CN101110103A - Image registration self-verifying method based on learning - Google Patents

Abstract

The invention belongs to a computer visual and module recognition, which discloses an automatic detection method for image registering based on machine learning. The method comprises the following parts: adopt phase correlation diagram as sample data; construct feature data via the phase correlation diagram; classify the feature data via a classifier; conduct registering detection according to the classification result. The invention adopts supervision machine learning method to design the classifier; the classifier is adopted to conduct registering detection of classification result. After a registering experiment of 400 groups of different images without disturbance, it is proved that the correct detection rate reaches 100 per cent, which indicates that the image registering detection method based on classifier has high efficiency.

Description

A kind of image registration self-verifying method based on study

Technical field

The invention belongs to computer vision and area of pattern recognition.Specifically, relate to the check of image registration results.

Background technology

Image registration is a basic problem in computer vision and the related application field thereof.Whether real how to measure two width of cloth images registration, in other words, how rationally to measure the similarity between two width of cloth images behind the registration transformation, be a key problem of image registration, directly determined whether can carry out full-automatic registration.The present invention has proposed a kind of image registration self-verifying method based on machine learning to be example based on Fourier-Mellin conversion registration Algorithm.

We do a detail analysis and explanation to the problem that exists in the image registration algorithm based on the Fourier-Mellin conversion earlier.

1, based on the method for registering images of Fourier-Mellin conversion

1.1 phase correlation method

If f ₂(x y) is f ₁(x is y) at x and y direction difference translation x ₀And y ₀After image, that is:

f ₂(x，y)＝f ₁(x-x ₀，y-y ₀) (1)

If f ₁And f ₂Corresponding Fourier conversion is respectively F ₁(u, v) and F ₂(u, v), so,, satisfy following relation between them according to Fourier conversion shift invariant theory:

$F_2(u,v)=F_1(u,v)e^{-j({\mathrm{<figure-callout\; id="0"\; label="ux"\; filenames="A20061010325800191.png"\; state="\{\{state\}\}">ux</figure-callout>}}_0+{\mathrm{vy}}_0)}---\left(2\right)$

F then ₁(x, y) and f ₂(x, cross power spectrum y) is

$\frac{F_1(u,v){\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="A20061010325800211.png"\; state="\{\{state\}\}">F</figure-callout>}}_2^{*}(u,v)}{\left|F_1(u,v){\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="A20061010325800211.png"\; state="\{\{state\}\}">F</figure-callout>}}_2^{*}\right(u,v\left)\right|}=e^{j({\mathrm{<figure-callout\; id="0"\; label="ux"\; filenames="A20061010325800191.png"\; state="\{\{state\}\}">ux</figure-callout>}}_0+{\mathrm{vy}}_0)}---\left(3\right)$

F wherein ₂ ^*Expression F ₂Complex conjugate.As can be seen, the phase place of cross power spectrum is equivalent to the phase differential of two width of cloth images.By (3) formula being carried out Fourier inverse transformation (also claiming the phase place related function), at (x, the y) (x in space ₀, y ₀) locate impulse function of formation, the peak value of pulse position is the relative translation amount x of two width of cloth images ₀And y ₀

1.2 the similarity transformation parameter of two-step approach computed image

Two width of cloth image s that consider to be registered (x, y) and r (x, y), wherein (x is that (x is y) through the image after translation, rotation and consistent scale (the change of scale factor that is both direction the is equal) conversion, promptly for r y) to s

s(x，y)＝r[(σ(xcosα+ysinα)-x ₀，σ(-xsinα+ycosα)-y ₀] (4)

So s (x, y) and r (x, y) Dui Ying Fourier conversion S (u, v) and R (u, satisfy between v):

$S(u,v)=e^{-j{\mathrm{\&phi;}}_s(u,v)}{\mathrm{\&sigma;}}^{-2}\left|R[{\mathrm{\&sigma;}}^{-1}(u\cos \mathrm{\&alpha;}+v\sin \mathrm{\&alpha;}),{\mathrm{\&sigma;}}^{-1}(-u\sin \mathrm{\&alpha;}+v\cos \mathrm{\&alpha;})]\right|---\left(5\right)$

φ wherein _s(u, v) be image s (this phase dependent is in translation, rotation and scale for x, spectral phase y), still, spectrum amplitude

|S(u，v)|＝σ ^-2|R[σ ^-1(ucosα+vsinα)，σ ^-1(-usinα+vcosα)]| (6)

It is the translation invariant amount.

Formula (6) illustrates that if image has rotated an angle, so Dui Ying amplitude spectrum also will rotate same angle, if the graphical rule zoom factor is σ, spectrum amplitude is scaled σ accordingly so ^-1

The translation invariance of spectrum amplitude make anglec of rotation α and zoom factor σ can with translational movement x ₀And y ₀Carry out decouples computation.Spectrum amplitude is only relevant with zoom factor σ with rotation angle α, and with translational movement (x ₀, y ₀) irrelevant, therefore, can obtain anglec of rotation α and zoom factor σ by the picture amplitude spectrum.

(1) first step: ask anglec of rotation α and zoom factor σ at transformation space with phase correlation method,

With picture amplitude spectrum be transformed into earlier polar coordinates (ρ, θ) under, obtain

r _p(θ，ρ)＝|R(ρcosθ，ρsinθ)| (7)

s _p(θ，ρ)＝|S(ρcosθ，ρsinθ)| (8)

Notice that spectrum amplitude is the periodic function of polar angle θ, again because image is a real function, so

r _p(θ+nπ，ρ)＝r _p(θ，ρ)，n＝…，-2，-1，0，+1，+2，… (9)

Therefore can be only (0≤θ＜π) carries out subsequent calculations with the poincare half plane of amplitude spectrum.Again with the ρ coordinate conversion to log ρ space, according to the rotation and the change of scale character of Fourier conversion, the translation problem that the rotation and the scale of image can be reduced to logarithm-utmost point (log-polar) space like this.

Definition:

r _p1(θ，logρ)＝r _p(θ，ρ) (10)

s _p1(θ，logρ)＝s _p(θ，ρ) (11)

R wherein _pAnd s _pThe amplitude spectrum that is r and s respectively is in polar coordinate system (θ, ρ) middle expression.Be easy to so draw:

s _p1(θ，logρ)＝r _p1(θ-α，logρ-logσ) (12)

Perhaps s _P1(θ, λ)=r _P1(θ-α, λ-κ) (13)

λ=log ρ wherein, κ=log σ.

As can be seen, by above-mentioned conversion, formula (13) is transformed to and the identical form of formula (1), so just can according to formula (2) and (3), try to achieve α and κ at logarithm-utmost point (Log-Polar) space application phase correlation method.

If the end of logarithm, be taken as e, so

σ＝e ^κ (14)

Anglec of rotation α and scale factor σ have so just been obtained.

Formula (10) or (11) are called as the Fourier-Mellin conversion.

(2) second steps: ask translation parameters x with phase correlation method at image space ₀And y ₀

(x y) carries out consolidation (warp) and obtains image s to image s according to the α that obtains and σ _t(x, y), at this moment, s ₁(x, y) and r (x has only the translation distortion between y), and then an application phase correlation method, and through type (2)～(3) calculate s at image space ₁(x, y) and r (x, y) the translational movement x between ₀And y ₀

2, based on the method for registering images analysis of Fourier-Mellin conversion

From the content of last branch as can be known, find the solution similarity transformation parameter (anglec of rotation α, scale coefficient S and translation parameters T) in two steps in different spaces based on the method for registering of Fourier-Mellin conversion.The first step is found the solution the anglec of rotation and scale coefficient in logarithm-utmost point (log-polar) space of picture amplitude spectrum, and second step was found the solution translation parameters at image space.

Angle from signal Processing, between two signals, do not disturb, and when translation transformation is satisfied in strictness, (we claim this to be transformed to the phase place related function later in the contrary Fourier conversion of these two signal cross power spectrum (formula 3), because the value of this function all is plural number usually, the correlation values size of indication all is meant the mould of plural number) be an impulse function, as shown in Figure 1a, pulse position is corresponding to the mutual translation of two signals; But, in actual applications, generally speaking, signal always exists certain interference and error, and at this moment the phase place related function is not a desirable impulse function, but presents the shape of Fig. 1 b, at this moment, the position of maximum related value is still corresponding to the translational movement of two signals; If it is very big that signal disturbs, perhaps do not satisfy the translation transformation relation between the signal, the phase place related function will not have tangible peak value so, and present irregular distribution, shown in Fig. 1 c.

In order to narrate conveniently the back, the correlation function value that phase correlation method drew when the first step in the Fourier-Mellin algorithm was calculated the anglec of rotation and scale coefficient is called correlation I, corresponding maximum related value is called peak I, the correlation function value that phase correlation method drew when second step was calculated translation parameters is called correlation II, and corresponding maximum related value is called peak I I.

2.1 first step phase correlation method is analyzed

In formula (4)～formula (6) derivation of Fourier-Mellin algorithm, an important prerequisite is arranged, the Fourier transform frequency spectrum after promptly piece image rotates to an angle is equivalent to the identical angle of Fourier transform frequency spectrum rotation without the image of rotation.People such as Stone [1] Harold S.Stone, Bo Tao, and Morgan McGuirre, " Analysis of image registrationnoise due to rotationally dependent aliasing; " Journal of VisualCommunication and Image Representation, vol.14, pp.114-135,2003, the caused image registration noise of spectral aliasing that produces owing to the image rotation has been carried out labor, and derived, though for the endless view data, this hypothesis is correct, but for limit for length's discrete image data was arranged, this basic premise was incorrect.Its main cause is owing to depend on the artifacts that interpolation error produces in artifacts that the spectral aliasing (being different to its spectral aliasing degree of the different anglecs of rotation promptly) of rotation causes and the rotational transform and cause.People's such as Stone research draws: first, owing to depend on the influence of the spectral aliasing of rotation, in first step phase place correlation computations, may produce correlation peak and a correct correlation peak of a mistake, and false peaks may be greater than correct peak value, therefore, the first step phase correlation method peak I of trying to achieve can not corresponding reliably correct matching parameter position; The second, because the appearance of false peaks, the peak I that first step phase correlation method is tried to achieve is significantly smaller than theoretical value 1.0, even has dropped to below 0.03.

Document [2] Luca Lucchese and Guido Maria Cortelazzo, " A noise-robustfrequency domain technique for estimating planar roto-translations; " IEEETrans.Signal Processing, vol.48, no.6, pp.1769-1786,2000

[3] Luca Lucchese and Guido Maria Cortelazzo, " High resolutionestimation of planar rotations based on Fourier transform and radialprojection; " In Proc.ISCAS 97, vol.2, pp.1181-1184, June 1997 grades all study in great detail at this problem that causes owing to rotation, and taked some to improve peak value, reduce spectral aliasing, increase robustness, but still fail fundamentally to address this problem such as measures such as windowing and filtering.

Of particular note, in document [1-3], although provided the quantitative analysis of spectral aliasing, and also taked some effective measures to improve the influence that spectral aliasing causes, but, these measures are applicable to that two width of cloth picture materials are identical, and certain effect is arranged during the corresponding problem of only considering that image rotation brings.But practical problems is simple so far from, in document [1], also spells out the error that causes owing to interpolation problem, but this influence is difficult to quantitative estimation, does not also propose what very effective measure and solves this problem.If the influence that various factors is caused combines again, with regard to more difficult quantitative analysis.Such as, in common application, only overlapped by between two width of cloth images that mate, also may there be distortion such as translation and scale simultaneously, also have other multiple noise.To this class situation, can't derive the influence that these factors cause quantitatively in theory at present.

Find by our a large amount of experiment, also can't judge the correctness of matching result according to the absolute size of peak I.Document [4] B.S.Reddy and B.N.Chatterji, " AnFFT-Based technique for translation; rotation; and scale-invariant imageregistration; " IEEE Trans.Image Processing, vol.5, no.8, pp.1266-1271, mention in 1996, generally speaking, peak I is just unreliable less than 0.03 result, but we test discovery, even peak I is greater than 0.1, the result also may not be reliable, and two width of cloth images are when really mating, and peak I is very common less than 0.03 situation under the bigger situation of noise.Therefore can think that this value 0.03 is relevant with concrete application.At document [5] Q.-S.Chen, M.Defrise, and F.Deconinck, " Symmetric phase-only matched filteringof Fourier-Mellin transforms for image registration and recognition; " IEEE Trans.Pattern Analysis and Machine Intelligence, vol.16, no.12, pp.1156-1168 in 1994, has defined 3 kinds of quantitatively evaluating indexs to the performance of this algorithm, it is output signal-to-noise ratio, the acuteness of peak value and PD (Percent Discrimination), but all be not suitable for as determining registration whether criterion.

Experiment finds that also carrying out the registration check by the position distribution of correlation I also is not have rule governed.

2.2 second step phase correlation method analysis

Fourier conversion displacement theory is applied to only have between two width of cloth images registration problems of translation, if when the translational movement between two width of cloth images is the integral multiple of pixel, this method is a kind of accurate method for registering.Though also have the problem of spectral aliasing at frequency domain, be different from situation with rotation because at this moment for two width of cloth images that are registered its influence be identical [1].

In using based on the image registration of Fourier-Mellin conversion, the hypothesis of concrete condition and Fourier conversion displacement theory is different, this is mainly reflected in: the first, and image itself is discrete sampling, the translational movement between image may be corresponding to non-integral multiple pixel value; The second, in actual application, require that two width of cloth images of registration are not strict to satisfy the similarity transformation relation; The zone in most cases only overlaps between the three, two width of cloth image; The 4th, in the image registration rudimentary algorithm based on the Fourier-Mellin conversion, all there is interpolation error in the image consolidation of the Log-Polar coordinate transform and the second step calculating process in the first step calculating process; The 5th, because transformation parameter all is discrete value,, and will directly influence second computing that goes on foot so the anglec of rotation that the first step is tried to achieve and scale coefficient always have small error; The 6th, some other also can introduce error such as reasons such as ground unrests.

Find by theoretical analysis and a large amount of experiments, because the existence of above-mentioned multiple noise has caused influence in various degree to the size of correlation II and the distribution of relevant position, but generally speaking, has presented following three class distribution forms:

1, unimodal distribution

In ideal conditions, promptly under the situation without any error, the correlation maximum at correct matched position place, and equal 1, and the correlation of other position is 0, is the impulse function of standard, as shown in Figure 1a; Have under the situation of less error, still have tangible unimodal value, promptly peak I I is obviously greater than the correlation at other place, shown in Fig. 1 b.

2, irregular distribution

With unimodal distribution antithesis, when various interference were very serious, correlation II is very little at every numerical value, and was disorderly and unsystematic, presents irregular distribution.Shown in Fig. 1 c.

3, the Local Convex peak distributes

Consider above-mentioned various The noise, the correlation II between two width of cloth images of registration also usually can present another kind of the distribution mutually.This distribution neither resembles has tangible peak value structure the unimodal distribution, neither have no the distribution of rule.The form that shows is, preceding several maximum correlation value successively are more or less the same, and its corresponding relevant position all or major part all concentrate be distributed in the maximal correlation position than small neighbourhood (being not must be to be the symmetrical distribution at center with the maximal correlation position), form one " protruding peak ".Say that more specifically this protruding peak distributes and can also further be refined as following three kinds of forms:

(1) preceding several maximum related value is relatively large, but negligible amounts has only 2～3, usually shown in Fig. 2 a.

(2) preceding several maximum related value numerical value less (even and noise data be more or less the same), but quantity is more, can reach 4 usually to more than 10, shown in Fig. 2 b.

(3) sometimes, have this zone, protruding peak of concentrating of indivedual position deviations in the relevant position of preceding several maximum related value correspondences, but these positions are isolated often, can not form the zone of concentrating relatively, this is normally caused by enchancement factor, shown in Fig. 2 c.

Above-mentioned three kinds of distribution situations can be interpreted as: under ideal situation comparatively, correlation energy mainly concentrates on certain a bit, and numerical value is bigger; Along with the increase of error, main correlation energy is dispersed in a less zone, and numerical value is big more, and distribution range is narrow more, and numerical value is more little, and distribution range is wide more; When two width of cloth images just are unworthy of itself, perhaps to can't judge whether registration the time, correlation energy presents irregular distribution to error, and every correlation is all very little greatly.

Summary of the invention

In the image registration algorithm of above-mentioned Fourier-Mellin conversion, because the uncertainty of the registration parameter that first step phase place correlation computations is come out, add various The noise, make the size and the distribution situation of the correlation that the second step phase place correlation computations is come out become very complicated, be difficult to quantitatively and exactly describe these situations, the objective of the invention is to solve the check problem of image registration results in the classic method, judge the correctness of the matching parameter that the Fourier-Mellin registration Algorithm is calculated, promptly judge whether registration of two width of cloth images automatically according to these parameters, for realizing that the full-automatic registration of image provides sound assurance, for this reason, the present invention proposes a kind of automatic image registration method of inspection based on study.

The image registration self-verifying step is as follows among the present invention: adopt the phase place correlogram as sample data; Utilize phase place correlogram structural attitude data; The design category device is classified to characteristic, carries out the registration check according to classification results.

According to embodiments of the invention, described employing phase place correlogram is to adopt based on the correlation in the second step phase place related algorithm in the Fourier-Mellin changing image registration Algorithm as original sample data as sample data.

According to embodiments of the invention, described structural attitude data are to come the structural attitude data according to size and distribution based on preceding n maximum in the second step phase place related algorithm in Fourier-Mellin changing image registration Algorithm correlation.

According to embodiments of the invention, described structural attitude data, its first kind of characteristic make is: extract in preceding n maximum in the correlation in the second step phase place related algorithm correlation, if it is a certain size neighborhood of center that these correlations are positioned at the maximum related value, then keep these correlations, if these these zones of correlation position deviation then are changed to 0 with corresponding correlation.

According to embodiments of the invention, described structural attitude data, its second kind of characteristic make is: will utilize the characteristic of first kind of characteristic make structure, and carry out dimension-reduction treatment through principal component analysis (PCA), and constitute second kind of characteristic.

According to embodiments of the invention, described classifier design, sorter model adopts support vector machine (SVD), and kernel function is a Gaussian function.

According to embodiments of the invention, described first kind of characteristic, in final preceding n the maximum related value of selecting, n=6, corresponding proper vector number is 17.

According to embodiments of the invention, described second kind of characteristic, in final preceding n the maximum related value of selecting, n=2, corresponding proper vector number is 13.

According to embodiments of the invention, in the gaussian kernel function that sorter model adopted, parameter σ ²Span be 0.0l～0.1.

Beneficial effect of the present invention: to the automated graphics registration method of inspection that proposes among the present invention based on study, test by the image registration results of 400 groups of different images under difference is disturbed, correct check rate reaches 100%, has solved in the classic method whether this difficult problem of registration of automatic gauging image preferably.100% accuracy has illustrated that this image registration method of inspection based on sorter is very effective and robust.Certainly, in our experiment, do not find the situation of misclassification, but this is not mistake under any circumstance all can not occur to divide, but illustrates that at least this method has very high confidence level.

Description of drawings

Fig. 1 a is the correlation typical case desirable peak Distribution figure of prior art Fourier conversion displacement theory when being used for images match

Fig. 1 b is the correlation typical case actual peak Distribution of prior art Fourier conversion displacement theory when being used for images match

Fig. 1 c is the peak Distribution of the correlation typical case of prior art Fourier conversion displacement theory when being used for images match when not matching

Fig. 2 a is the narrower protruding peak distribution schematic diagram of prior art Local Convex peak distribution pattern

Fig. 2 b is the protruding peak distribution schematic diagram of prior art Local Convex peak distribution pattern broad

Fig. 2 c is the protruding peak distribution schematic diagram that prior art Local Convex peak distribution pattern has burr

Fig. 3 is the image registration self-verifying method process flow diagram that the present invention is based on study

Fig. 4 is the different images type that is used among the present invention by machine learning design category device

Fig. 5 is the machine learning basic model that prior art has supervision

Fig. 6 is a prior art optimal classification face synoptic diagram

Embodiment

Below in conjunction with accompanying drawing the present invention is described in detail, be to be noted that described embodiment only is intended to be convenient to the understanding of the present invention, and it is not played any qualification effect.

How the problem of being concerned about in the present invention judges the correctness of the matching parameter that the Fourier-Mellin registration Algorithm is calculated, and in other words, how judges whether registration of two width of cloth images automatically according to these parameters.

Analysis according to a preceding part, correlation peak I's is big or small unreliable, any rule is not found in the distribution of correlation I yet, and correlation II seems some rule, so first idea of the present invention is: do not rely on size and the distribution of correlation I, judge the correctness of matching parameter and mainly rely on the size of correlation II and distribute.

For the problem that the present invention was concerned about, the idea of nature is: set a threshold value, if correlation II promptly is judged to be registration greater than this threshold value, otherwise be judged to be not registration.Yet, because the Fourier-Mellin registration Algorithm has higher robustness, when even the entire system error ratio is big, still may draw correct matching parameter, just in this case, it is very little that maximum related value becomes, even and the correlation of other position be more or less the same, it is very difficult therefore choosing an appropriate thresholds.Based on this, the present invention has got rid of the idea of setting threshold, and size and distribution by considering correlation II simultaneously, the registration situation of coming the process decision chart picture.

In addition, from the analysis of above-mentioned background technology 2.2 as can be seen, although the size of correlation II and distribution have certain rules, be quantitatively and describe but difficulty relatively of these rules exactly, especially the variation that protruding peak distributes makes problem description become very complicated.The thinking that addresses this problem has constituted second idea of the present invention: regard size and the distribution of correlation II as a vectorial sample (being the phase place correlogram among Fig. 3), from the phase place correlogram, extract appropriate characteristic then and be input to the sorter of having succeeded in school, automatically be divided into registration and two kinds of situations of registration not by sorter, like this, just the coupling metric question of image has been changed into the pattern classification problem of parameter space.

A kind of automated graphics registration method of inspection based on machine learning has been proposed among the present invention.The entire block diagram of this method adopts the phase place correlogram as sample data as shown in Figure 3; Utilize phase place correlogram structural attitude data; The design category device is classified to characteristic, carries out the registration check according to classification results.Image 1 and image 2 are two width of cloth images that are registered among Fig. 3, and image 1 and image 2 feed the registration module 3 based on the image registration algorithm of Fourier-Mellin conversion, are used for two width of cloth image registrations; Registration module 3 export to applying aspect correlogram module 4, be used for correlation II is constituted the phase place correlogram; Characteristic extraction module 5 extracts the characteristic of phase place correlogram in the correlogram modules 4, and sorter 6 is classified the characteristic of characteristic extraction module 5 outputs and exported registration 7 or registration 8 information not.

The phase place correlogram can be understood like this: imagine such piece image, the gray-scale value of each picture element is by phase place correlation II that should the position is replaced in the image, the correlation of this position is big, be similar to the gray-scale value height of this point in the normal image, equally, the correlation of this position is little, and the gray-scale value that is similar to this point is low, and we just can regard size and the distribution of correlation II as a width of cloth " phase place correlogram " like this.

In specific implementation process, most importantly determine the characteristic make that performance is best and design autoregistration inspection-classification device by machine learning.

The present invention adopts has the learning method of supervision to come the design category device, the basic model of its machine learning can be represented with Fig. 5, at first use the known sample (claiming that these samples are training sample) of some to carry out classifier design, form a categorised decision function by training process.After classifier design is finished,,, can export the i.e. output of prediction among the figure of a classification results automatically by the categorised decision function for arbitrary new test data.Because support vector machine (SVM) has the ability of promoting preferably, so this chapter adopts support vector machine as sorter model [6] Vapnik, The Nature of Statistical Learning Theory, Springer Verlag, NewYork, 1995

[7]T.Joachims，Making large-Scale SVM Learning Practical.Advances in Kernel Methods-Support Vector Learning，B.Schlkopf andC.Burges and A.Smola(ed.)，MIT-Press，1999。

1, support vector machine (SVM)

Support vector machine is to be based upon the algorithm of realizing Statistical Learning Theory on the structural risk minimization principle basis.It seeks optimal compromise according to limited sample information between model complicacy and learning ability, in the hope of obtaining maximum generalization ability.It does not need supposition and sample estimates distribution parameter in advance, by seek maximum classification space in small sample, obtains the linear interphase of two class problems.For non-linear classification problem, it replaces inner product operation by kernel function, and former problem is converted to the linear classification problem of higher dimensional space, and the maximum classification of utilization gap algorithm is handled again.

We at first go out to send the analysis support vector machine from the situation of linear separability.

To two class linear separability problems (is prior art optimal classification face synoptic diagram referring to Fig. 6), establishing the linear separability sample set is (x _i, y _i), i=1 ..., n, x ∈ R ^d, {+1 ,-1} is a category label to y ∈.The general type of d dimension space neutral line discriminant function is f (x)=wx+b, and the classifying face equation is:

w·x+b＝0 (15)

We carry out normalization with discriminant function, and all samples of two classes are all satisfied | f (x) | and 〉=1, promptly make to separate the nearest sample of class face | f (x) |=1, the class interval just equals 2/ ‖ w ‖ like this, therefore, the interval maximum is equivalent to makes ‖ w ‖ (or ‖ w ‖ ²) minimum; And require classifying face that all samples are correctly classified, require it to satisfy exactly

y _i[(w·x _i)+b]-1≥0，i＝1，2，…，n (16)

Therefore, satisfy above-mentioned condition and make ‖ w ‖ ²Minimum classifying face is exactly optimal classification face (shown in a heavy line among Fig. 6).Crossing in the two class samples from nearest point of classifying face and the training sample that is parallel on the lineoid (shown in two fine lines among Fig. 6) of optimal classification face is exactly those samples that equal sign is set up, and they are called support vector.

Support vector machine manages to seek this optimal classification face by training sample exactly.

In a broad aspect, find the solution the optimal classification face and can be summed up as following quadratic programming problem [6]:

$\underset{w,b}{\min }\mathrm{\&phi;}\left(w\right)=\frac{1}{2}(w\&CenterDot;w)+C\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&xi;}}_i---\left(17\right)$

s.t. y _i[(x _i·w)-b]≥1-ξ _i，ξ _i≥0，i＝1，2，…，n (18)

C＞0th wherein, by certain constant of user's appointment, in fact it play control and divide the degree of sample punishment to mistake, is implemented in compromise between wrong ratio of dividing sample and the algorithm complex.

Actually utilize the antithesis technology when finding the solution quadratic programming formula (17), can obtain its Wolf dual program [6] and be

$\underset{\mathrm{\&alpha;}}{\max }\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i-\frac{1}{2}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{\mathrm{\&alpha;}}_j{y}_i{y}_j(x_i\&CenterDot;x_j)---\left(19\right)$

$s.t.\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y}_i{\mathrm{\&alpha;}}_i=\mathrm{0,0}\&le;{\mathrm{\&alpha;}}_i\&le;C,i=\mathrm{1,2},...,n---\left(20\right)$

Its optimum solution α ^*With optimum lineoid w ^*X+b ^*Relation between=0 has

$w^{*}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y}_i{\mathrm{\&alpha;}}_i^{*}{x}_i---\left(21\right)$

And b ^*Obtain by duality relation.Note w in the formula (21) ^*Calculating only with the α of non-zero _i ^*Relevant, claim to satisfy ${\mathrm{\&alpha;}}_i^{*}>0$ Corresponding training sample vector x _iBe support vector (sv).The discriminant function of linear support vector machine has following form:

$f\left(x\right)=\mathrm{sgn}(w^{*}\&CenterDot;x+b^{*})=\mathrm{sgn}(\underset{i\&Element;\mathrm{sv}}{\mathrm{\&Sigma;}}{y}_i{\mathrm{\&alpha;}}_i^{*}(x_i\&CenterDot;x)+b^{*})---\left(22\right)$

In order to handle non-linear classification problem, introduced the generalized linear classification function: promptly adopt Nonlinear Vector mapping Ф: x ∈ R ^d→ Ф (x) ∈ F, F is a higher-dimension (or even infinite dimension) space here, is called feature space.After selecting suitable mapping Ф (x), can be with data set { x that originally can not linear classification ₁, x ₂..., x _n) ∈ R ^dBe mapped as the sample { Ф (x of linear separability ₁), Ф (x ₂) ..., Ф (x _n) ∈ F, adopt the method for front linear classification can obtain the linear classification lineoid at feature space F.Notice that in training process formula (19) and checkout procedure formula (22), sample point all is the form appearance with dot product, i.e. x _iX _jIf exist a kernel function to make following formula set up

K(x _i，x _j)＝(Ф(x _i)·Ф(x _j)) (23)

We need only and replace the dot product (at feature space) of sample data with kernel function in training process and checkout procedures so, and do not need to know the expression formula of mapping function Ф.Kernel function K is brought in the dual program formula (19), obtain nonlinear support vector machine

$\underset{\mathrm{\&alpha;}}{\max }\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i-\frac{1}{2}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{\mathrm{\&alpha;}}_j{y}_i{y}_{j}K(x_i{,x}_j)---\left(24\right)$

$s.t.\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y}_i{\mathrm{\&alpha;}}_i=\mathrm{0,0}\&le;{\mathrm{\&alpha;}}_i\&le;C,i=\mathrm{1,2},...,n---\left(25\right)$

The discriminant function of non-linear support vector machine is

$f\left(x\right)=\mathrm{sgn}(\underset{i\&Element;\mathrm{sv}}{\mathrm{\&Sigma;}}{y}_i{\mathrm{\&alpha;}}_{i}K(x_i,x)+b)---\left(26\right)$

Determined α in the formula (24) by the machine learning method that supervision is arranged _iAnd corresponding support vector x _iBehind b, also just finished the design of sorter formula (26).After arbitrary new sample data x input category device formula (26), two kinds of different values of sign function f (x) have been represented the classification results of two class problems respectively.

In specific implementation process of the present invention, adopt the SVM implementation method in the document [7], the C value is 5 in the formula (25), the kernel function of selecting for use in the formula (26) is a Gaussian function, is defined as

$K(x,x_j)=\exp (-\frac{{|x-x_i|}^2}{{\mathrm{\&sigma;}}^2})---\left(27\right)$

Described classifier design, sorter model adopts support vector machine, and kernel function is a Gaussian function.In the gaussian kernel function that is adopted, parameter σ ²Span is 0.01 or 0.05 or 0.1.

2, raw data is obtained

The hand-held digital camera, rotate different angles, regulate different focal lengths, choose some kinds of different scene type, as Fig. 4 is the different images type that is used for machine learning in the embodiment of the invention, 5 kinds of scenes have wherein been chosen, every kind of scene shooting is some to picture, and in our invention, 5 kinds of scenes have been taken 400 pairs of images altogether.Attention: some approximately satisfies the similarity transformation relation to make these images when taking, and some does not then satisfy this relation specially, image registration data when being respectively applied for machine learning and registration data not.

Described employing phase place correlogram is to adopt based on the correlation in the second step phase place related algorithm in the Fourier-Mellin changing image registration Algorithm as original sample data as sample data.

Application is calculated matching parameter between the Same Scene different images based on the basic registration Algorithm of Fourier-Mellin conversion, adopts the image mosaic technology to come whether registration of subjective judgement two width of cloth images then.Like this, each experimental result is all noted, as raw data base.Each record format in the database is as follows:

Record _i＝{BaseInfo _i，Corr _i，Sort _i}

Wherein, BaseInfo _i, Corr _i, Sort _iBe three arrays of corresponding each record.Some essential informations of record among the BaseInfo are as image name, image size, registration etc. whether; Corr is array, and record is the correlation size of each position in the neighborhood of 5 * 5 sizes at center with the maximal correlation position, also is each record Corr _iA corresponding width of cloth phase place correlogram; Sort is an array with the identical size of Corr, in the record Corr array correlation of correspondence position in all correlations of image by from big to small arrangement sequence number.

In these data, some is the data of registration, and some is the data of registration not, and from these data, each selects a part of data to form training set, and remainder is formed test set, chooses a half data respectively and is used for training, and second half is used for test.

3, characteristic structure

The quality that characteristic is chosen has significant effects to the performance of pattern classification system.We have carried out a large amount of experiments and comparison to different characteristic makes, and the result shows, below two kinds of characteristic makes obtained best effect, table 1 is the classifier parameters of final design and to the classification results of 400 pairs of images.

Described structural attitude data are to come the structural attitude data according to size and distribution based on preceding n maximum in the second step phase place related algorithm in Fourier-Mellin changing image registration Algorithm correlation.

(1) described structural attitude data, its first kind of characteristic make is: preceding n maximum number in second step of the extraction phase place related algorithm among all correlation II pressed descending order and formed n dimensional feature data, if it is a certain size the neighborhood (we adopt the neighborhood of 5 * 5 sizes) at center that the position of these correlation correspondences is positioned at the maximum related value, then keep these data, if these these zones of correlation position deviation then are changed to 0 with corresponding correlation.

(2) described structural attitude data, its second kind of characteristic make is: will carry out dimension-reduction treatment through principal component analysis (PCA) by the characteristic of first kind of characteristic make structure.Account for the principle of all eigenwert sums 95% by preceding several eigenvalue of maximum sums, keep these eigenwert characteristic of correspondence vectors, then with data projection to these characteristic vector spaces.Promptly constitute second kind of characteristic.

Table 1 is by the characteristic parameter of machine learning design and final classification results

The characteristic type	Data dimension (n)	The SVM learning outcome
					The support vector number	Training set accuracy (%)	Test set accuracy (%)
		Make 1	6	17				100	100
Make 2	2				13	100	100

4, embodiment brief summary

At first adopt certain training sample, adopt the SVM implementation method in the document [7], calculate α in the sorter formula (26) _iAnd corresponding support vector x _iAnd b, promptly finished classifier design; In the time need judging check to new image registration results, at first calculate correlation II (being the phase place correlogram) by Fourier-Mellin conversion method for registering, then, adopt any one characteristic building method structural attitude data in the table 1, at last, characteristic is input to the sorter formula (26) that has designed, and so, the registration and the situation of registration have not been represented in two kinds of sorter different outputs respectively.

Need to prove that although the method that proposes among the present invention is at based on the registration Algorithm of Fourier-Mellin conversion, this image registration check thought based on study can be applied in other method for registering equally.

Describe above and be only used for realizing the present invention and embodiment, therefore, scope of the present invention should not described by this and limit.According to those skilled in the art's understanding,, all belong to claim restricted portion of the present invention in any modification or partial replacement that does not depart from the scope of the present invention.

Claims (9)

1. image registration self-verifying method based on machine learning, it is characterized in that: the image registration self-verifying step is as follows:

Adopt the phase place correlogram as sample data;

Utilize phase place correlogram structural attitude data;

The design category device is classified to characteristic, carries out the registration check according to classification results.

2. by the described image registration self-verifying method of claim 1 based on machine learning, it is characterized in that: described employing phase place correlogram is to adopt based on the correlation in the second step phase place related algorithm in the Fourier-Mellin changing image registration Algorithm as original sample data as sample data.

3. by the described image registration self-verifying method of claim 1 based on machine learning, it is characterized in that: described structural attitude data are to come the structural attitude data according to size and distribution based on preceding n maximum in the second step phase place related algorithm in Fourier-Mellin changing image registration Algorithm correlation.

4. by the described image registration self-verifying method of claim 3 based on machine learning, it is characterized in that: described structural attitude data, its first kind of characteristic make is: preceding n maximal value in second step of the extraction phase place related algorithm among all correlation II pressed descending order and formed n dimensional feature data, if it is a certain size neighborhood of center that these correlations are positioned at the maximum related value, then keep these correlations, if these these zones of correlation position deviation then are changed to 0 with corresponding correlation.

5. by the described image registration self-verifying method of claim 3 based on machine learning, it is characterized in that: described structural attitude data, its second kind of characteristic make is: the characteristic that will utilize first kind of characteristic make structure, carry out dimension-reduction treatment through principal component analysis, promptly constituted second kind of characteristic.

6. by the described image registration self-verifying method of claim 1, it is characterized in that based on machine learning: described classifier design, sorter model adopts support vector machine, and corresponding kernel function is a Gaussian function.

7. by characteristic make and the classifier design described in the claim 4 and 6, it is characterized in that: described characteristic, in final preceding n the maximum related value of selecting, n=6, corresponding proper vector number is 17.

8. by the image registration self-verifying method described in the claim 5 and 6, it is characterized in that based on machine learning: described characteristic, in final preceding n the maximum related value of selecting, n=2, corresponding proper vector number is 13.

9. by the described image registration self-verifying method of claim 6, it is characterized in that based on machine learning: in the gaussian kernel function that is adopted, parameter σ ²Span be 0.01～0.1.

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