CN101071505A - Multi likeness measure image registration method - Google Patents
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Abstract
The invention discloses a measure image registration method of multi-comparability, including the following steps: First, according to the current installed annealing temperature coefficient, in T transform space within the selected vertices simplex, and calculate the mutual information of the vertex values Variable polyhedron search using simplex method search the local minimum vertex points, recorded as the optimal solution alpha0 (2) obtaining the optimal solution alpha0 Neighborhood Sampling series, choose a different measure similar to Measure as evidence calculated similarity measure in alpha0 Neighborhood series of sampling the function of the sample value as evidence, according to evidence samples value of the evidence to measure the basic probability distribution, and basic probability distribution integration, in accordance with the outcome of the integration of the optimal solution alpha0 making judgments, access to decision-making results (3) According to updated results of the decision-making annealing coefficient into steps (1), (4) Hutchison optimal solution alpha0 for registration ultimate solute alpha *, output alpha *. This invention overcomes a single measure Registration extreme vulnerability to local problems; improve the registration accuracy and reliability.
Description
Technical Field
The invention belongs to the field of image processing, and particularly relates to a method for realizing image registration by using multiple similarity measures.
Background
Image registration techniques have been studied for over 20 years, and the process of registering images is actually one that seeks to align two or more images at the same spatial location. The application range of image registration relates to the fields of remote sensing image processing, computer vision, medical application, target identification, environment monitoring, weather forecast, geographic information processing and the like. The key data processing processes of image fusion, change detection and the like are all based on image registration. A core problem in image registration is finding the transformation parameters for image registration. Image registration is a difficult task due to the complex image data, rich gray levels and free and diverse transformation relations among the images to be registered. In this field, a large number of scholars have done a lot of meaningful work.
Barbara and Jan performed a more detailed summary comparison of registration documents prior to 2003 (Image registration methods: a surveiy, Image and Vision Computing, 2003, 21 (11): 977-. Image registration can be divided into grayscale-based image registration and feature-based image registration, divided in the way image data is used in the registration process. The former method has the advantage of high algorithm precision and reliability, and the main discussion content in this document belongs to this method. Defining a function to describe the similarity between the images to be registered based on the image registration method of gray scale, wherein the function is called similarity measure; when the similarity measure obtains a global optimal value, the transformation parameters required by the registration are corresponding to the global optimal value. The process of finding the global optimum of the similarity measure is called optimization. The similarity measures used in the current registration process are: mutual information (MutualInformation), Joint Entropy (Joint Entropy), normalized cross-Correlation coefficient (normalized cross Correlation), and the like. The optimization method mainly comprises the following steps: simulated Annealing (strained Annealing), Gaussian-Newton (Gauss-Newton), Gradient Descent (Gradient Description), and the like.
Due to the complexity of image data, the multi-dimensionality of transformation parameters, and the influence of specific implementation factors such as an interpolation method, the similarity measure function curve not only obtains extreme values at the registration position, but also has a plurality of extreme values at other positions, and the extreme values are called local extreme values. In addition, due to some limitations of the optimization algorithm, the optimization result may fall into a local extremum, which not only results in high optimization cost, but also results in failure to obtain correct registration parameters. This is a major disadvantage of this type of process. For example, the simulated annealing method can theoretically improve the overall convergence, but the optimization cost is high, and the time complexity is difficult to accept. Reducing the time complexity can bring about that the algorithm is difficult to obtain the global optimal solution, which causes the error of the registration result. A great deal of literature carries out a lot of comparative research work on the existing similarity measurement and optimization methods, and the accuracy of optimization is improved from the viewpoint of selecting the similarity measurement and optimization method with better performance. In the context of registration of a specific registration task, there is certainly a good or bad performance between the measures, but in general, there are many local extrema for substantially all measures, even the measure with the best performance, and the registration process still needs to pay attention to the problem that the optimization algorithm falls into the local extrema. In the context of different registration tasks, the situation will be more complex, a single measure may perform well in one type of image registration process, but not suitable for another type of image registration. For example, normalized cross-correlation coefficients are suitable for registration of images of the same spectral band, but not for registration of images of multiple spectral bands; mutual information measure is suitable for multi-spectral image registration, and good registration cannot be performed when the image provides insufficient information (the overlapping area of the images is small or the images themselves are small).
Disclosure of Invention
The invention provides a method for realizing image registration by fusing various similarity measures based on a D-S (Dempster-Shafer) evidence theory, which improves the reliability and the accuracy of a registration process, aims to overcome the problem that the registration process using single measure at present is easy to fall into a local extreme value, and judges whether the optimal solution of the registration process is a global optimal solution or not by utilizing the complementarity and the mutual evidence relationship of various similarity measures with excellent performance. The invention uses the Method for improving the registration process of SMSA (Simulated Annealing-Simplex Method), and greatly improves the registration accuracy and reliability.
The invention is completed according to the following steps:
step one setting initial temperature t0And an initial value of the annealing coefficient lambda, and enabling the cycle number h to be 1;
step two, calculating the temperature value t of the h-th cycleh＝λth-1，th-1The temperature value of the h-1 th cycle is obtained;
step three in the transformation space
Randomly selecting each vertex of the simplex
m is 1, 2, …, 5, and the reference image is calculated according to the formula (1)
And floating images
Mutual information value at each vertex of simplex
m＝1，2，...，5，
Wherein e and f denote reference images, respectivelyAnd floating images
Pixel gray value of p1(e, f) denotes a reference image
And floating imagesIs combined with the probability density distribution function, p2(e) Representing a reference image
P of the pixel gray value probability density distribution function3(f) Representing floating images
The probability density distribution function of the pixel gray value, rand () returns random variables which are uniformly distributed in 0-1;
step four, according to mutual information value
1, 2, 5, searching simplex vertexes by adopting a variable polyhedron searching method 1, 2, 5, and recording the local minimum point as an optimal solution
Procedure if th＜tmin，tminAt a predetermined termination temperature, proceed to step r; otherwise, entering the step sixthly;
procedure number tε≤th，tεIf the preset temperature threshold is reached, h is h +1, and the step II is executed; otherwise, go to step (c);
step (c) to optimize the solutionAnd (4) judging: obtaining an optimal solution
Selecting different similarity measures as evidence measures in the neighborhood sampling sequence, and calculating the optimal solution of the similarity measures
Function value under the sampling sequence of neighborhoodFor the evidence sample values, calculating the basic probability distribution of the evidence measure according to the evidence sample values, fusing the basic probability distribution, and calculating the upper-decision variable r according to the fusion result1And the variable under decision r2Reference to the decision variable r1And the variable under decision r2For the optimal solution
Judging to obtain a decision result V;
updating an annealing coefficient lambda according to a formula (2);
wherein λ iscIs a predetermined annealing constant,. epsilon1Is a predetermined decision upper threshold, epsilon2A predetermined decision lower threshold;
ninthly, changing to h +1, and turning to the step II;
step (r) records the optimal solution
For registering the final solution
Outputting the final solution
The step (c) is as follows:
(7.1) optimal solution
The neighborhood of (1) is sampled for n times to obtain the optimal solution
Sample array of neighborhood, note
i＝0，1，...，n；
(7.2) selecting k different similarity measures and calculating the sequence of the similarity measures in the sample sequence
i-0, 1.. said, function values under n, and k different similarity measures are taken as evidence measures
PjJ is 1, 2, …, k, and k different similarity measures are respectively arranged in the sampling sequence
The function value under n, i-0, 1, corresponding to the value assigned to the evidence samplei＝0，1，...，n，j＝1，2，...，k；
(7.3) calculation of P according to the following procedurejJ — 1, 2, …, k:
(7.3.1)j＝1；
(7.3.2) calculating evidence samples according to equation (3)
i 0, 1, n and
mean of absolute differences centered on
Wherein,
(7.3.3) calculating a weight coefficient omega according to the formula (4),
wherein, the value of REAL () takes 1 when the proposition is established, and takes 0 when the proposition is not established;
(7.3.4) identifying the space Θ as a power set of the set { t, f }, i.e. Θ { { t }, { f }, { t, f } }, where t denotes confidence and f denotes uncertainty, calculating the evidence measure P in turn according to equations (5) - (8)jFundamental probability distribution m under the discrimination space ΘPj(φ)、mPj({t})、mPj({f})、mPj({t，f})：
Where φ represents the null set, mPj({ t }) represents the optimal solution
Confidence probability value of mPj({ f }) represents the optimal solution
Is a non-trusted probability value of mPj({ t, f }) represents the optimal solutionThe suspected confidence probability value of (a); m is to bePj(φ)、mPj({t})、mPj({f})、mPj({ t, f }) collectively referred to as mPj()；
(7.3.5) if j < k, j ═ j +1, proceed to step (7.3.2); otherwise, entering the step (7.4);
(7.4) pairing m according to the following procedurePj() J ═ 1, 2, …, k for fusion:
(7.4.1) calculating a collision factor S according to equation (9),
(7.4.2) when S is less than or equal to Sε，SεEntering step (7.4.5) for a predetermined evidence conflict threshold, otherwise, entering step (7.4.3);
(7.4.3) calculation of m according to the Jousseme methodPj() Normalized confidence crd (m) for j ═ 1, 2, …, kPj())，j＝1，2，…，k；
(7.4.4) pairing m according to equation (10)Pj() J is 1, 2, …, k;
(7.4.5) for m according to equation (11)Pj() J is 1, 2, …, k, to obtain a fusion result m (),
(7.5) obtaining the optimal solution according to the following steps
Decision result V of (a):
(7.5.1) let ψ ═ t, calculate the belief function Bel (ψ) and the plausibility function Pl (ψ) of ψ in accordance with equation (12) and equation (13),
(7.5.2) calculating the decision variable r according to equation (14) and equation (15)1And the variable under decision r2，
(7.5.3) calculating the decision result V according to the formula (16),
wherein True represents the optimal solutionCredible as global optimal solution, False represents optimal solution
The solution is not credible as the global optimal solution, and Question represents the optimal solution
Is suspected to be credible.
The evidence conflict threshold SεThe value is 2.5-5, and the temperature threshold tεThe value is 0.05-0.1, and the annealing constant lambda iscA value of 0.9, an upper decision threshold epsilon1The value is 0.05-0.4, and a lower threshold value epsilon is decided2The value is 0.05-0.4, t0And tminIs between (20, 50).
The invention has the beneficial effects that: 1. mutual evidences and complementary relations of a plurality of similarity measures with excellent performance are fully utilized, and articles are not made on one similarity measure; 2. the accurate judgment result of the decision model is applied to guide the temperature updating process of the SMSA optimization algorithm, so that the reliability and the precision of image registration are improved to a greater extent.
Drawings
FIG. 1 shows a flow chart of a multi-measure decision model based on D-S evidence theory;
FIG. 2 shows an overall flow diagram of the present invention;
FIG. 3 shows a schematic diagram of a decision interval in a multi-measure decision model decision step based on D-S evidence theory;
fig. 4 shows an example of registration of the present invention, wherein,
fig. 4(a) is a visible band imaging diagram of the city paris district, fig. 4(b) is an infrared band imaging diagram of the city paris district, and fig. 4(c) is a registration result diagram;
fig. 5 shows a background fact illustration proposed by the present invention, wherein,
fig. 5(a) is a first experimental image, fig. 5(b) is a second experimental image, fig. 5(c) is a curve of each measurement function for translational mismatching of the first experimental image, and fig. 5(d) is a curve of each measurement function for rotational mismatching of the second experimental image;
fig. 6 shows a comparison of the results of 18-pair image registration of the present invention with a conventional SMSA-optimized registration algorithm in different scenes.
FIG. 7 is a graph comparing the results of 16 pairs of sequence image registration of the same scene with the conventional SMSA optimized registration method;
Detailed Description
The present invention will be described in detail with reference to the accompanying drawings and examples.
The invention provides a Method for realizing image registration by using multiple similarity measures based on a D-S evidence theory, which provides a multi-measure decision model based on the D-S evidence theory and applies the model in a registration process based on an SMSA (normalized imaging-Simplex Method) optimization algorithm, thereby improving the reliability and the accuracy of the registration process.
As shown in fig. 2, the present invention is accomplished as follows.
1) Setting an initial temperature t0The initial value of the annealing coefficient λ was set to 1. Make the cycle number h equal to1。
2) Calculating the temperature value t of the h-th cycleh＝λth-1，th-1The temperature value of the h-1 th cycle is obtained;
3) in a transformation space
The top points of the simplex are arranged in the table.
In the present invention, the transformation space is <math> <mrow> <mover> <mi>T</mi> <mo>→</mo> </mover> <mo>=</mo> <mrow> <mo>(</mo> <mi>θ</mi> <mo>,</mo> <msub> <mi>t</mi> <mi>x</mi> </msub> <mo>,</mo> <msub> <mi>t</mi> <mi>y</mi> </msub> <mo>,</mo> <mi>sl</mi> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math> Where θ represents a reference image
And floating images
Relative angle of rotation between, θ e [ -50, 50]；tx，tyRespectively representing the number of horizontal and vertical relative translation pixels, tx∈[-50，50]，ty∈[-50，50](ii) a s represents the relative scaling factor, sl ∈ [0.8, 1.2 ∈]And is dimensionless.
In a transformation space
Selecting vertices of simplex within
1.. 5. each vertex is a four-dimensional vector <math> <mrow> <mover> <mi>T</mi> <mo>→</mo> </mover> <mo>=</mo> <mrow> <mo>(</mo> <mi>θ</mi> <mo>,</mo> <msub> <mi>t</mi> <mi>x</mi> </msub> <mo>,</mo> <msub> <mi>t</mi> <mi>y</mi> </msub> <mo>,</mo> <mi>sl</mi> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math> The initial value of each component of the vector is in the transformation space
And randomly selecting the selected range.
Computing an image according to equation (1)And
at each vertex of the simplex
mutual information value under the condition of 1, 2, …, 5
A value of 1, 2, 5,
wherein e and f denote reference images, respectively
And floating images
Pixel gray value of p1(e, f) denotes a reference image
And floating images
Is combined with the probability density distribution function, p2(e) Showing a reference chartImage
P of the pixel gray value probability density distribution function3(f) Representing floating images
The probability density distribution function of the pixel gray value, rand () returns random variables which are uniformly distributed in 0-1;
4) according to1, 2, 5, searching the simplex according to a variable polyhedron searching method in the simplex theory
1, 2, 5, and recording the local minimum point as an optimal solution
5) If th＜tminEntering step 10); otherwise, go to step 6). t is tminThe predetermined termination temperature may be defined as the initial temperature t in the present invention 01/20-1/50.
6) If tε≤thIf h is h +1, the step 2) is carried out; otherwise, go to step 7). t is tεThe value of the temperature threshold is 0.01-0.1, such as 0.05.
7) Using a multi-measure decision model based on a D-S evidence theory to solve the optimal solution according to the following steps
The decision is made and the flow chart of the model is shown in figure 1.
7.1) pairs
N (general value 12 ~ 36)Sub-sampling, the neighborhood sampling range is limited to-1- +1 degree, -1- +1 pixel, and the scaling factor is 0.98-1.02. Obtained
Sample number of neighborhood is listed as
i＝0，1，...，n。
7.2) to solve the optimum
Making a decision, selecting k different similarity measures, and calculating the similarity measures in the evidence sample
i-0, 1.. said, function values under n, and k distinct similarity measures are taken as evidence measures PjJ 1, 2 … k, and ranking each similarity measure in a sample sequence
The function value under n, i-0, 1, corresponding to the value assigned to the evidence sample
i is 0, 1., n, j is 1,. k. In the implementation of the method, the value of k is 2-5.
In the invention, three similarity measures with relatively excellent performance are selected: correlation ratio COR (correlation ratio), cluster value CRA (Cluster corrected Algorithm) and normalized Cross-correlation coefficient NCC (normalized Cross correlation), so that k is 3, where P is1Representing the evidence measure COR, P2Representing evidence measures CRA, P3The evidence measure NCC is represented.
Evidence measure COR, evidence measure CRA, evidence measure NCC
The calculation formula of the function value is shown in formulas (2) to (4).
Where Cov () represents the covariance of the variable, Var () represents the variance of the variable, and E () represents the expectation of the variable. 
L＝M×M，
Represents the joint histogram distribution of the two graphs,
respectively representing the histogram distribution of the reference image and the floating image, and M is the number of gray levels of the image.
7.3) computing the evidence measure P according to the following stepsjJ-1, 2, …, k, base Probability assignment bpa (basic Proavailability assignment).
7.3.1)j＝1；
7.3.2) computational evidence samples
i 0, 1, n and
mean of absolute differences centered on 
Presentation pair
The value after the normalization is carried out,
7.3.3) calculating the weight coefficient ω of the probability distribution function as follows: the value of REAL () takes 1 when the proposition is established and 0 when it is not.
7.3.4) discriminating the space Θ to be a power set of the set { t, f }, i.e. Θ { { t }, { f }, { t, f } }, where t denotes trustworthiness and f denotes untrustworthiness, calculating an evidence measure P according to equation (7)jFundamental probability distribution m under the discrimination space ΘPj(φ)、mPj({t})、mPj({f})、mPj({t，f})：
Where φ represents the null set, mPj({ t }) representsConfidence probability value of mPj({ f }) represents
Untrusted probability value, mPj({ t, f }) represents
A suspected confidence probability value; m is to bePj(φ)、mPj({t})、mPj({f})、mPj({ t, f }) collectively referred to as mPj()。
7.3.5) if j < k, j equals j +1, and proceed to step (7.3.2); otherwise, go to step (7.4).
7.4) pairing m according to the following procedurePj() J is 1, 2, …, k.
7.4.1) calculating the collision factor S according to equation (8).
7.4.2) when S is less than or equal to SεWhen so, go to step 7.4.5); otherwise, go to step 7.4.3); sεFor a predetermined evidence conflict threshold, in the present invention, a conflict threshold SεThe value 3 is optimal.
7.4.3) according to the method of Jousselme (Jousselme) (see Jousselme A.L., Dominic G., Bosse E.A new distance between two books of existence [ J.]Information effect, 2001, 2: 91-101.), calculate the basic probability distribution mPj() Normalized confidence crd (m) for j-1, 2 … kPj(ψ))，mPj()，j＝1，2…k；
7.4.4) assigning m to the respective elementary probabilities according to equation (9)Pj() J is 1, 2 … k,
7.4.5) according to equation (10) for mPj() And j is 1, 2 … k.
7.5) obtaining the optimal solution according to the following steps
And (4) determining a result.
7.5.1) hereinafter, let ψ ═ t }. After obtaining the fused BPA, the belief function Bel (ψ) and the plausibility function Pl (ψ) of ψ are calculated in accordance with the following equation.
7.5.2) calculating the decision variable r according to the following equation1And the variable under decision r2。
7.5.3) the final decision result is represented by V, and the optimal solution is represented by True respectively
Credible as global optimal solution, False represents optimal solution
The solution is not credible as the global optimal solution, and Question represents the optimal solutionIs suspected to be credible. Epsilon1The value of the upper decision threshold is generally 0.05-0.4; epsilon2For deciding the lower threshold, the value is generally 0.05-0.4. The decision result V is calculated by equation (15).
Fig. 3 is a diagram illustrating a decision interval. Bel (psi) and Pl (psi) are expressed in a two-dimensional space according to the definition and value range of Bel (psi), and a shaded area in the graph is an area where a decision conclusion is located, and the area is divided into three sub-areas. When r is1Less than circle o1Radius of (e)1When the decision result is set to True, namely the optimal solutionCredible as global optimal solution; when r is2Less than circle o2Radius of (e)2Then, the decision result is False, i.e. the optimal solutionCan not be regarded as the global optimal solution; if the two judgment conditions are not satisfied, setting the decision result as Question to represent the optimal solution
Is determined to be knottedIf the fruits are suspected to be credible.
8) The annealing coefficient lambda is calculated.
Based on r1And r2And the decision result V, lambda is calculated according to equation (16).
As can be seen from equation (16), ε is determined when the decision result is True2＞r2，1+ε1/r1Is > 2, so that this time <math> <mrow> <mi>λ</mi> <mo>></mo> <msubsup> <mi>λ</mi> <mi>c</mi> <mn>2</mn> </msubsup> <mo>,</mo> </mrow> </math> The accelerated temperature reduction process is realized; when making a decisionThe result is False due to ε2＞r2，1+ε2/r2Is > 2, so that this time <math> <mrow> <mi>λ</mi> <mo>></mo> <msubsup> <mi>λ</mi> <mi>c</mi> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msubsup> <mo>></mo> <mn>1</mn> <mo>,</mo> </mrow> </math> The temperature rise process is realized. After the steps are carried out, the SMSA optimization method is scientifically and effectively improved based on a D-S evidence theory multi-measure decision model, and the algorithm convergence speed is accelerated when the optimal solution is credible; when the algorithm is not credible, the algorithm is prevented from falling into a local extreme value.
9) h + 1, go to step 2).
10) Recording the optimal solution
For registering the final solutionOutputting a final solution of registration
FIG. 1 shows a flow chart of a multi-measure decision model based on D-S evidence theory. The decision model has the function of judging the optimal solution to obtain the confidence coefficient and the judgment result of the optimal solution which are global extreme values (namely correct registration parameters). In the model, firstly, the optimal solution is sampled, then the value of each evidence sample is calculated, and then the basic probability distribution is carried out according to the value of the evidence sample to obtain the confidence coefficient of each evidence measure to the optimal solution. And deciding the optimal solution after acquiring the total confidence degree through the fusion of the basic probability distribution of the plurality of evidence measures. The decision result is divided into credible True, incredible False and suspected credible Question. Figure 2 shows a flow chart of the improved method of the present invention.
Figure 2 shows a flow chart of the improved method of the present invention. The features and advantages of the present invention, as seen in connection with fig. 1, are: the mutual evidence and complementary relation of a plurality of similarity measures with excellent performance are fully utilized, and an article is not made on one similarity measure; and secondly, a method for introducing a decision process in the registration process is provided, and a decision model used by combining multiple similarity measures based on a D-S evidence theory is established. Thirdly, an accurate decision result of the decision model is applied to guide the temperature updating process of the SMSA optimization algorithm, and the processes of accelerating temperature reduction and temperature rise are introduced on the basis of only the temperature reduction process originally, so that the convergence speed of the algorithm is increased, and the robustness of the algorithm is improved.
Fig. 4 shows an example of registration according to the present invention. Fig. 4(a) and 4(b) are original to-be-registered image pairs. Fig. 4(c) shows a graph of the mean superposition result after registration, and it can be seen that there are shape changes between images in three components of relative rotation, horizontal relative translation and vertical relative translation.
Fig. 5 gives an illustration of the background fact proposed by the present invention, namely complementarity and mutual corroboration relationship of different similarity measures at different registration occasions: the local extrema of the measure are not necessarily the same, but are obtained at the correct registration. This is because different measures have not exactly the same mechanism in describing image data similarity, but the image data objects they describe are identical.
Fig. 6 shows the comparison of the results of the registration of 16 pairs of sequence images of the scene with the original SMSA optimization method. The 16 images were registered using the present invention and conventional methods and the registration result was subtracted from the actual result to obtain an error value for both methods. The four component errors obtained by the present invention and the conventional method are respectively plotted in the four subgraphs in fig. 6, where symbol "represents the error corresponding to the original method and symbol" represents the error corresponding to the present invention. The horizontal line with zero ordinate represents the "flagpole line" with zero error. FIG. 6(a) is a schematic diagram of a rotational component error, where Δ θ represents the rotational error component; FIG. 6(b) is a schematic diagram of the horizontal translation error, Δ X representing the horizontal translation error component; FIG. 6(c) is a schematic diagram of the vertical translation error, Δ Y representing the vertical translation error component; fig. 6(d) is a diagram of the scaling factor error, and Δ S represents the scaling factor error variable. The further the error sign is from the target bar line, the larger the registration error of the corresponding map pair at that point.
Fig. 6 shows the results of the 18-pair image registration of the present invention with the original SMSA optimization method in different scenes. From the results given in the figure it can be seen that: in the registration task of different scenes, under most conditions, the improved method can effectively improve the robustness and the precision of registration; secondly, the method can effectively help the optimization algorithm to jump out of local extremum under most conditions. And thirdly, in 18 pairs of images, the registration result error is about 1/3, which shows that the invention and the original optimization process converge according to the same path in the partial registration process.
The four component errors obtained by the present invention and the conventional method are respectively plotted in the four subgraphs in fig. 7, where symbol "represents the error corresponding to the original method and symbol" represents the error corresponding to the method of the present invention. The horizontal line with zero ordinate represents the "flagpole line" with zero error. FIG. 7(a) is a schematic diagram of a rotational component error, where Δ θ represents the rotational error component; FIG. 7(b) is a schematic diagram of the horizontal translation error, Δ X representing the horizontal translation error component; FIG. 7(c) is a schematic diagram of the vertical translation error, Δ Y representing the vertical translation error component; fig. 7(d) is a diagram of the scaling factor error, and Δ S represents the scaling factor error variable. It can be seen from the "vertical translation error" sub-graph of fig. 7 that the error of the registration result using the original method is about-10 to +3 degrees, while the error of the registration result using the method of the present invention is about-1 to +1 degrees, which shows that the registration using the method of the present invention can achieve higher precision than the original method, and the precision improvement range is larger. Statistically, the error values all make irregular oscillations around the marker post line, and carefully observing the oscillation amplitude of the symbol "+" sequence in the graph is smaller and more regular, which shows that the invention has stronger stability.
Claims (4)
1. The invention discloses a multi-similarity measurement image registration method, which is characterized by comprising the following steps of:
step one setting initial temperature t0And an initial value of the annealing coefficient lambda, and enabling the cycle number h to be 1;
step two, calculating the temperature value t of the h-th cycleh＝λth-1，th-1. The temperature value of the h-1 th cycle is obtained;
step three in the transformation space
Randomly selecting each vertex of the simplex
M is 1, 2, …, 5, and the reference image is calculated according to equation (1)
And floating images
Mutual information value at each vertex of simplex
，m＝1，2，...，5，
Wherein e and f are respectively shown inIndicating reference image
And floating images
Pixel gray value of p1(e, f) denotes a reference image
And floating images
Is combined with the probability density distribution function, p2(e) Representing a reference image
P of the pixel gray value probability density distribution function3(f) Representing floating images
The probability density distribution function of the pixel gray value, rand () returns random variables which are uniformly distributed in 0-1;
step four, according to mutual information value
1, 2, 5, searching simplex vertexes by adopting a variable polyhedron searching method
Local minimum point of 1, 2, 5, which is recorded as the optimal solution；
Step five if qi th＜tmin，tminAt a predetermined termination temperature, proceed to step r; otherwise, entering the step sixthly;
procedure number tε≤th，tεIf the preset temperature threshold is reached, h is h +1, and the step II is executed; otherwise, go to step (c);
step (c) toOptimal solution
And (4) judging: obtaining an optimal solution
Selecting different similarity measures as evidence measures in the neighborhood sampling sequence, and calculating the optimal solution of the similarity measures
Taking a function value under the sampling sequence of the neighborhood as an evidence sample value, calculating basic probability distribution of evidence measure according to the evidence sample value, fusing the basic probability distribution, and calculating a variable r on decision according to a fusion result1And the variable under decision r2Reference to the decision variable r1And the variable under decision r2For the optimal solution
Judging to obtain a decision result V;
updating an annealing coefficient lambda according to a formula (2);
wherein λ iscIs a predetermined annealing constant,. epsilon1Is a predetermined decision upper threshold, epsilon2A predetermined decision lower threshold;
ninthly, changing to h +1, and turning to the step II;
step (r) records the optimal solution
For registering the final solution
Outputting the final solution
。
2. The method according to claim 1, wherein the step (c) is as follows:
(7.1) optimal solution
The neighborhood of (1) is sampled for n times to obtain the optimal solution
Sample array of neighborhood, note
，i＝0，1，...，n；
(7.2) selecting k different similarity measures and calculating the sequence of the similarity measures in the sample sequence
I-0, 1.. said, function values under n, the k distinct similarity measures are taken as evidence measures PjJ is 1, 2, …, k, and k different similarity measures are respectively arranged in the sampling sequence 
The function value under n, i-0, 1
i＝0，1，...，n，j＝1，2，...，k；
(7.3) calculation of P according to the following procedurejJ — 1, 2, …, k:
(7.3.1)j＝1；
(7.3.2) calculating evidence samples according to equation (3)
I is 0, 1, n and
mean of absolute differences centered on
Wherein, <math> <mrow> <msub> <mi>Q</mi> <msub> <mi>P</mi> <mi>j</mi> </msub> </msub> <msup> <mrow> <mo>(</mo> <msub> <mover> <mi>α</mi> <mo>-</mo> </mover> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>′</mo> </msup> <mo>=</mo> <mfrac> <mrow> <msub> <mi>Q</mi> <msub> <mi>P</mi> <mi>i</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mover> <mi>α</mi> <mo>-</mo> </mover> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <munder> <mi>min</mi> <mi>i</mi> </munder> <mrow> <mo>(</mo> <msub> <mi>Q</mi> <msub> <mi>P</mi> <mi>j</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mover> <mi>α</mi> <mo>‾</mo> </mover> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <munder> <mi>max</mi> <mi>i</mi> </munder> <mrow> <mo>(</mo> <msub> <mi>Q</mi> <msub> <mi>P</mi> <mi>j</mi> </msub> </msub> <mo>(</mo> <msub> <mover> <mi>α</mi> <mo>‾</mo> </mover> <mi>i</mi> </msub> <mo>)</mo> <mo>-</mo> <munder> <mi>min</mi> <mi>i</mi> </munder> <mrow> <mo>(</mo> <msub> <mi>Q</mi> <msub> <mi>P</mi> <mi>j</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mover> <mi>α</mi> <mo>‾</mo> </mover> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>)</mo> </mrow> </mrow> </mrow> </mfrac> <mo>;</mo> </mrow> </math>
(7.3.3) calculating a weight coefficient omega according to the formula (4),
wherein, the value of REAL () takes 1 when the proposition is established, and takes 0 when the proposition is not established;
(7.3.4) identifying the space Θ as a power set of the set { t, f }, i.e. Θ { { t }, { f }, { t, f } }, where t denotes confidence and f denotes uncertainty, calculating the evidence measure P in turn according to equations (5) - (8)jFundamental probability distribution m under the discrimination space ΘPj(φ)、mPj({t})、mPj({f})、mPj({t，f})：
Where φ represents the null set, mPj({ t }) represents the optimal solutionConfidence probability value of mPj({ f }) represents the optimal solution 
Is a non-trusted probability value of mPj({ t, f }) represents the optimal solution
The suspected confidence probability value of (a); m is to bePj(φ)、mPj({t})、mPj({f})、mPj({ t, f }) collectively referred to as mPj()；
(7.3.5) if j < k, j ═ j +1, proceed to step (7.3.2); otherwise, entering the step (7.4);
(7.4) pairing m according to the following procedurePj() J ═ 1, 2, …, k for fusion:
(7.4.1) calculating a collision factor S according to equation (9),
(7.4.2) when S is less than or equal to Sε，SεEntering step (7.4.5) for a predetermined evidence conflict threshold, otherwise, entering step (7.4.3);
(7.4.3) calculation of m according to the Jousseme methodPj() Normalized confidence crd (m) for j ═ 1, 2, …, kPj())，j＝1，2，…，k；
(7.4.4) pairing m according to equation (10)Pj() J is 1, 2, …, k;
(7.4.5) for m according to equation (11)Pj() J is 1, 2, …, k, to obtain a fusion result m (),
(7.5) obtaining the optimal solution according to the following steps
Decision result V of (a):
(7.5.1) let ψ ═ t, calculate the belief function Bel (ψ) and the plausibility function Pl (ψ) of ψ in accordance with equation (12) and equation (13),
(7.5.2) calculating the decision variable r according to equation (14) and equation (15)1And the variable under decision r2，
(7.5.3) calculating the decision result V according to the formula (16),
wherein True represents the optimal solution
Credible as global optimal solution, False represents optimal solution
The solution is not credible as the global optimal solution, and Question represents the optimal solution
Is suspected to be credible.
3. The method of claim 2, wherein the evidence conflict threshold S is set asεThe value is 2.5-5.
4. A method of multi-similarity measure image registration according to claim 1, 2 or 3, wherein the temperature threshold T isεThe value is 0.05-0.1, and the annealing constant lambda iscA value of 0.9, an upper decision threshold epsilon1The value is 0.05-0.4, and a lower threshold value epsilon is decided2The value is 0.05-0.4, t0And tminIn the ratio of (20, 5)0) In the meantime.
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