of the distortion content fingerprint (x i, j), a fingerprint (x i) and the other the original content of the original content of the original content ( generating a cost function ε (A) that is minimized when the distance between the fingerprints of x k ) is made large (S 220), (B-3) Determining each parameter of the distance metric by finding a case where the cost function [ε (A)] is minimized (S 230) Method for determining the distance metric used in the matching process of the fingerprint printing system, characterized in that through learning. The distance used in the registration process of the fingerprint printing system that recognizes content by matching the fingerprint (x i, j ) of the distorted content extracted from the distorted content of the original content with the fingerprint (x i ) of the original content. As a way to determine metrics by learning, (A) providing training data consisting of a fingerprint (x i ) of the original content and a fingerprint (x i, j ) of the distorted content; (B) using the training data to determine a distance metric capable of producing improved recognition performance through learning (learning), Step (B) is, (B-1) generating a parameterized distance metric by parameterizing the distance metric (S 210); (B-2) fingerprint (x i) and the making the distance between the smaller of the distortion content fingerprint (x i, j), a fingerprint (x i) and the other the original content of the original content of the original content ( generating a cost function ε (A) that is minimized when the distance between the fingerprints of x k ) is made large (S 220), (B-3) determining a case where the cost function [epsilon (A)] is minimized and determining each parameter of the distance metric (S 230), In the step (B-1), the distance metric matrix (A) is defined by the following equation, the method for determining the distance metric used in the matching process of the finger printing system through learning.

[Wherein the function φ (·) is φ (x) = Wx (W is an N × N matrix) and A = W ^T W] The distance used in the registration process of the fingerprint printing system that recognizes content by matching the fingerprint (x i, j ) of the distorted content extracted from the distorted content of the original content with the fingerprint (x i ) of the original content. As a way of determining metrics by learning, (A) providing training data consisting of a fingerprint (x i ) of the original content and a fingerprint (x i, j ) of the distorted content; (B) using the training data to determine a distance metric capable of producing improved recognition performance through learning (learning), Step (B) is, (B-1) generating a parameterized distance metric by parameterizing the distance metric (S 210); (B-2) fingerprint (x i) and the making the distance between the smaller of the distortion content fingerprint (x i, j), a fingerprint (x i) and the other the original content of the original content of the original content ( generating a cost function ε (A) that is minimized when the distance between the fingerprints of x k ) is made large (S 220), (B-3) determining a case where the cost function [epsilon (A)] is minimized and determining each parameter of the distance metric (S 230), In the step (B-2), the cost function [epsilon (A)] is defined by the following equation, the method for determining the distance metric used in the matching process of the finger printing system through learning.

[Where, [z] ₊ = max (z, 0), and M represents a margin,

Is an unmatched fingerprint that is closest to the fingerprint (x i , j ) of the distorted content. The distance used in the registration process of the fingerprint printing system that recognizes content by matching the fingerprint (x i, j ) of the distorted content extracted from the distorted content of the original content with the fingerprint (x i ) of the original content. As a way to determine metrics by learning, (A) providing training data consisting of a fingerprint (x i ) of the original content and a fingerprint (x i, j ) of the distorted content; (B) using the training data to determine a distance metric capable of producing improved recognition performance through learning (learning), Step (B) is, (B-1) generating a parameterized distance metric by parameterizing the distance metric (S 210); (B-2) fingerprint (x i) and the making the distance between the smaller of the distortion content fingerprint (x i, j), a fingerprint (x i) and the other the original content of the original content of the original content ( generating a cost function ε (A) that is minimized when the distance between the fingerprints of x k ) is made large (S 220), (B-3) determining a case where the cost function ε (A) is minimized and determining each parameter of the distance metric (S 230), In the step (B-2), the cost function [ε (A)] is a convex function, characterized in that the distance metric used in the matching process of the fingerprint printing system to determine through learning. The distance used in the registration process of the fingerprint printing system that recognizes content by matching the fingerprint (x i, j ) of the distorted content extracted from the distorted content of the original content with the fingerprint (x i ) of the original content. As a way to determine metrics by learning, (A) providing training data consisting of a fingerprint (x i ) of the original content and a fingerprint (x i, j ) of the distorted content; (B) using the training data to determine a distance metric capable of producing improved recognition performance through learning (learning), Step (B) is, (B-1) generating a parameterized distance metric by parameterizing the distance metric (S 210); (B-2) fingerprint (x i) and the making the distance between the smaller of the distortion content fingerprint (x i, j), a fingerprint (x i) and the other the original content of the original content of the original content ( generating a cost function ε (A) that is minimized when the distance between the fingerprints of x k ) is made large (S 220), (B-3) determining a case where the cost function [epsilon (A)] is minimized and determining each parameter of the distance metric (S 230), In the step (B-3), the case where the cost function [epsilon (A)] is minimized is characterized by using a projected gradient method. The distance metric used in the registration process of the finger printing system. How to determine through learning.

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