CN107679131B - A kind of quick spectrogram matching process - Google Patents

A kind of quick spectrogram matching process Download PDF

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CN107679131B
CN107679131B CN201710863532.1A CN201710863532A CN107679131B CN 107679131 B CN107679131 B CN 107679131B CN 201710863532 A CN201710863532 A CN 201710863532A CN 107679131 B CN107679131 B CN 107679131B
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CN107679131A (en
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郑亚莉
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University of Electronic Science and Technology of China
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Abstract

A kind of quick spectrogram matching process of the disclosure of the invention is related to the figure matching field in computer vision, more particularly to a kind of spectrogram matching process of quick high accuracy.Method space complexity proposed by the present invention is only O (n1n2), time complexity is O (kn1n2), wherein k is the number of basic matrix；By increasing expansion factor Y and ranks normalization, the speed of algorithmic statement is accelerated, effectively inhibits noise and exterior point for scheming matched interference, improves the matched precision of figure.The present invention also has the advantages that matching speed fast, high reliablity, at low cost, energy saving.

Description

A kind of quick spectrogram matching process
Technical field
The present invention relates to the figures in computer vision to match field, matches more particularly to a kind of spectrogram of quick high accuracy Method.
Background technique
In computer vision field, figure matching can be used for solving the problems, such as feature corresponding points, be based on geometry Image retrieval, target identification, shape matching, target following etc. have a wide range of applications.For simple, figure is point and line is opened up Structure is flutterred, figure matching is that two width figure midpoints of searching are corresponding with point.Spectrogram matching is by Leordeanu and Hebert 2005 One kind " artistic grade " method that year proposes, referred to as spectrogram matching (Spectral Matching, SM).They are corresponding points Figure matching problem is modeled as a quadratic assignment problem.Since quadratic assignment problem is a np hard problem, in the process of solution In, spectrogram is matched the problem of relaxation is at feature vector corresponding to a maximum eigenvalue by Duchenne etc., that is, solves two figures Then feature vector corresponding to the maximum eigenvalue of similar matrix carries out 0-1ization by Hungary Algorithm, to obtain a little With the matching relationship of point.However, the above-mentioned disadvantage based on spectrogram matching process is to need to construct O (n4) similar matrix, Therefore be not suitable for solving medium or ultra-large figure matching problem.In order to reduce the memory space of similar matrix, Kang etc. It proposes and similar matrix is approximated by a series of O (n2) sparse basic matrix and index matrix Kronecker product and shape Formula, referred to as FaSM method.Although the construction similar matrix that this approximate expression is not shown, in its calculating process In, need to construct O (n4) approximate similar matrix, and because the approximation of matrix causes so that there are information losses for similar matrix It is declined compared with the matched precision of spectrogram.
Summary of the invention
Be not suitable for solving medium or large-scale spectrogram matching problem present invention aim to address spectrogram matching process, A kind of spectrogram matching process of quick high accuracy is provided.The method of proposition only needs O (n2) space complexity, O (kn2) when Between complexity, and can effectively inhibit the interference matched for spectrogram of noise and exterior point, improve the matched precision of spectrogram.
The technical scheme is that a kind of quick spectrogram matching process, this method comprises:
Step 1: known figure G1With figure G2Vertex and side set be respectively (V1,E1) and (V2,E2), number of vertices difference For n1, n2；If scheming G1In the distance between i-th of vertex and j-th of vertex beScheme G2In i-th vertex and j-th of vertex The distance between beTo figure G1In the distance between any two points matrix be D1, to D1Middle element is ranked up, it is assumed that most Big value is dmax, minimum value dmin, by dmaxWith dminBetween divide m sections, every section of width w=(dmax-dmin)/m；To dijIt carries out close Like expression, representation method is as follows:
Judge d 'ijPositioned at which of m segmentation segmentation, the intermediate value d ' of the segmentation is then usedkInstead of original d ′ij；
Step 2: construction basic matrix BkWith index matrix Hk；Initialize HkFor n1xn1Full null matrix, k be [0, m-1] it is whole Number, approximate precision is preset m as needed；
Step 2.1 sets Bk=4.5- (d 'k-D2)2/2σ2, in which: D2Indicate G2In vertex between distance matrix, σ2It indicates Adjustable factors；
Step 2.2 searches G1Distance matrix D1Element value is between [dmin+w×(k-1),dmin+ w × k] between element, Enable HkIn index accordingly element be 1；
Step 3: initialization matrixInitialization M is n1×n2Full null matrix；By X =X0；Initialization error threshold value Error=1 initializes the number of iterations maximum value ItersMax, initializes α, β, p；
Step 4: calculating initial matching matrix X；
Step 4.1, taking k is the integer of [0, m-1], is repeated in calculatingCalculate Mm
Step 4.2, assignment calculates:Y=eβX/max(X)；
Step 4.3, the normalization of row and column is carried out to Y, i.e. repeated assignment of values calculates:
Until | | Yk-Yk+1||2< 1e-25；YajIndicate the element of a row jth column in Y, Y value at this time is Yk+1；
Step 4.4, α X+ (1- α) Y is assigned to X, then carries out the normalization of row and column, i.e. repeated assignment of values meter to X after assignment It calculates
Until | | Xk-Xk+1||2< 1e-25, XajIndicate the element of a row jth column in X, the value of X is X at this timek+1；
Step 4.5, Error=is calculated | | Xp-Xp-1||2, XpIndicate the calculated X value of previous cycle, Xp-1Indicate last The X value that cycle calculations go out, then assignment calculate p=p+1；
Step 4.6, if Error>1e-25 and p<ItersMax, otherwise return step 4.1 saves the value of X at this time, into Enter in next step；
Step 5 carries out 0-1 discretization to the X sought using Hungary Algorithm, to obtain n1×n2Matching matrix, The corresponding relationship on vertex in two images is indicated with matrix.
Compared with prior art, method space complexity proposed by the present invention is only O (n1n2), time complexity is O (k n1n2), wherein k is the number of basic matrix；It is normalized by increasing expansion factor Y and ranks, accelerates the speed of algorithmic statement, It effectively inhibits noise and exterior point for scheming matched interference, improves the matched precision of figure.In a specific embodiment, pass through We add different noise or exterior point to figure, as shown in Figure 5, Figure 6, illustrate the had matching speed of the present invention fastly, can The advantage high, at low cost, energy saving by property.
Detailed description of the invention
The figure G that Fig. 1 is generated at random1With G2Schematic diagram；
Fig. 2 adds the comparative test of exterior point, control methods SM, FaSM on generating data；
The comparative test of noise, control methods SM, FaSM is added in Fig. 3 on generating data；
Fig. 4 reality pictures example；
Comparative test result of the Fig. 5 in reality pictures example.It (a) is that the method for proposition and the matching precision of FaSM compare As a result；(b) be propose method and FaSM runing time comparing result；
Exterior point comparative test of the Fig. 6 on truthful data.(a) it is the method for proposition in the exterior point for adding different proportion and consolidates Determine the comparing result of matching precision under the conditions of noise (σ=50)；(b) it is the method for proposition in the exterior point for adding different proportion and consolidates Determine the comparing result of runing time under the conditions of noise (σ=50).
Specific embodiment
A kind of quick spectrogram matching process, this method comprises:
Step 1: known figure G1With figure G2Vertex and side set be respectively (V1,E1) and (V2,E2), number of vertices difference For n1, n2；If scheming G1In the distance between i-th of vertex and j-th of vertex beScheme G2In i-th vertex and j-th of vertex The distance between beTo figure G1In the distance between any two points matrix be D1, to D1Middle element is ranked up, it is assumed that most Big value is dmax, minimum value dmin, by dmaxWith dminBetween divide m sections, every section of width w=(dmax-dmin)/m；To dijIt carries out close Like expression, representation method is as follows:
Judge d 'ijPositioned at which of m segmentation segmentation, the intermediate value d ' of the segmentation is then usedkInstead of original d ′ij；
Step 2: construction basic matrix BkWith index matrix Hk；Initialize HkFor n1xn1Full null matrix, k be [0, m-1] it is whole Number, m=11；
Step 2.1 sets Bk=4.5- (d 'k-D2)2/2σ2, in which: D2Indicate G2In vertex between distance matrix, σ2It indicates Adjustable factors；
Step 2.2 searches G1Distance matrix D1Element value is between [dmin+w×(k-1),dmin+ w × k] between element, Enable HkIn index accordingly element be 1；
Step 3: initialization matrixInitialize the full null matrix that M is n1 × n2；It will X=X0；Initialization error threshold value Error=1 initializes the number of iterations maximum value ItersMax=300；Initialize α=0.3, β =30, p=0；
Step 4: calculating initial matching matrix X；
Step 4.1, taking k is the integer of [0, m-1], is repeated in calculatingCalculate Mm
Step 4.2, assignment calculates:Y=eβX/max(X)；
Step 4.3, the normalization of row and column is carried out to Y, i.e. repeated assignment of values calculates:
Until | | Yk-Yk+1||2< 1e-25；YajIndicate the element of a row jth column in Y, Y value at this time is Yk+1；
Step 4.4, α X+ (1- α) Y is assigned to X, then carries out the normalization of row and column, i.e. repeated assignment of values meter to X after assignment It calculates
Until | | Xk-Xk+1||2< 1e-25, XajIndicate the element of a row jth column in X, the value of X is X at this timek+1；
Step 4.5, Error=is calculated | | Xp-Xp-1||2, XpIndicate the calculated X value of previous cycle, Xp-1Indicate last The X value that cycle calculations go out, then assignment calculate p=p+1；
Step 4.6, if Error>1e-25 and p<ItersMax, otherwise return step 4.1 saves the value of X at this time, into Enter in next step；
Step 5 carries out 0-1 discretization to the X sought using Hungary Algorithm, to obtain n1×n2Matching matrix, The corresponding relationship on vertex in two images is indicated with matrix.
The image generated at random and true picture is selected to do figure matching in the present embodiment.Generating figure or reality pictures In, 20 random addition noises of experiment operation and exterior point generate G2, obtained in calculating average matching precision and operation time ?.Fig. 1 is the example to be matched generated at random for implementing effectively figure matching process in the present invention.Red point is G in Fig. 11In Point；By adding the noise and exterior point of different proportion, G is formed2In point, i.e., green point.G1Generation obey N (0,30) Normal distribution.Wherein exterior point and noise are randomly generated；Noise is added to G2In distance between points.Fig. 3 is true Graphic example.Fig. 2 illustrates the G that 0-20 exterior point of addition generates on generating data2It is matched as a result, simultaneously and SM, FaSM Matching result compare.Fig. 3, which illustrates to be added on generating data, generates the matched knot of noise progress that 10-100 is not waited Fruit, and compared with the matching result of SM, FaSM.It is in kind in Fig. 4 --- the edge of clock is extracted first, to down-sampling It is differed at 200 to 1000 points.It is similar with figure is generated with the mode of exterior point that noise is added.What Fig. 5 was shown works as figure number of vertices When being 200, equal exterior point does not carry out figure matching in the comparing result of matching precision and runing time to random addition 10-100.Fig. 6 When showing that reality pictures number of vertices distinguishes 300-1000,10%-50% is added in steady noise condition (σ=50) and differs Comparing result under conditions of exterior point.
In conclusion method of the invention does not need building n1n2×n1n2Similar matrix, space complexity is only O (n1n2), time complexity is O (kn1n2)；Expansion factor and ranks normalization processing method, the algorithm of acceleration are incorporated simultaneously The speed of operation improves the matched precision of figure.

Claims (1)

1. a kind of quick spectrogram matching process, this method comprises:
Step 1: known figure G1With figure G2Vertex and side set be respectively (V1,E1) and (V2,E2), number of vertices is respectively n1, n2；If scheming G1In the distance between i-th of vertex and j-th of vertex beScheme G2In between i-th of vertex and j-th of vertex Distance isTo figure G1In the distance between any two points matrix be D1, to D1Middle element is ranked up, it is assumed that maximum value is dmax, minimum value dmin, by dmaxWith dminBetween divide m sections, every section of width w=(dmax-dmin)/m；To dijCarry out approximate table Show, representation method is as follows:
Judge d 'ijPositioned at which of m segmentation segmentation, the intermediate value d ' of the segmentation is then usedkInstead of original d 'ij；
Step 2: construction basic matrix BkWith index matrix Hk；Initialize HkFor n1xn1Full null matrix, k be [0, m-1] integer, m Approximate precision is preset as needed；
Step 2.1 sets Bk=4.5- (d 'k-D2)2/2σ2, in which: D2Indicate G2In vertex between distance matrix, σ2Indicate adjustable The factor；
Step 2.2 searches G1Distance matrix D1Element value is between [dmin+w×(k-1),dmin+ w × k] between element, enable Hk In index accordingly element be 1；
Step 3: initialization matrixInitialization M is n1×n2Full null matrix；By X=X0； Initialization error threshold value Error=1 initializes the number of iterations maximum value ItersMax, initializes α, β, p；
Step 4: calculating initial matching matrix X；
Step 4.1, taking k is the integer of [0, m-1], is repeated in calculatingCalculate Mm
Step 4.2, assignment calculates:Y=eβX/max(X)；
Step 4.3, the normalization of row and column is carried out to Y, i.e. repeated assignment of values calculates:
Until | | Yk-Yk+1||2< 1e-25；YajIndicate the element of a row jth column in Y, Y value at this time is Yk+1；
Step 4.4, α X+ (1- α) Y is assigned to X, then carries out the normalization of row and column to X after assignment, is i.e. repeated assignment of values calculates
Until | | Xk-Xk+1||2< 1e-25, XajIndicate the element of a row jth column in X, the value of X is X at this timek+1；
Step 4.5, Error=is calculated | | Xp-Xp-1||2, XpIndicate the calculated X value of previous cycle, Xp-1Indicate last circulation Calculated X value, then assignment calculate p=p+1；
Step 4.6, if Error>1e-25 and p<ItersMax, otherwise return step 4.1 saves the value of X at this time, under One step；
Step 5 carries out 0-1 discretization to the X sought using Hungary Algorithm, to obtain n1×n2Matching matrix, match square The corresponding relationship on vertex in two image of matrix representation.
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