CN112465881A - Improved robust point registration method and system - Google Patents

Improved robust point registration method and system Download PDF

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CN112465881A
CN112465881A CN202011254115.5A CN202011254115A CN112465881A CN 112465881 A CN112465881 A CN 112465881A CN 202011254115 A CN202011254115 A CN 202011254115A CN 112465881 A CN112465881 A CN 112465881A
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point
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registration
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point sets
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冯全
桑强
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Changzhou Code Library Data Technology Co ltd
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/30—Determination of transform parameters for the alignment of images, i.e. image registration
    • G06T7/33—Determination of transform parameters for the alignment of images, i.e. image registration using feature-based methods
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/24—Classification techniques
    • G06F18/241—Classification techniques relating to the classification model, e.g. parametric or non-parametric approaches
    • G06F18/2415—Classification techniques relating to the classification model, e.g. parametric or non-parametric approaches based on parametric or probabilistic models, e.g. based on likelihood ratio or false acceptance rate versus a false rejection rate
    • G06F18/24155—Bayesian classification
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/30—Determination of transform parameters for the alignment of images, i.e. image registration
    • G06T7/35—Determination of transform parameters for the alignment of images, i.e. image registration using statistical methods
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/10—Image acquisition modality
    • G06T2207/10004—Still image; Photographic image
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2210/00—Indexing scheme for image generation or computer graphics
    • G06T2210/44—Morphing

Abstract

The invention discloses an improved robust point registration method and system in the technical field of image registration, which can keep the corresponding consistency between local point sets while registering an integral point set, improve the accuracy of point set registration and improve the robustness of an algorithm when abnormal points exist. The method comprises the following steps: a. giving two point sets, initializing registration model parameters and assigning initial values; b. solving prior probability of matching consistency between local point pairs in the two point sets based on a point local structure retention theory; c. b, further solving the posterior probability based on the mixed probability model and the prior probability obtained in the step b; d. c, further solving deformation parameters of the registration model based on the posterior probability obtained in the step c; e. rearranging the points in the two point sets based on the deformation parameters obtained in the step d; f. and e, repeating the steps b to e until the registration model is converged, and outputting the corresponding relation between the two point sets.

Description

Improved robust point registration method and system
Technical Field
The invention belongs to the technical field of image registration, and particularly relates to an improved robust point registration method and system.
Background
The image registration technology is a very important research topic in the fields of computer vision and image processing. And many research results have been widely applied to a plurality of important fields such as pattern recognition, medical image processing and digital media. The technique can be roughly classified into a gray registration algorithm and a point registration algorithm according to a registration object. The point registration algorithm can effectively reduce the complexity of the algorithm, has the advantage of real-time performance, can be applied in actual industrial level, and is a hotspot of research in the industry at present. In recent years, many technical documents have been proposed, and the technical lines are generally divided into the following two categories: one is a graph matching based approach; another class is probabilistic model-based classification methods. The first category of methods translates the registration problem of points into a matching problem of the graph. When the point neighbor relation is calculated, the matching probability among all neighborhood points is counted, and a large amount of redundant information is contained, so that the accuracy of registration is reduced. The second method uses a simplified registration probability model to influence the accuracy and robustness of the algorithm.
Disclosure of Invention
In order to solve the defects in the prior art, the invention provides an improved robust point registration method and system, which maintain the correspondence consistency between local point sets while registering the whole point set, improve the accuracy of point set registration and improve the robustness of an algorithm in the presence of abnormal points.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows: an improved robust point registration method, comprising: a. giving two point sets, initializing registration model parameters and assigning initial values; b. solving prior probability of matching consistency between local point pairs in the two point sets based on a point local structure retention theory; c. b, further solving the posterior probability based on the mixed probability model and the prior probability obtained in the step b; d. c, further solving deformation parameters of the registration model based on the posterior probability obtained in the step c; e. rearranging the points in the two point sets based on the deformation parameters obtained in the step d; f. and e, repeating the steps b to e until the registration model is converged, and outputting the corresponding relation between the two point sets.
Further, the joint probability density function of the mixed probability model is:
Figure BDA0002772556500000021
wherein the content of the first and second substances,
Figure BDA0002772556500000022
is a modelParameter, parameter
Figure BDA0002772556500000023
Indicating the probability that the ith point belongs to the jth gaussian component.
Further, in the step b, the prior probability of matching consistency between local point pairs in the two point sets is solved through the following formula:
Figure BDA0002772556500000024
wherein the content of the first and second substances,
Figure BDA0002772556500000025
to represent
Figure BDA0002772556500000026
Is composed of
Figure BDA0002772556500000027
The neighborhood of the point(s) of the neighborhood,
Figure BDA0002772556500000028
Figure BDA0002772556500000029
the number of neighborhood points.
Further, in the step c, the posterior probability is solved by the following formula:
Figure BDA00027725565000000210
where U is a uniform distribution.
Further, in the step d, the model deformation parameters of the mixed probability model are solved by the following formula:
Figure BDA00027725565000000211
wherein G is highThe gaussian function, W is the deformation parameter,
Figure BDA00027725565000000212
is the variance of the gaussian component of the model.
An improved robust point registration system, comprising: the first module is used for giving two point sets, initializing registration model parameters and assigning initial values; the second module is used for solving the prior probability of matching consistency between local point pairs in the two point sets based on a point local structure keeping theory; a third module, configured to further solve the posterior probability based on the mixed probability model and the prior probability obtained in step b; the fourth module is used for further solving the deformation parameters of the registration model based on the posterior probability acquired by the third module; a fifth module for rearranging the points in the two point sets based on the deformation parameters acquired by the fourth module; and the sixth module is used for outputting the corresponding relation between the two point sets after the registration model is converged.
A computer-readable storage medium comprising a stored computer program, wherein the computer program, when executed by a processor, controls an apparatus in which the storage medium is located to perform the aforementioned improved robust point registration method.
Compared with the prior art, the invention has the following beneficial effects: according to the consistency of the registration relationship between two local point sets, calculating the prior probability of matching between the local point pairs; then calculating parameters of a Gaussian mixture model by a maximum posterior probability estimation method, and finishing registration among point sets; when the integral point set is registered, the corresponding consistency among the local point sets is kept, the accuracy of the point set registration is improved, and the robustness of the algorithm when abnormal points exist is improved.
Detailed Description
The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
The first embodiment is as follows: an improved robust point registration method, comprising: a. giving two point sets, initializing registration model parameters and assigning initial values; b. solving prior probability of matching consistency between local point pairs in the two point sets based on a point local structure retention theory; c. b, further solving the posterior probability based on the mixed probability model and the prior probability obtained in the step b; d. c, further solving deformation parameters of the registration model based on the posterior probability obtained in the step c; e. rearranging the points in the two point sets based on the deformation parameters obtained in the step d; f. and e, repeating the steps b to e until the registration model is converged, and outputting the corresponding relation between the two point sets.
1) Two point sets are given, registration model parameters are initialized and initial values are assigned
Given two sets of points
Figure BDA0002772556500000041
And
Figure BDA0002772556500000042
here, the
Figure BDA0002772556500000043
And
Figure BDA0002772556500000044
is a 2-dimensional vector, i.e. the coordinates of a point. And can be extended to higher dimensional vectors. N and L are the number of points in the two point sets.
Point matching is to find a matching function f:
Figure BDA0002772556500000045
a mapping relationship is established between the two sets of points.
Figure BDA0002772556500000046
θtRepresenting deformation parameters of the registration model. And finally, solving the one-to-one correspondence between the two point sets under the registration model.
When the number of points in two point sets is not equal or there are abnormal points in the point sets, a one-to-one correspondence relationship cannot be formed. At this time, a pseudo point nie is added to each of the two point sets to represent the unmatched points or abnormal points, and the unmatched points or abnormal points correspond to the pseudo point nie.
When the two point sets are deformed non-rigidly, the change in distance between the points may be arbitrary. However, a relatively fixed relationship is maintained between the point and its neighborhood. Namely, under non-rigid deformation, the local neighborhood relationship or topological structure of the point still keeps stability.
2) Solving prior probability of matching consistency between local point pairs in two point sets based on point local structure retention theory
In the point registration algorithm based on the mixed probability model, one point set is used as the centroid of the mixed model component, and the other point set is used as sample data. Namely, the sample and the component of the mixed model to which the sample belongs are found, and the corresponding relation is established between the sample and the component of the mixed model. Defining its joint probability density function as:
Figure BDA0002772556500000047
wherein the content of the first and second substances,
Figure BDA0002772556500000048
is the weight of the mixed model and is,
Figure BDA0002772556500000049
is a model parameter, function f in the case of a Gaussian mixture modelj() As a gaussian function:
Figure BDA0002772556500000051
wherein the content of the first and second substances,
Figure BDA0002772556500000052
is a Gaussian mean value and is the centroid coordinate of a Gaussian component in a Gaussian registration model, namely the point set Y to be registered
Figure BDA0002772556500000053
The point registration problem is used as a clustering problem of a point set;
Figure BDA0002772556500000054
is the variance of the gaussian function; wherein, the Gaussian model parameters
Figure BDA0002772556500000055
May be found by an expectation maximization algorithm. In order to solve the corresponding relation between point sets, a vector is introduced
Figure BDA0002772556500000056
Indicating points
Figure BDA0002772556500000057
Mapping to
Figure BDA0002772556500000058
The probability of (d); if it is not good
Figure BDA0002772556500000059
Is a point
Figure BDA00027725565000000510
When the point of interest is a corresponding point of (c),
Figure BDA00027725565000000511
if not, the value is 0; given probability density function
Figure BDA00027725565000000512
Known from the Bayes rule:
Figure BDA00027725565000000513
when parameter
Figure BDA00027725565000000514
When known, points can be obtained by solving the following formula through Bayesian classification rules
Figure BDA00027725565000000515
The corresponding relation of (1):
Figure BDA00027725565000000516
when the point sets have no abnormal points and the number of the point sets is consistent, the model can be solved through an expectation-maximization algorithm. Otherwise, outliers can be treated as several false gaussian components, resulting in the expectation-maximization algorithm not converging properly. If a uniform gaussian distribution composition is used. I.e. the parameters
Figure BDA00027725565000000521
Is a constant. The hybrid probabilistic model is simplified. So that the posterior probability in expectation maximization is:
Figure BDA00027725565000000517
is simplified as follows:
Figure BDA00027725565000000518
to solve the above problem, the embodiment defines a new model parameter in the mixed probability model
Figure BDA00027725565000000519
Indicating the probability that the ith point belongs to the jth gaussian component. Equation (1) can be redefined as:
Figure BDA00027725565000000520
the above formula defines a more general problem and therefore
Figure BDA0002772556500000061
Is expressed by the formula (7) To a specific example thereof. The following defines the complete data as
Figure BDA0002772556500000062
In which the variables are implicit
Figure BDA0002772556500000063
Vectors are randomly indicated as L × 1. Each component from the set
Figure BDA0002772556500000064
Taking the value in the step (1). Here, the
Figure BDA0002772556500000065
Is an lx 1 vector, where one component takes the value of 1 and the remaining components are zero. Then
Figure BDA0002772556500000066
Is a discrete random variable having a value of
Figure BDA0002772556500000067
Equation (7) becomes:
Figure BDA0002772556500000068
given parameters
Figure BDA0002772556500000069
The mixed model can be obtained by maximizing a posterior probability estimation:
Figure BDA00027725565000000610
under the probabilistic model framework, the local corresponding consistency of the point set is introduced as prior probability. Even if the point set is subjected to large-scale inelastic deformation, the local relationship of the point set still maintains strong stability in terms of local small range of the point set. That is, the local point set neighbor structure cannot be changed at will because it receives a certain physical constraint.
Figure BDA00027725565000000611
Wherein N ismIs a neighborhood of point m, while the neighborhood relationship is symmetric, i.e., if i ∈ NmThen m ∈ Ni. f (m), f (i) representing a neighborhood system of corresponding points in the two point sets; d (f (m), f (i)) measures the distance between the two neighborhood systems; a distance of 1 indicates that the two neighborhood systems are matched, namely the better the neighborhood relationship is kept; otherwise it is 0. The algorithm uses the Euclidean distance between points to describe the neighborhood relationship and the difference between the neighborhoods. In this case, equation (10) is:
Figure BDA00027725565000000612
wherein the content of the first and second substances,
Figure BDA0002772556500000071
as is apparent from the above equation, when the mapping function f realizes an accurate one-to-one correspondence, then the minimum value obtained by equation (11) is zero. In order to obtain the inter-neighborhood matching consistency probability, the following neighborhood relationships are redefined in the embodiment:
Figure BDA0002772556500000072
that is to say point
Figure BDA0002772556500000073
Is a point
Figure BDA0002772556500000074
At one point in the neighborhood, the function d () takes the value 1, otherwise it takes the value 0. Points are defined herein
Figure BDA0002772556500000075
Is a departure point
Figure BDA0002772556500000076
The nearest N points, called points
Figure BDA0002772556500000077
Where the value of N takes 5. According to the local correspondence consistency principle, the prior probability of matching between point pairs is provided in the embodiment, and the prior probability of matching consistency between local point pairs in two point sets is solved through the following formula:
Figure BDA0002772556500000078
wherein the content of the first and second substances,
Figure BDA0002772556500000079
is shown to
Figure BDA00027725565000000710
Is that
Figure BDA00027725565000000711
Neighborhood points of, statistics
Figure BDA00027725565000000712
Is that
Figure BDA00027725565000000713
The number of neighborhood points.
Figure BDA00027725565000000714
Is that
Figure BDA00027725565000000715
Can be determined by the posterior probability formula (11) of the mixed model;
Figure BDA00027725565000000716
representing the number of all neighborhood points. From the above formula, the point if
Figure BDA00027725565000000717
Is a point in another set of points
Figure BDA00027725565000000718
A neighborhood of points, then
Figure BDA00027725565000000719
Matching and points
Figure BDA00027725565000000720
The probability of (c) is the maximum, and the value is 1. Otherwise, the value is between 0 and 1.
3) Further solving the posterior probability based on the mixed probability model and the prior probability obtained in the step 2)
Solving the posterior probability of the mixed probability model by the following formula:
Figure BDA00027725565000000721
where U is a uniform distribution used to fit outliers in the data. Finally, the position estimation of the point of CPD (Myronenko,2010) is adopted,
Figure BDA00027725565000000722
y is the initial coordinate, G is a Gaussian basis function for the regularization constraint, and W is the deformation parameter.
4) Further solving deformation parameters of the registration model based on the posterior probability obtained in the step 3)
Redefined as a maximum a posteriori equation (6) based on equation (14):
Figure BDA0002772556500000081
obtaining model deformation parameters of the hybrid probability model by taking the derivative of equation (15), wherein G is a Gaussian basis function, W is a deformation parameter,
Figure BDA0002772556500000082
is the variance of the gaussian component of the model.
5) Rearranging the points in the two point sets based on the deformation parameters obtained in the step 4)
6) And repeating the steps until the registration model is converged, and outputting the corresponding relation between the two point sets.
In the non-rigid point registration process, the more stable the local relationship of the points, the higher the accuracy and robustness of the algorithm. Therefore, in the global point registration technology based on the hybrid model, the key point is to maintain the corresponding consistency relationship between the local point pairs in the registration process. Meanwhile, the point displacement change of the non-rigid deformation can be any, and the local corresponding relation is relatively stable, so that the shape characteristic of the point set is ensured by keeping the local corresponding relation of the point set stable. And finally, the overall corresponding relation between the registration point sets is maintained in the registration process. How to quantify correspondence between pairs of points becomes a key technology therein.
The present embodiment considers the local correspondence of points, and takes the correspondence between local points as the prior probability of point registration. A local correspondence probability calculation method is provided, and is defined in (formula 10). The method is based on prior knowledge of stable structure between point set neighborhood points, guides the global probability of matching between two point sets through local consistency local matching probability, and finally obtains registration model parameters through maximum posterior probability estimation, which is shown in a formula (15). Therefore, in the point registration process, the corresponding consistency between the point and the neighborhood point is always kept. The quasi-determination and robustness of the algorithm are improved.
Example two:
based on the improved robust point registration method described in the first embodiment, the present embodiment provides an improved robust point registration system, including: the first module is used for giving two point sets, initializing registration model parameters and assigning initial values; the second module is used for solving the prior probability of matching consistency between local point pairs in the two point sets based on a point local structure keeping theory; a third module, configured to further solve the posterior probability based on the mixed probability model and the prior probability obtained in step b; the fourth module is used for further solving the deformation parameters of the registration model based on the posterior probability acquired by the third module; a fifth module for rearranging the points in the two point sets based on the deformation parameters acquired by the fourth module; and the sixth module is used for outputting the corresponding relation between the two point sets after the registration model is converged.
Example three:
based on the improved robust point registration method of embodiment one, this embodiment provides a computer-readable storage medium comprising a stored computer program, wherein when the computer program is executed by a processor, the apparatus in which the storage medium is controlled performs the improved robust point registration method of embodiment one.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

Claims (7)

1. An improved robust point registration method, comprising:
a. giving two point sets, initializing registration model parameters and assigning initial values;
b. solving prior probability of matching consistency between local point pairs in the two point sets based on a point local structure retention theory;
c. b, further solving the posterior probability based on the mixed probability model and the prior probability obtained in the step b;
d. c, further solving deformation parameters of the registration model based on the posterior probability obtained in the step c;
e. rearranging the points in the two point sets based on the deformation parameters obtained in the step d;
f. and e, repeating the steps b to e until the registration model is converged, and outputting the corresponding relation between the two point sets.
2. The improved robust point registration method of claim 1 wherein the joint probability density function of said mixed probability model is:
Figure FDA0002772556490000011
wherein the content of the first and second substances,
Figure FDA0002772556490000012
is a model parameter, a parameter
Figure FDA0002772556490000013
Indicating the probability that the ith point belongs to the jth gaussian component.
3. The improved robust point registration method according to claim 1, wherein in said step b, the prior probability of matching consistency between local point pairs in the two point sets is solved by the following formula:
Figure FDA0002772556490000014
wherein the content of the first and second substances,
Figure FDA0002772556490000015
to represent
Figure FDA0002772556490000016
Is composed of
Figure FDA0002772556490000017
The neighborhood of the point(s) of the neighborhood,
Figure FDA0002772556490000018
Figure FDA0002772556490000019
the number of neighborhood points.
4. The improved robust point registration method of claim 1 wherein in said step c, the a posteriori probability is solved by the following formula:
Figure FDA0002772556490000021
where U is a uniform distribution.
5. The improved robust point registration method according to claim 1 wherein in said step d, model deformation parameters of the mixed probability model are solved by the following formula:
Figure FDA0002772556490000022
wherein G is a Gaussian basis function, W is a deformation parameter,
Figure FDA0002772556490000023
is the variance of the gaussian component of the model.
6. An improved robust point registration system, comprising:
the first module is used for giving two point sets, initializing registration model parameters and assigning initial values;
the second module is used for solving the prior probability of matching consistency between local point pairs in the two point sets based on a point local structure keeping theory;
a third module, configured to further solve the posterior probability based on the mixed probability model and the prior probability obtained in step b;
the fourth module is used for further solving the deformation parameters of the registration model based on the posterior probability acquired by the third module;
a fifth module for rearranging the points in the two point sets based on the deformation parameters acquired by the fourth module;
and the sixth module is used for outputting the corresponding relation between the two point sets after the registration model is converged.
7. A computer-readable storage medium, characterized in that the computer-readable storage medium comprises a stored computer program, wherein the computer program, when being executed by a processor, controls an apparatus in which the storage medium is located to carry out the improved robust point registration method according to any one of claims 1 to 5.
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