 presegmenting each threedimensional model of a threedimensional model class to obtain threedimensional model patches for the each threedimensional model
 constructing a histogram for the threedimensional model patches of the each threedimensional model to obtain a patch feature vector for the each threedimensional model
 performing a sparse and lowrank representation to the patch feature vector for the each threedimensional model to obtain a representation coefficient and a representation error of the each threedimensional model
 determining a confident representation coefficient for the each threedimensional model according to the representation coefficient and the representation error of the each threedimensional model
 and clustering the confident representation coefficient of the each threedimensional model to cosegment the each threedimensional model, respectively.
Method for cosegmentating threedimensional models represented by sparse and lowrank feature
Updated Time 12 June 2019
Patent Registration DataPublication Number
US10152797
Application Number
US15/448540
Application Date
02 March 2017
Publication Date
11 December 2018
Current Assignee
BEIHANG UNIVERSITY
Original Assignee (Applicant)
BEIHANG UNIVERSITY
International Classification
G06K9/34,G06T7/11,G06T7/60,G06T17/00
Cooperative Classification
G06T7/11,G06T17/00,G06T7/60,G06T2200/04,G06K9/00201
Inventor
CHEN, XIAOWU,GUO, KAN,ZHAO, QINPING
Patent Images
This patent contains figures and images illustrating the invention and its embodiment.
Abstract
Presently disclosed is a method for cosegmenting threedimensional models represented by sparse and lowrank feature, comprising: presegmenting each threedimensional model of a threedimensional model class to obtain threedimensional model patches for the each threedimensional model; constructing a histogram for the threedimensional model patches of the each threedimensional model to obtain a patch feature vector for the each threedimensional model; performing a sparse and lowrank representation to the patch feature vector for the each threedimensional model to obtain a representation coefficient and a representation error of the each threedimensional model; determining a confident representation coefficient for the each threedimensional model according to the representation coefficient and the representation error of the each threedimensional model; and clustering the confident representation coefficient of the each threedimensional model to cosegment the each threedimensional model respectively.
Claims
1. A method for cosegmenting threedimensional models represented by sparse and lowrank feature, comprising:
presegmenting each threedimensional model of a threedimensional model class to obtain threedimensional model patches for the each threedimensional model; constructing a histogram for the threedimensional model patches of the each threedimensional model to obtain a patch feature vector for the each threedimensional model; performing a sparse and lowrank representation to the patch feature vector for the each threedimensional model to obtain a representation coefficient and a representation error of the each threedimensional model; determining a confident representation coefficient for the each threedimensional model according to the representation coefficient and the representation error of the each threedimensional model; and clustering the confident representation coefficient of the each threedimensional model to cosegment the each threedimensional model, respectively.
2. The method according to claim 1, wherein the presegmenting each threedimensional model of a threedimensional model class to obtain threedimensional model patches of the each threedimensional model comprises:
obtaining a base geometrical feature combination for the each threedimensional model of the threedimensional model class; and determining, by presegmenting the base geometrical feature combination of the each threedimensional model using a NCuts algorithm, the threedimensional model patches of the each threedimensional model.
3. The method according to claim 2, wherein the base geometrical feature combination comprises the following features: a normal vector and a geometric coordinate; and
a block number of the threedimensional model patches of the each threedimensional model is 50.
4. The method according to claim 1, wherein the constructing a histogram for the threedimensional model patches of the each threedimensional model to obtain a patch feature vector for the each threedimensional model comprises:
determining, by performing a geometric feature value calculation to the each threedimensional model patch of the each threedimensional model, a triangle patch feature value combination for the each threedimensional model patch of the each threedimensional model, wherein the triangle patch feature value combination comprises at least one triangle patch feature value; determining, by constructing a histogram for the triangle patch feature value combination of the each threedimensional model patch of the each threedimensional model respectively, a feature histogram for the each threedimensional model patch of the each threedimensional model; and determining, by arranging feature histograms of all the threedimensional model patches for the each threedimensional model, the patch feature vector for the each threedimensional model.
5. The method according to claim 4, wherein the triangle patch feature value combination comprises: a Shape Diameter Function (SDF) value, a Distance from Medial Surface (DMS) value, an Average Geodesic Distance (AGD) value and a Shape Context (SC) value.
6. The method according to claim 1, wherein the performing a sparse and lowrank representation to the patch feature vector for the each threedimensional model to obtain a representation coefficient and a representation error of the each threedimensional model comprises:
constructing a patch feature vector matrix D_{i}=D_{k}Z_{ki}+E_{ki }for a model according to the patch feature vectors of the threedimensional model, wherein D_{k }represents the patch feature vector matrix of model k, Z_{ki }represents the representation coefficient, E_{ki }represents the representation error, i∈[1,n], k∈[1,n], and i, n and k are positive integers; constructing a sparse and lowrank constraint
determining a solution formula
solving the solution formula to obtain each representation coefficient Z_{ki }and each representation error E_{ki }for the each threedimensional model.
7. The method according to claim 6, wherein the solving the solution formula to obtain each representation coefficient Z_{ki }and each representation error E_{ki }for the each threedimensional model comprises:
using Augmented Lagrange Multiplier (ALM) method to solve the solution formula, to obtain each representation coefficient Z_{ki }and each representation error E_{ki }for the each threedimensional model.
8. The method according to claim 1, wherein the determining a confident representation coefficient for the each threedimensional model according to the representation coefficient and the representation error of the each threedimensional model comprises:
normalizing all representation errors of the each threedimensional model to obtain a normalized representation error EE_{i}={E_{i1}, E_{i2}, . . . , E_{in}} for the each threedimensional model, wherein i∈[1,n], and i and n are positive integers; determining an error sum
9. The method according to claim 1, wherein the clustering the confident representation coefficient of the each threedimensional model to cosegment the each threedimensional model respectively comprises:
using a Kmeans method to cluster the confident representation coefficient of the each threedimensional model to obtain a cosegmentation outcome for the each threedimensional model.
10. The method according to claim 1, wherein after the clustering the confident representation coefficient of the each threedimensional model to cosegment the each threedimensional model respectively, further comprising:
determining, by using a Fuzzy Cuts method to perform boundary smoothing and optimization for the cosegmentation outcome for the each threedimensional model, an optimized cosegmentation outcome for the each threedimensional model.
Claim Tree

11. A method for cosegmenting threedimensional models represented by sparse and lowrank feature, comprising:

2. The method according to claim 1, wherein
 the presegmenting each threedimensional model of a threedimensional model class to obtain threedimensional model patches of the each threedimensional model comprises:

4. The method according to claim 1, wherein
 the constructing a histogram for the threedimensional model patches of the each threedimensional model to obtain a patch feature vector for the each threedimensional model comprises:

6. The method according to claim 1, wherein
 the performing a sparse and lowrank representation to the patch feature vector for the each threedimensional model to obtain a representation coefficient and a representation error of the each threedimensional model comprises:

8. The method according to claim 1, wherein
 the determining a confident representation coefficient for the each threedimensional model according to the representation coefficient and the representation error of the each threedimensional model comprises:

9. The method according to claim 1, wherein
 the clustering the confident representation coefficient of the each threedimensional model to cosegment the each threedimensional model respectively comprises:

10. The method according to claim 1, wherein
 after the clustering the confident representation coefficient of the each threedimensional model to cosegment the each threedimensional model respectively, further comprising:

Description
CROSSREFERENCE TO RELATED APPLICATIONS
This application claims priority to Chinese Patent Application No. 201610534020.6, filed on Jul. 7, 2016, which is hereby incorporated by reference in its entirety.
TECHNICAL FIELD
The present disclosure relates to the field of computer graphics technology, and particularly to a method for cosegmenting threedimensional models represented by sparse and lowrank feature.
BACKGROUND
As computer science and technologies continue to evolve, threedimensional model processing techniques have become one of the essential parts of daily lives, with applications in film producing, medical treatment, industrial manufacturing and various other domains. As one of the fundamental techniques in threedimensional model interpretation and processing, threedimensional model cosegmentation plays a key role in threedimensional modeling, threedimensional animation, threedimensional simulation and many other threedimensional technologies. Threedimensional model cosegmentation is about jointly segmenting various parts of individual models in a model class including a plurality of models.
In the prior art, threedimensional model cosegmentation methods include unsupervised threedimensional model set jointsegmentation method and interactive threedimensional model set cosegmentation method, etc. In the unsupervised threedimensional model set jointsegmentation method, each model of an input model set is initially segmented. Then, the presegmented parts of different models are jointly segmented in pairs in order to identify similar parts between the models. Finally, all model parts are globally optimized to obtain a consistent cosegmentation outcome for the threedimensional model set. In the interactive threedimensional model cosegmentation method, an initial segmentation outcome is produced through a presegmentation. Then, a user preemptively imposes constraints on a small number of models regarding the parts which belong to the same or different classes. The constraints are utilized to optimize further cosegmentation outcomes iteratively, until a consistent segmentation outcome of the threedimensional model set is obtained.
However, in the prior art, the unsupervised threedimensional model set jointsegmentation method relies on the initial presegmentation outcome. If the part segmentation outcome generated by the presegmentation process is inappropriate, nor will the final segmentation outcome be. Meanwhile, since the unsupervised threedimensional model set jointsegmentation method also relies on correlations among the models, in case any erroneous correlation is introduced due to diversity of the models, erroneous segmentation outcome will consequently be produced. In short, the possibility of obtaining a correct cosegmentation outcome is relatively low. The possibility of obtaining a correct cosegmentation outcome through the interactive threedimensional model set cosegmentation method is, unfortunately, also relatively low. The cause being that, a small amount of user interaction is required to propagate correct correlations among model parts to other models, yet without a true segmentation outcome as the guidance, teachings from the user interaction still have some limitations in terms of correcting erroneous model part correlations, again making correct segmentation outcome unachievable, and the possibility of obtaining a correct cosegmentation outcome is also relatively low.
SUMMARY
Accordingly, the present disclosure provides a method for cosegmenting threedimensional models represented by sparse and lowrank feature.
The present disclosure provides a method for cosegmenting threedimensional models represented by sparse and lowrank feature, the method including:
presegmenting each threedimensional model of a threedimensional model class to obtain threedimensional model patches for the each threedimensional model;
constructing a histogram for the threedimensional model patches of the each threedimensional model to obtain a patch feature vector for the each threedimensional model;
performing a sparse and lowrank representation to the patch feature vector for the each threedimensional model to obtain a representation coefficient and a representation error of the each threedimensional model;
determining a confident representation coefficient for the each threedimensional model according to the representation coefficient and the representation error of the each threedimensional model; and
clustering the confident representation coefficient of the each threedimensional model to cosegment the each threedimensional model respectively.
In the aforementioned method, the presegmenting each threedimensional model of a threedimensional model class to obtain threedimensional model patches for the each threedimensional model includes:
obtaining a base geometrical feature combination for the each threedimensional model of the threedimensional model class; and
determining, by presegmenting the base geometrical feature combination of the each threedimensional model using a NCuts algorithm, the threedimensional model patches of the each threedimensional model.
In the aforementioned method, the base geometrical feature combination comprises the following features: a normal vector and a geometric coordinate; and
a block number of the threedimensional model patches of the each threedimensional model is 50.
In the aforementioned method, the constructing a histogram for the threedimensional model patches of the each threedimensional model to obtain a patch feature vector for the each threedimensional model includes:
determining, by performing a geometric feature value calculation to the each threedimensional model patch of the each threedimensional model, a triangle patch feature value combination for the each threedimensional model patch of the each threedimensional model, wherein the triangle patch feature value combination comprises at least one triangle patch feature value;
determining, by constructing a histogram for the triangle patch feature value combination of the each threedimensional model patch of the each threedimensional model respectively, a feature histogram for the each threedimensional model patch of the each threedimensional model; and
determining, by arranging feature histograms of all the threedimensional model patches for the each threedimensional model, the patch feature vector for the each threedimensional model.
In the aforementioned method, the triangle patch feature value combination includes: a Shape Diameter Function (SDF) value, a Distance from Medial Surface (DMS) value, an Average Geodesic Distance (AGD) value, and a Shape Context (SC) value.
In the aforementioned method, the performing a sparse and lowrank representation to the patch feature vector for the each threedimensional model to obtain a representation coefficient and a representation error of the each threedimensional model includes:
constructing a patch feature vector matrix D_{i}=D_{k}Z_{ki}+E_{ki }for a model according to the patch feature vectors of the threedimensional model, wherein D_{k }represents the patch feature vector matrix of model k, Z_{ki }represents the representation coefficient, E_{ki }represents the representation error, i∈[1,n], k∈[1,n], and i, n and k are positive integers;
constructing a sparse and lowrank constraint
wherein Z_{ki}≥ZZ_{k }is a representation coefficient set constructed to represent all models using model k as the dictionary, and ZZ_{k}={Z_{k1}, Z_{k2}, . . . , Z_{kn}}, ∥·∥_{* }represents a nuclear norm of a matrix, and ∥·∥_{* }is a sum of eigenvalues of a matrix, ∥·∥_{2,1 }represents l_{2,1 }norm,
np represents the block number of threedimensional model patches of each models, Z_{ki}(*,j) represents the jth column of Z_{ki}, ∥·∥_{1,1 }represents l_{1,1 }norm, ∥E∥_{1,1}=Σ_{i,j}E_{i,j}∥, i and j are row index and column index of the matrix E respectively, j∈[1,n*np], j and np are positive integers, and α and λ are balancing weight factors;
determining a solution formula
according to the patch feature vector matrix of each model and the sparse and lowrank constraint, wherein D_{i}=D_{k}R_{ki}+E_{ki}, Z_{ki}=S_{ki}, Z_{ki}=R_{ki}, S_{ki}≥R_{ki}≥0; and
solving the solution formula to obtain each representation coefficient Z_{ki }and each representation error E_{ki }for the each threedimensional model.
In the aforementioned method, the solving the solution formula to obtain each representation coefficient Z_{ki }and each representation error E_{ki }for the each threedimensional model includes:
using Augmented Lagrange Multiplier (ALM) method to solve the solution formula, to obtain each representation coefficient Z_{ki }and each representation error E_{ki }for the each threedimensional model.
In the aforementioned method, the determining a confident representation coefficient for the each threedimensional model according to the representation coefficient and the representation error of the each threedimensional model includes:
normalizing all representation errors of the each threedimensional model to obtain a normalized representation error EE_{i}={E_{i1}, E_{i2}, . . . , E_{in}} for the each threedimensional model, wherein i∈[1,n], and i and n are positive integers;
determining an error sum
for the each threedimensional model according to all the normalized representation errors of the each threedimensional model, wherein i∈[1,n], j∈[1,n*np], and j and np are positive integers;
normalizing all error sums of the each threedimensional model to obtain each weight value NSE_{i }of the each threedimensional model; and
determining each confident representation coefficient ZZ_{confident}_{i}=ZZ_{i}·(1+exp^{−β*NSE}^{i}), for the each threedimensional model according to the each weight value NSE_{i }and the representation coefficient set ZZ_{i }of the threedimensional model, wherein β is a control parameter.
In the aforementioned method, the clustering the confident representation coefficients of the each threedimensional model to cosegment the each threedimensional model respectively includes:
using a Kmeans method to cluster the confident representation coefficient of the each threedimensional model to obtain a cosegmentation outcome for the each threedimensional model.
In the aforementioned method, after the clustering the confident representation coefficient of the each threedimensional model to cosegment the each threedimensional model respectively, further including:
determining, by using a Fuzzy Cuts method to perform boundary smoothing and optimization for the cosegmentation outcome for the each threedimensional model, an optimized cosegmentation outcome for the each threedimensional model.
The technical effects of the present disclosure are: presegmenting each threedimensional model of a threedimensional model class to obtain threedimensional model patches for the each threedimensional model; constructing a histogram for the threedimensional model patches of the each threedimensional model to obtain a patch feature vector for the each threedimensional model; performing a sparse and lowrank representation to the patch feature vector for the each threedimensional model to obtain a representation coefficient and a representation error of the each threedimensional model; determining a confident representation coefficient for the each threedimensional model according to the representation coefficient and the representation error of the each threedimensional model; and clustering the confident representation coefficient of the each threedimensional model to cosegment the each threedimensional model respectively. Therefore, a new threedimensional model cosegmentation method based on sparse and lowrank representation is presented, in which a single threedimensional model is used as the dictionary for exploring correlations between individual threedimensional models while preserving global consistency among threedimensional models of the same class without missing individual features of individual threedimensional models. Meanwhile, by using the representation error to weight the representation coefficient by level of confidence, representation outcomes of multiple runs may be correctly combined and clustered to obtain the final threedimensional model cosegmentation outcome with higher accuracy rate.
BRIEF DESCRIPTION OF DRAWINGS
FIG. 1 is a flowchart illustrating a method for cosegmenting threedimensional models represented by sparse and lowrank feature provided by a first embodiment of the present disclosure;
FIG. 2 is a schematic diagram illustrating threedimensional models of a method for cosegmenting threedimensional models represented by sparse and lowrank feature provided by the first embodiment of the present disclosure;
FIG. 3 is a flowchart illustrating a method for cosegmenting threedimensional models represented by sparse and lowrank feature provided by a second embodiment of the present disclosure;
FIG. 4 is a schematic diagram illustrating threedimensional models of a method for cosegmenting threedimensional models represented by sparse and lowrank feature provided by the second embodiment of the present disclosure;
FIG. 5 is a schematic diagram illustrating a geometric feature value calculation for threedimensional models of a method for cosegmenting threedimensional models represented by sparse and lowrank feature provided by the second embodiment of the present disclosure;
FIG. 6 is a schematic diagram illustrating a sparse and lowrank feature representation calculation for threedimensional models of a method for cosegmenting threedimensional models represented by sparse and lowrank feature provided by the second embodiment of the present disclosure;
FIG. 7 is a schematic diagram illustrating a sparse confidence weighting calculation for threedimensional models of a method for cosegmenting threedimensional models represented by sparse and lowrank feature provided by the second embodiment of the present disclosure; and
FIG. 8 is a schematic diagram illustrating cosegmentation outcome for threedimensional models of a method for cosegmenting threedimensional models represented by sparse and lowrank feature provided by the second embodiment of the present disclosure.
DESCRIPTION OF EMBODIMENTS
In order to make objectives, technical solutions and advantages of the present disclosure clearer, the technical solutions in the embodiments of the present disclosure will be described hereunder clearly and completely with reference to accompanying drawings in the embodiments of the present disclosure. Obviously, the described embodiments are only a part of embodiments of the present disclosure, rather than all of them. Any other embodiments obtained by persons skilled in the art based on the embodiments of the present disclosure herein without making any creative effort shall fall into the protection scope of the present disclosure.
FIG. 1 is a flowchart illustrating a method for cosegmenting threedimensional models represented by sparse and lowrank feature provided by a first embodiment of the present disclosure. As depicted in FIG. 1, the present embodiment method includes:
At step 101, presegmenting each threedimensional model of a threedimensional model class to obtain threedimensional model patches for the each threedimensional model.
In the present embodiment, particularly, a threedimensional model class has a plurality of threedimensional models. For example, in a threedimensional model class of human bodies, as depicted in FIG. 2, a schematic diagram illustrating threedimensional models of a method for cosegmenting threedimensional models represented by sparse and lowrank feature provided by the first embodiment of the present disclosure, there is a plurality of human body threedimensional models. Similarly, a threedimensional model class of tables may have a plurality of table threedimensional models, and a threedimensional model class of cats may have a plurality of cat threedimensional models. It is desired to segment all threedimensional models of a threedimensional model class, so that each threedimensional model is segmented into several parts. For example, each human body threedimensional model of a human body class may be cosegmented into parts such as heads, torsos, and limbs.
Firstly, each threedimensional model of the threedimensional model class needs to be presegmented to obtain threedimensional model patches for each threedimensional model. A threedimensional model patch consists of continuously aggregated threedimensional model triangle patches. Each threedimensional model may have a plurality of threedimensional model patches.
At step 102, constructing a histogram for the threedimensional model patches of the each threedimensional model to obtain a patch feature vector for the each threedimensional model.
In the present embodiment, particularly, a histogram is constructed for threedimensional model patches of each threedimensional model respectively. In particular, this may start from extracting geometric features of threedimensional model patches of the each threedimensional model, proceed to obtaining SDF value, DMS value, AGD value and SC value for each threedimensional model patches of the each threedimensional model, normalizing the calculated geometric feature value for individual threedimensional model patches of each threedimensional model, and performing calculation to obtain a histogram of the features of each threedimensional model patch for each threedimensional model. Following that, feature histograms of all threedimensional model patches for each threedimensional model are rearranged and joined, thus obtaining a patch feature vector for each threedimensional model.
At step 103, performing a sparse and lowrank representation to the patch feature vector for the each threedimensional model to obtain a representation coefficient and a representation error of the each threedimensional model.
In the present embodiment, particularly, feature histograms of all threedimensional models in a threedimensional model class may be collected into a dictionary for sparsely representing each model in the threedimensional model class, i.e. to derive a sparse and lowrank representation of the patch feature vector. Meanwhile, a sparse and lowrank constraint is constructed to make the representation coefficient as lowrank as possible. Finally, calculation is performed to obtain a representation coefficient set and a representation error set for each threedimensional model, where one representation coefficient set has a plurality of representation coefficients, and one representation error set has a plurality of representation errors.
At step 104, determining a confident representation coefficient for the each threedimensional model according to the representation coefficient and the representation error of the each threedimensional model.
In the present embodiment, particularly, representation error of a threedimensional model may be normalized for each threedimensional model. The normalized representation error may be taken as the weighting for the representation coefficient corresponding to the representation error. Thus, each representation error is weighted for calculating a confident representation coefficient for each threedimensional model respectively, where one threedimensional model has one confident representation coefficient.
At step 105, clustering the confident representation coefficient of the each threedimensional model to cosegment the each threedimensional model respectively.
In the present embodiment, particularly, confident representation coefficients of all threedimensional models are clustered into divisions so that cosegmentation outcome for each threedimensional model can be obtained. Therefore, each threedimensional model is divided into several parts consistently grouped into classes. Afterwards, Fuzzy Cuts method may be used to perform boundary smoothing and optimization for the cosegmentation outcome for each threedimensional model to obtain the final threedimensional model cosegmentation outcome.
The present embodiment presegments each threedimensional model of a threedimensional model class to obtain threedimensional model patches for the each threedimensional model; constructs a histogram for the threedimensional model patches of the each threedimensional model to obtain a patch feature vector for the each threedimensional model; performs a sparse and lowrank representation to the patch feature vector for the each threedimensional model to obtain a representation coefficient and a representation error of the each threedimensional model; determines a confident representation coefficient for the each threedimensional model according to the representation coefficient and the representation error of the each threedimensional model; and clusters the confident representation coefficient of the each threedimensional model to cosegment each threedimensional model respectively. Therefore, a new threedimensional model cosegmentation method based on sparse and lowrank representation is presented, in which a single threedimensional model is used as the dictionary for exploring correlations between individual threedimensional models while preserving global consistency among threedimensional models of the same class without missing individual features of individual threedimensional models. Meanwhile, by using the representation error to weight the representation coefficient by level of confidence, representation outcomes of multiple runs may be correctly combined and clustered to obtain the final threedimensional model cosegmentation outcome with higher accuracy rate.
FIG. 3 is a flowchart illustrating a method for cosegmenting threedimensional models represented by sparse and lowrank feature provided by a second embodiment of the present disclosure. On the basis of the first embodiment, as depicted in FIG. 3, step 101 in the present embodiment of the method particularly includes:
obtaining a base geometrical feature combination for the each threedimensional model of the threedimensional model class; and
determining, by presegmenting the base geometrical feature combination of the each threedimensional model using a NCuts algorithm, the threedimensional model patches of the each threedimensional model.
Here, the base geometrical feature combination includes the following features: a normal vector, and a geometric coordinate; and a block number of the threedimensional model patches of the each threedimensional model is 50.
In the present embodiment, particularly, FIG. 4 is a schematic diagram illustrating threedimensional models of the method for cosegmenting threedimensional models represented by sparse and lowrank feature provided by the second embodiment of the present disclosure. As depicted in FIG. 4, a threedimensional model class has a plurality of threedimensional models. The plurality of threedimensional models in the threedimensional model class are input into a computer to obtain a base geometrical feature combination for each threedimensional model, where the base geometrical feature combination includes features such as normal vector and geometric coordinate.
Following that, the base geometrical feature combination of the threedimensional models may be respectively presegmented using NCuts algorithm, so as to presegment each threedimensional model, thus continuously aggregated threedimensional model patches of each threedimensional model can be obtained, where the number of threedimensional model patches for each threedimensional model is usually set at 50.
Step 102 particularly includes:
determining, by performing a geometric feature value calculation to the each threedimensional model patch of the each threedimensional model, a triangle patch feature value combination for the each threedimensional model patch of the each threedimensional model, where the triangle patch feature value combination comprises at least one triangle patch feature value;
determining, by constructing a histogram for the triangle patch feature value combination of the each threedimensional model patch of the each threedimensional model respectively, a feature histogram for the each threedimensional model patch of the each threedimensional model; and
determining, by arranging feature histograms of all the threedimensional model patches for the each threedimensional model, the patch feature vector for the each threedimensional model.
Here, the triangle patch feature value combination includes: a Shape Diameter Function (SDF) value, a Distance from Medial Surface (DMS) value, an Average Geodesic Distance (AGD) value, and a Shape Context (SC) value.
In the present embodiment, particularly, for each threedimensional model in a threedimensional model class, geometric feature value for each threedimensional model patch of each threedimensional model needs to be firstly calculated to obtain the triangle patch feature value, e.g. the SDF value, DMS value, AGD value, and SC value, which together form a triangle patch feature value combination for each threedimensional model patch. FIG. 5 is a schematic diagram illustrating a geometric feature value calculation for a threedimensional model of the method for cosegmenting threedimensional models represented by sparse and lowrank feature provided by the second embodiment of the present disclosure. As depicted in FIG. 5, the SDF value, DMS value, AGD value, and SC value of each threedimensional model patch can be obtained for each model.
Then, a histogram is constructed for the triangle patch feature value combination of the each threedimensional model patch of each threedimensional model, so as to determine a feature histogram for the each threedimensional model patch of each threedimensional model. Since one threedimensional model has 50 threedimensional model patches, it can be known that one threedimensional model has 50 feature histograms. When constructing the histogram, the number of divisions therein is often set at 50.
Finally, feature histograms of all threedimensional model patches for each threedimensional model may be arranged so that feature values of all feature histograms of each model are in one column. The arranged feature histograms are taken as the patch feature vector of the threedimensional model, where each threedimensional model has a plurality of patch feature vectors.
Step 103 particularly includes:
constructing a patch feature vector matrix D_{i}=D_{k}Z_{ki}+E_{ki }for a model according to the patch feature vectors of the threedimensional model, where D_{k }represents the patch feature vector matrix of model k, Z_{ki }represents the representation coefficient, E_{ki }represents the representation error, i∈[1,n], k∈[1,n], and i, n and k are positive integers;
constructing a sparse and lowrank constraint
where Z_{ki}≥0, ZZ_{k }is a representation coefficient set constructed to represent all models using model k as the dictionary, and ZZ_{k}={Z_{k1}, Z_{k2}, . . . , Z_{kn}}, ∥·∥_{* }represents a nuclear norm of a matrix, and ∥·∥_{* }is a sum of eigenvalues of a matrix, ∥·∥_{2,1 }represents l_{2,1 }norm,
np represents the block number of threedimensional model patches of each models, Z_{ki}(*,j) represents the jth column of Z_{ki}, ∥·∥_{1,1 }represents l_{1,1 }norm, ∥E∥_{1,1}=Σ_{i,j}E_{i,j}, i and j are row index and column index of the matrix E respectively, j∈[1,n*np], j and np are positive integers, and α and λ are balancing weight factors;
determining a solution formula
according to the patch feature vector matrix of each model and the sparse and lowrank constraint, where D_{i}=D_{k}R_{ki}+E_{ki}, Z_{ki}=S_{ki}, Z_{ki}=R_{ki}, S_{k}≥0, R_{ki}≥0; and
solving the solution formula to obtain each representation coefficient Z_{ki }and each representation error E_{ki }for the each threedimensional model.
Here, the solving the solution formula to obtain each representation coefficient Z_{ki }and each representation error E_{ki }for each threedimensional model includes:
using Augmented Lagrange Multiplier (ALM) method to solve the solution formula, so as to obtain each representation coefficient Z_{ki }and each representation error E_{ki }for the each threedimensional model.
In the present embodiment, particularly, for each threedimensional model in a threedimensional model class, when patch feature vectors of the threedimensional models have been obtained, all patch feature vectors of model k may be joined, thus obtaining a patch feature vector matrix D_{k }for model k. Then, based on each patch feature vector of each threedimensional model, formula of patch feature vector matrix D_{i}=D_{k}Z_{ki}+E_{ki }is obtained for each model, where Z_{ki }represents the representation coefficient, E_{ki }represents the representation error, i∈[1,n], k∈[1,n], i, and n and k are positive integers. For now, representation coefficient Z_{ki }and representation error E_{ki }are unknowns.
For the purpose of obtaining a tightly consistent correlation among the models, the present embodiment needs to construct a sparse and lowrank constraint
where Z_{ki}≥0, ZZ_{k }is a representation coefficient set constructed to represent all models using model k as the dictionary, and ZZ_{k}={Z_{k1}, Z_{k2}, . . . , Z_{kn}}, ∥·∥_{* }represents a nuclear norm of a matrix, and is the sum of eigenvalues of a matrix, ∥·∥_{2,1 }represents l_{2,1 }norm;
np represents the number of threedimensional model patches of each models, Z_{ki}(*,j) represents the jth column of Z_{ki}, ∥·∥_{1,1 }represents l_{1,1 }norm, ∥E∥_{1,1}=Σ_{i,j}E_{i,j}, i and j are row index and column index of the matrix E respectively, j∈[1,n*np], j and np are positive integers, and α and λ are balancing weight factors.
Then, for each model, equivalent transformation is performed on the patch feature vector matrix D=D_{k}Z_{ki}+E_{ki }and the sparse and lowrank constraint
to obtain a solution formula
where the D_{i}=D_{k}R_{ki}+E_{ki}Z_{ki}=S_{ki}, Z_{ki}=R_{ki}, S_{ki}≥0, R_{ki}≥0, i∈[1,n], k∈[1,n], and i, n and k are positive integers.
Then, ALM method is used to solve the described solution formula
to obtain, for each threedimensional model, each representation coefficient Z_{ki}, and the one representation error E_{ki }correspondent to each one of the representation coefficients Z_{ki}. It is known that one threedimensional model may have a plurality of representation coefficients and representation errors, with oneonone correspondence between the representation coefficient and the representation error.
FIG. 6 is a schematic diagram illustrating a sparse and lowrank feature representation calculation for a threedimensional model of the method for cosegmenting threedimensional models represented by sparse and lowrank feature provided by the second embodiment of the present disclosure. As depicted in FIG. 6, individual threedimensional models in a threedimensional model class may be used as the dictionary to obtain a sparse and lowrank representation for all the threedimensional models in the threedimensional model class. Then, the each representation coefficient Z_{ki}, and the one representation error E_{ki }correspondent to each one of the representation coefficients Z_{ki}, are calculated.
Step 104 particularly includes:
normalizing all representation errors of the each threedimensional model to obtain a normalized representation error EE_{i}={E_{i1}, E_{i2}, . . . , E_{in}} for the each threedimensional model, where i∈[1,n], and i and n are positive integers;
determining an error sum
for the each threedimensional model according to all the normalized representation errors of the each threedimensional model, where i∈[1,n], j∈[1,n*np], and j and np are positive integers;
normalizing all error sums of the each threedimensional model to obtain each weight value NSE_{i }of the each threedimensional model; and
determining each confident representation coefficient ZZ_{confident}_{i}=ZZ_{i}·(1+exp^{−β*NSE}^{i}), for the each threedimensional model according to the each weight value NSE_{i }and the representation coefficient set ZZ_{i }of the threedimensional model, where β is a control parameter.
In the present embodiment, particularly, a method to weight a coefficient by confidence is presented, which allows assessing and weighting the obtained representation coefficients by using the representation errors, so that reliable confident representation coefficients can be obtained.
In particular, firstly, all representation errors E_{ki }of each threedimensional model are normalized to obtain a normalized representation error EE_{i}={E_{i1}, E_{i2}, . . . , E_{in}} for each threedimensional model, where i∈[1,n], and i and n are positive integers.
Then, as depicted in FIG. 7, which is a schematic diagram illustrating a sparse confidence weighted calculation for a threedimensional model of the method for cosegmenting threedimensional models represented by sparse and lowrank feature provided by the second embodiment of the present disclosure, an error sum
for each column of each threedimensional model may be calculated according to all the normalized representation errors EE_{i}={E_{i1}, E_{i2}, . . . , E_{in}} of each threedimensional model, where i∈[1,n], j∈[1,n*np], and j and np are positive integers.
Following that, all error sums SE_{i }of each threedimensional model are normalized to obtain each weight value NSE_{i}. Then, each confident representation coefficient ZZ_{confident}_{i}=ZZ_{i}·(1+exp^{−β*NSE}^{i}) for each threedimensional model is solved according to the each weight value NSE_{i }and the representation coefficient set ZZ_{i}. The β is a control parameter. In general, β takes the value of 5.
Step 105 particularly includes:
using a Kmeans method to cluster the confident representation coefficient of the each threedimensional model to obtain a cosegmentation outcome for the each threedimensional model.
In the present embodiment, particularly, confident representation coefficients of all threedimensional models are clustered into divisions by the Kmeans method, so that cosegmentation outcome for each threedimensional model can be obtained. By now, each threedimensional model of a threedimensional model class has been segmented into a plurality of parts consistently grouped into classes.
For example, each of the plurality of human body threedimensional models of a human body class is segmented into a plurality of parts, such as heads, torsos, and limbs, without incorrectly segmenting the parts.
Following step 105, further includes:
At step 201, determining, by using a Fuzzy Cuts method to perform boundary smoothing and optimization for the cosegmentation outcome for the each threedimensional model, an optimized cosegmentation outcome for the each threedimensional model.
In the present embodiment, particularly, after the step 105, an initial cosegmentation outcome is obtained for each threedimensional model of a threedimensional model class. By now, for each threedimensional model, a Fuzzy Cuts method is required to perform boundary smoothing and optimization for the cosegmentation outcome for each threedimensional model in step 105. FIG. 8 is a schematic diagram illustrating a cosegmentation outcome for threedimensional models of the method for cosegmenting threedimensional models represented by sparse and lowrank feature provided by the second embodiment of the present disclosure. As depicted in FIG. 8, the final threedimensional model cosegmentation outcome is obtained. That is, an optimized cosegmentation outcome for each threedimensional model of a threedimensional model class is obtained, ensuring correctness of the cosegmentation.
The present embodiment presegments each threedimensional model of a threedimensional model class to obtain threedimensional model patches for the each threedimensional model; constructs a histogram for the threedimensional model patches of the each threedimensional model to obtain a patch feature vector for the each threedimensional model; performs a sparse and lowrank representation to the patch feature vector for the each threedimensional model to obtain a representation coefficient and a representation error of the each threedimensional model; determines a confident representation coefficient for the each threedimensional model according to the representation coefficient and the representation error of the each threedimensional model; clusters the confident representation coefficients of the each threedimensional model to cosegment each threedimensional model respectively; and uses Fuzzy Cuts method to perform boundary smoothing and optimization for the cosegmentation outcome for each threedimensional model to determine an optimized cosegmentation outcome for each threedimensional model. Therefore, a new threedimensional model cosegmentation method based on sparse and lowrank representation is presented, in which a single threedimensional model is used as the dictionary for exploring correlations between individual threedimensional models while preserving global consistency among threedimensional models of the same class without missing individual features of individual threedimensional models. Meanwhile, by using the representation error to weight the representation coefficient by level of confidence, representation outcomes of multiple runs may be correctly combined and clustered to obtain the final threedimensional model cosegmentation outcome with higher accuracy rate.
Persons of ordinary skill in the art may understand that, all or a part of steps of the foregoing method embodiments may be implemented by a program instructing relevant hardware. The foregoing program may be stored in a computer readable storage medium. When the program runs, the steps of the foregoing method embodiments are performed. The foregoing storage medium includes various mediums capable of storing program codes, such as a ROM, a RAM, a magnetic disk, or an optical disc.
Lastly, it should be noted that the foregoing embodiments are merely intended for explaining, rather than limiting, the technical solutions of the present disclosure. Although the present disclosure is explained in detail with reference to the foregoing embodiments, persons of ordinary skill in the art should understand that it remains possible to make modifications to the technical solutions described in the foregoing embodiments, or make equivalent replacements to some of the technical features therein, and these modifications or replacements do not make the essence of corresponding technical solutions depart from the spirit and scope of the technical solutions in the embodiments of the present disclosure.
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