CN109118589A - Geometrical model full range details restorative procedure - Google Patents
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Abstract
Geometrical model full range details restorative procedure of the present invention, the restorative procedure of the original details of geometrical model is kept based on adaptive decomposition, migration reparation is carried out with the geometric detail information effectively to model surface missing, to solve the problems, such as that boundary alignment process is complicated and model is distorted.It include following steps, step (1) geometrical model full range details catabolic phase, using average curvature as the input signal of the adaptive decomposition of triangle grid model, this signal is decomposed, obtains including the full range geometric detail information for accumulateing mode function and signal margin in one group；Step (2) Patch model Optimum Matching stage；Step (1) is obtained full range geometric detail information, is migrated by similitude patch to target patch by step (3), geometry information transmitting and model full range repairing phase according to the matching result that step (2) obtains；The reconstruction that grid model is carried out for each signal obtains different geometric detail reparations as a result, to make model editable.
Description
Technical Field
The invention relates to a full-frequency detail restoration method of a data-driven geometric model, and belongs to the technical field of grid model data processing and model restoration.
Background
Modeling of cultural relics with high reduction degree is basically completed by means of three-dimensional scanning, but the scanned three-dimensional model often has damaged surfaces, so that more and more repair algorithms for keeping the geometric details of the model are proposed.
The current major methods include voxel-based, texture synthesis-based, and template library-based methods. Model restoration is an ill-defined problem because most methods can achieve better restoration effects in certain model situations, but cannot be guaranteed to be applicable to other situations. For example, for some small holes, a good repairing effect can be achieved, but holes containing abundant geometric detail information and large areas cannot be well repaired.
In recent years, more and more similarity measurement model-based repairing methods emerge, and the core idea is to define an effective patch descriptor, then find out the patch of the complete area most similar to the hole area according to the descriptor, and fill the hole by copying the patches of other areas of the model or similar models.
The model restoration method for geometric detail preservation based on similarity measurement achieves the restoration purpose mainly by copying the existing region to the hole region, and meanwhile guarantees the restoration of geometric details. However, it is the operation of copy-and-paste that increases computational complexity and decreases time efficiency. Because when the similarity area is pasted to the hole target area, the boundary alignment of the similarity area and the hole target area needs to be carried out. Firstly, finding the corresponding relation between the points required by alignment is difficult to define; secondly, in the alignment, the deformation of the mesh model is necessarily performed, which is not an intended result, and the desired goal is to minimize the influence of the repair on the existing model area during the repair process. Therefore, how to find an alignment method for reducing the degree of model deformation and completely avoiding the deformation is a technical problem to be solved.
In addition, the model restoration algorithm with the maintained geometric details plays an important role in various fields such as archaeology, 3D printing, material object manufacturing, mold defect detection and rapid restoration, is widely applied, and has a wide application prospect and a huge market value. However, the current research on the model repairing method with geometric detail preservation also faces many challenges, such as the complexity of the hole boundary alignment process mentioned above and the distortion of model deformation caused by the alignment process.
In view of this, the present patent application is specifically proposed.
Disclosure of Invention
The invention discloses a full-frequency detail restoration method for a geometric model, which aims to solve the problems in the prior art, and is a restoration method for keeping original details of the geometric model based on self-adaptive decomposition so as to effectively perform migration restoration on geometric detail information missing from the surface of the model, thereby solving the problems of complex boundary alignment process and model distortion.
In order to achieve the above purpose, the method for restoring the full frequency details of the geometric model comprises the following implementation steps:
in the step (1), in a full-frequency detail decomposition stage of the geometric model, average curvature is used as an input signal of adaptive decomposition of a triangular mesh model, and the signal is decomposed to obtain full-frequency geometric detail information comprising a group of Intrinsic Mode Functions (IMFs) and signal margins (residual);
in the patch model optimal matching stage, based on the adjacent structural features of the damaged region of the model, full-frequency features determined by anisotropic heat transfer relationship weighted values in different time domains are used for model matching; by defining a statistical information descriptor related to adjacent structural features of a damaged region of the model, extending an anisotropic descriptor from a vertex descriptor to a descriptor of a patch, effectively searching a similarity patch which is most matched with a target patch, and storing a matching result;
in the stage of geometrical structure information transmission and full-frequency model restoration, full-frequency geometrical detail information obtained in the step (1) is migrated to a target patch from the similarity patch according to the matching result obtained in the step (2); in the migration process, adjusting the weights of intrinsic mode functions in different scales to obtain different signals; and respectively reconstructing the grid model aiming at each signal to obtain different geometric detail repairing results, so that the model can be edited.
According to the basic scheme, in order to solve the problems of complex boundary alignment and model distortion, a model repairing mode for protecting geometric details is provided based on a self-adaptive decomposition method, geometric detail information missing from the surface of a model is effectively repaired, and the complex process of boundary alignment in the copying and pasting process can be avoided. Meanwhile, the migration of geometric details is effectively realized through a calculation method instead of the migration and pasting of the whole patch, and the distortion degree of the model is reduced.
In a further preferred embodiment, in the step (1), the adaptively decomposed input signal of the triangular mesh model is decomposed based on Ensemble Empirical Mode Decomposition (EEMD);
EEMD is an abbreviation of Ensemble Empirical Mode Decomposition, i.e. Ensemble Empirical Mode Decomposition, and is a noise-aided data analysis method proposed for the deficiency of EMD method. The decomposition principle is that when the attached white noise is uniformly distributed in the whole time-frequency space, the time-frequency space is composed of different scale components which are divided by a filter bank. When the signal is added to a uniformly distributed white noise background, the signal regions of different scales will automatically map to the appropriate scale associated with the background white noise.
And model smoothing processing is implemented based on an EEMD (ensemble empirical mode decomposition) algorithm, so that the initial repairing effect of the model is better.
Function g defined on the surface of the triangular mesh model: m → R, M denotes a mesh model, R denotes a set of real numbers,
wherein f iskDenotes the kth IMFs, k 1, N denotes the total number of intrinsic mode functions, rNRepresenting the corresponding signal margin;
the decomposition process is as follows,
first, the extreme point is defined, for the function g, if g (v)i) Satisfies the following conditions: g (v)i)≥g(vj) J ∈ N (i) or g (v)i)≤g(vj) J belongs to N (i), and vi is called a maximum value point or a minimum value point of g;
secondly, finding out extreme points according to the definition of the extreme points in the previous step, constructing upper and lower envelopes by the extreme points, solving the envelopes by using double harmonic interpolation calculation, wherein the double harmonic interpolation is the expansion of spline interpolation on a three-dimensional curved surface and is realized by an energy function defined on a potential manifold curved surface M where a minimized triangular mesh model is positioned,
∫M(ΔMφ)2dV.
the corresponding Lagrange equation isWherein ΔMIs the Laplace-Beltrami operator of the surface M, in particular, for a given interpolation point and corresponding value { (v)i,g(vi) I, ∈ C }, and the interpolation function phi ═ phi (v)1),φ(v2),...,φ(vn) Can be found by solving the following n × n linear system:
L2·φ＝0,s.t.,φ(vi)＝g(vi),i∈C,
wherein, C is an interpolation set, and L is an n multiplied by n Laplace matrix of a triangular mesh model;
finally, after calculating the upper envelope and the lower envelope according to the convergence standard of the iterative screening process, determining the current intrinsic mode function through the envelopes; the convergence standard of the screening is to judge whether the signal after the screening is an intrinsic mode function or not; the end process is to see if the standard deviation SD is less than a given threshold, the standard deviation SD is calculated using two adjacent screening results, the standard deviation SD is formulated as follows,
a further supplement and refinement to the step (2) is that a new descriptor is defined in the present application. The descriptor extends the anisotropic descriptor based on the model vertex to the statistical information descriptor related to the adjacent structural feature of the damaged region of the model by a statistical method, so that the precision of the whole similarity matching result is improved. Meanwhile, in the matching process, rigid registration constraint is added, and the best matching result with the minimum registration error is selected from the similar candidate set.
Specifically, a statistical information descriptor related to adjacent structural features of a model damaged area is defined to obtain a similarity matching result for the patch;
given a potential manifold surface M, the following equation exists:
wherein HTAs a thermodynamic operator, ht(x, y) the amount of heat transferred from point x to y at time t;
the matching process is as follows,
firstly, performing characteristic decomposition on thermonuclear to obtain a statistical information descriptor related to adjacent structural characteristics of a model damaged area:
wherein, λ itAnd ΩiRespectively, are eigenvalues and eigenfunctions corresponding to Laplace-belief operators (operators determined by satellite operators and external differential operators of star operators), and satisfy the equation Δ Μ Ωi＝λitΩiAdding the local structure information into the Laplace matrix construction;
secondly, according to the anisotropic heat transfer relationship weight value of the vertex calculated in the previous step, a statistical information descriptor related to the adjacent structural features of the model damage area is defined as follows,
wherein, [0,1 ]]Denotes normalization to the interval [0,1 ]]Selecting a plurality of time domain descriptors, namely each patch corresponds to a plurality of descriptors; in the time domainSampling 100 time points as an anisotropic heat transfer relationship weight vector of one point;
finally, calculating a matching result between patches according to a statistical information descriptor related to adjacent structural features of a defined model damaged area, calculating the distance between patch descriptors by adopting an Euclidean distance standard, and selecting k nearest and most similar source patches as candidate patches for each target patch;
the formula for the match error between the defined patches is,
wherein N isTThe number of patches in the target patch set T, D (T)i,Sj) Representing a target patch TiAnd source patch SjError after rigid registration;
and selecting the patch with the minimum matching error from the candidate patches as a matching result according to the formula.
The further supplement and refinement scheme aiming at the step (3) is that in order to realize the migration and full frequency editable of the geometric details of the model surface, a new combination is formed by the IMFs of the optimal patch corresponding to the geometric information with different scales and the signal margin of the corresponding target patch. And model reconstruction is performed according to the new signal, so that the migration of geometric details is realized. Meanwhile, the diversity boundary of the model is realized by adjusting the weight of the IMFs during migration.
Specifically, the information of the intrinsic mode function of the similarity patch is transferred to the corresponding target patch, so that the transfer of the geometric details is realized; meanwhile, full-frequency restoration of the model is implemented by adjusting the weights of the intrinsic mode functions in different layers;
the set of empirical mode decomposition equations defined over the target patch is,
wherein, gTRepresents a function, i.e. a signal, defined on the target patch; t represents a target patch;
comprises the following implementation steps of the following steps of,
firstly, migrating the intrinsic mode function of a source patch to a target patch according to the matching result of the step (2) and the intrinsic mode function information obtained in the step (1) to obtain a new signal defined on the surface of the model;
wherein,to form new signals, fk SBuilt-in modal function information, omega, for similar source patcheskAs a weight corresponding to the scale information, rN TSignal margin for the target patch;
secondly, while generating new signals in the previous step, the Laplace matrix is reconstructed to define LNIs the new laplacian matrix after the initial patch,the components of the matrix corresponding to the vertices inside the model,is the component corresponding to the vertex of the boundary,for newly adding the corresponding component of the vertex, i.e.The constructed new Laplace matrixThe components corresponding to the original Laplace matrix and the internal vertexes of the model are obtained;
and finally, reconstructing a three-dimensional grid model by adopting a Laplace minimum energy method according to the newly constructed signal and the new Laplace matrix, and obtaining different repairing effects, namely the editing effect of the model by adjusting the weight of the intrinsic mode function.
In the step (1), the threshold may be 0.1.
In summary, the full-frequency detail restoration method for the geometric model has the advantages that:
1. the application provides a repairing method based on an EEMD decomposition algorithm, on one hand, full-frequency geometric information can be extracted, full-frequency geometric detail repairing can be performed on a model more conveniently, on the other hand, geometric information is obtained, the migration process only aims at the geometric details, and patches do not need to be copied and pasted integrally, and a simpler and more effective method is provided.
2. Compared with the existing similarity measurement method, the statistical information descriptor related to the adjacent structural features of the damaged region of the model provided by the application reflects not only the local information of the model, but also the global information of the model, and has obvious advantages for describing the patch features.
3. The geometric detail migration process based on the EEMD decomposition algorithm can repair the model, and meanwhile, the model can be edited according to user requirements, so that diversified repair results are obtained, and the geometric detail migration process has a great application prospect in the fields of games and the like.
Drawings
FIG. 1 is a process flow diagram of a full frequency geometry detail restoration method for a mesh model based on adaptive decomposition and anisotropic thermonuclear descriptors;
FIG. 2 shows the result of smoothing the model in step (1) based on the EEMD decomposition method;
FIG. 3 is a schematic diagram of similarity matching results obtained from statistical information descriptors associated with neighboring structural features of a damaged region of a model;
FIG. 4 is a schematic diagram of the repair results of model simple holes;
FIG. 5 is a schematic diagram of a repair result of a model U-shaped cavity model;
fig. 6 is a schematic diagram of the full-frequency editing effect of the model.
Detailed Description
The present application will be further described with reference to the following drawings and examples.
Example 1, as shown in fig. 1, an overall process flow of a data-driven geometric model full-frequency geometric detail restoration method is given,
the geometric model full-frequency detail restoration method is based on EEMD decomposition algorithm to carry out full-frequency detail restoration, and obtains similarity matching results according to statistical information descriptors related to adjacent structural features of a model damage area, and has the characteristics of easiness in operation, high efficiency and high matching precision.
The method mainly comprises the following steps:
step (1) full frequency detail decomposition stage of geometric model
Taking the average curvature as an input signal of the self-adaptive decomposition of the triangular mesh model, decomposing the signal to obtain full-frequency geometric detail information comprising a group of intrinsic mode functions and signal margins; meanwhile, the mesh reconstruction is carried out on the signals only including the signal margin as new signals, and the purpose of model smoothing is achieved.
Step (2) patch model optimal matching stage
Performing model matching on full-frequency characteristics determined by anisotropic heat transfer relationship weight values in different time domains based on adjacent structural characteristics of a model damaged region; by defining a statistical information descriptor related to adjacent structural features of a damaged region of the model, extending an anisotropic descriptor from a vertex descriptor to a descriptor of a patch, effectively searching a similarity patch which is most matched with a target patch, and storing a matching result; that is, according to the newly defined descriptor, on the smooth model subjected to the initial smooth patching, the patch most similar to the target patch at the hole is found.
Step (3), geometric structure information transmission and model full-frequency restoration stage
According to the matching result obtained in the step (2), the full-frequency geometric detail information obtained in the step (1) is migrated to the target patch from the similarity patch; in the migration process, adjusting the weights of intrinsic mode functions in different scales to obtain different signals; and respectively reconstructing the grid model aiming at each signal to obtain different geometric detail repairing results, so that the model can be edited.
In step (1), firstly, the full-frequency geometric detail information of the model needs to be extracted, and meanwhile, the model needs to be subjected to smooth preprocessing. Therefore, the invention defines the average curvature of the surface of the model as a signal, then carries out an adaptive decomposition algorithm (EEMD), obtains the full-frequency geometric detail information of the grid model, and achieves the purpose of smooth preprocessing of the model through the surface reconstruction of the multi-information margin (residual).
The Laplace operator is a second-order differential operator which is used for defining the surface signal of the model and decomposing Laplace, and when the Laplace-Beltrami operator is expanded to a three-dimensional flow pattern surface, the Laplace-Beltrami operator can measure the deviation of the curved surface of the smooth thin plate and record the local information of the model. The discrete Laplace operator has been widely used in geometric model processing operations such as mesh smoothing, mesh model editing, model interpolation, and the like. The invention defines the model surface signal through the Laplace-Beltrami operator, and further carries out EEMD decomposition on the signal.
Defining a triangular mesh model M ═ (V, K), where V denotes the set of vertices: { vi＝(xi,yi,zi)∈R3K contains adjacency information for the edges of the grid model and the patch. By average weighting of vertices in the neighborhood, it can be calculatedDiscrete Laplace operator on the mesh model surface:
wherein N (i) represents a vertex viA ring of near points, Δ represents the laplacian operator, Δ viIs a vertex viThe laplacian of (a).
Adopting the cotangent weight:
ωij＝cotαij+cotβij(2)
at this time, the discrete Laplace vector is parallel to the normal vector of the vertex,
equation (1) will be deformed as: Δ vi＝4|Ai|kini(3)
Wherein, αijAnd βijRepresenting two angles, A, corresponding to the edges (i, j)iI and kiRespectively representing the surface area and the vertex v of a Voronoi latticeiThe average curvature of (d).
The Laplace vector Δ viAnd corresponding vertex normal vector niThe inner product of (d) is defined as the signal of the model surface:
s(vi)＝(Δvi·ni) (4)
this formula can be used as a measure of mean curvature and is dependent on the sampling density.
It is clearly seen that equation (4) has both translation and rotation invariance and can be used as input signal for the EEMD decomposition algorithm. In addition to this, it can be used to efficiently reconstruct mesh models, which are already ubiquitous in the processing of Laplacian surfaces.
In the hole-containing model, information of patches and edges at the hole is missing and there is no mechanism to compensate for surface tension.
Therefore, for the vertex of the hole boundary, a large proportion of tangent components exist in the Laplacian vector calculated by the cotangent weight method through equation (2).
To overcome this problem, the method of Wang et al was used, and the specific processing procedure was as follows:
each boundary vertex viAnd a ring of adjacent points v thereofjJ e N (i) is projected on the normal plane to obtain the corresponding projection point vi' and v‘ jJ ∈ N (i), where N (i) represents a vertex viA ring of adjacent points;
calculating a Laplacian vector on the normal plane:wherein ω isijCalculated by equation (2).
The Laplacian vector calculated by this method is parallel to the normal vector corresponding to the boundary vertex, and the tangent component in the original vector is removed.
One-dimensional EEMD decomposition is applied to a three-dimensional curved surface, and a limited number of intrinsic mode functions IMFs are extracted from functions defined on the three-dimensional surface, and the functions reflect basic modes in data.
Function g defined on the surface of the triangular mesh model: m → R, M represents the mesh model, R represents the set of real numbers, and the decomposition process of EEMD is as follows:
wherein f iskDenotes the kth IMFs, k 1.., N denotes the total number of IMFs, rNRepresenting the corresponding signal margin;
for the function g, if g (v)i) Satisfies the following conditions: g (v)i)≥g(vj)，j∈N(i) Or g (v)i)≤g(vj) J ∈ N (i), then v is callediA maximum point or minimum point of g;
in the decomposition process of the EEMD, the double harmonic function is used as the extension of cubic spline interpolation of the three-dimensional curved surface and can be used for calculating the upper envelope and the lower envelope of the surface of the three-dimensional model. Given a function defined on the surface M of the three-dimensional modelIt is also possible to minimize the function by means of a double harmonic functionThe energy of the thin plate of (a),
the euler-lagrange equation for the above equation is:
wherein, DeltaMAnd representing the Laplace-Beltrami operator on the three-dimensional curved surface M.
Given an interpolation point and corresponding value { (v)i，g(vi) I ∈ C) }, the interpolation function may be calculated by solving the following linear system of equations n × n
L2·φ＝0,s.t.,φ(vi)＝g(vi),i∈C, (8)
Where C is the set of interpolation points for scalar function g, and L is an n × n discrete laplacian matrix whose elements are represented as follows: omega1＝10.0 (9)
Wherein,representing the cotangent mean weight, αijAnd two angles correspond to the edges (i, j), AiIs a vertex ViArea of voronoi (v).
Convergence standard of iterative screening process in order to judge whether the function obtained by screening each time is an intrinsic mode function IMF, the convergence standard of the screening process is determined: for all vertices, twice-through screening results hjAnd hj-1Is less than a certain threshold, the screening is stopped and the current result is determined to be an IMF. The standard deviation is calculated as follows:
where SD denotes the standard deviation between two adjacent signal values, hjAnd hj-1Representing the signal values of two adjacent iterations.
As with the one-dimensional EEMD decomposition, the threshold is typically only in the interval 0.1,0.3, with smaller thresholds, larger numbers of IMFs, and vice versa. The preferred default threshold for this application is 0.1.
The decomposition of the model surface signal EEMD can be performed according to the above description by: setting initial signal allowance as the average curvature of a triangular mesh model, calculating local extreme points of the current allowance each time, interpolating all the extreme points, calculating the average value of upper and lower envelopes, and updating the result of subtracting the average value from the current allowance into a new allowance until the difference between the two allowances is smaller than a specified threshold or exceeds the maximum iteration number; in the process, the difference between two adjacent margins is the IMFs with different scales, and the final margin is the final signal margin.
Mesh model reconstruction from mean curvature
Based on the above, the mean curvature based model surface signal has been decomposed into several IMFs, which can be adjusted as needed to obtain a new signal. The invention aims to realize the grid reconstruction by adopting a least square method with a model original vertex set V as a constraint condition. This method has been widely used in the field of laplace surface treatment, and is calculated by minimizing the secondary energy as follows:
the above energy equation can be modified as:
obviously, the corresponding linear equation set AV' b is
Wherein L represents a discrete laplace matrix; n represents the normal vector matrix of the vertex, mu is the weight factor of the original vertex position, the default value of the invention is 0.1, and In×nThe method is an n multiplied by n unit matrix, s 'is a new signal of a model surface, V is an original point set, and V' is a new vertex set after reconstruction. From fig. 2, it can be seen that the EEMD decomposition not only can extract the geometric information of the model at different scales, but also can smooth the model if filtering out the high-level IMF information.
In the step (2), the statistical information descriptor definition and the similarity patch selection related to the adjacent structural features of the damaged region of the relevant model are obtained through the step (1), the geometric detail information and the signal margin of the model with different scales are obtained, then the grid reconstruction is carried out on the signal margin to obtain a smooth model, and the initial hole repairing is carried out on the model. The invention adopts a similarity measurement method to define a patch descriptor, then searches a source patch most similar to a target patch descriptor, and migrates the geometric detail information thereof to the target patch, thereby realizing the restoration of the geometric details.
The statistical information descriptor related to the adjacent structural features of the model damaged area reflects the inherent features of the mesh vertexes by describing the heat diffusion change of the model surface along with time, so that the statistical information descriptor can be used as a descriptor of the vertex features. At time t equal to 0, a unit heat source x is given, and a thermal kernel function ht(x, y) represents the total heat that propagates from point x to point y at time t. If only the field of point x is considered, the thermal kernel function will be transformed into ht(x, x). Therefore, the heat values in different time domains can provide an effective full frequency characteristic, and anisotropic information of patches is added in the process of constructing the descriptor, so that model matching can be better served.
Given a Riemannian manifold M, the heat at a point at time t is f (x, t), and the heat spread over M is governed by the thermodynamic diffusion equation:
where T (x) is the initial temperature defined at M and Δ is the Laplace-Beltrami operator. When the manifold contains a boundary, it is necessary for a point on the boundary to additionally satisfy f (x,0) being 0,given M in addition, the following equation exists:
wherein HTAs a thermodynamic operator, ht(x, y) can be considered as time t, fromHeat transferred from points x to y.
And (3) performing characteristic decomposition on the thermonuclear to obtain a statistical information descriptor related to the adjacent structural characteristics of the damaged region of the model:
wherein, λ itAnd ΩiRespectively corresponding characteristic values and characteristic functions of the anisotropic Laplace-Beltrami operator, and satisfying the equation: Δ M Ωi＝λitΩi. As is readily apparent from the above equation, the anisotropic heat transfer relationship reflects the geometric features of different scales at a certain vertex on the model, and also reflects the local and global geometric information and the local structural anisotropy information.
The descriptor definition expands point-based descriptor definition to the patch, and adopts a statistical method to define the descriptor of the patch:
wherein, [0,1 ]]Denotes normalization to the interval [0,1 ]]. The descriptor contains the mean and variance of the thermal transfer relationships of all vertices on the patch, and in order to make the descriptor adaptable to different models, three time-domain descriptors are selected, that is, three descriptors are corresponding to each patch, respectively: the entire time domain, 3/4 time domain, 1/2 time domain. In the time domain in the present invention100 time points are sampled as a heat transfer relationship weight vector for one point.
And calculating the distance between the patch descriptors according to the defined descriptors by adopting the Euclidean distance standard, and selecting k nearest and most similar source patches as candidate patches for each target patch.
Wherein the default value of k is 0.1% of the total number of vertices, and from the similar patch candidate set, the most similar patch needs to be selected for detail migration. The match error between patches is defined as follows:
wherein N isTThe number of patches in the target patch set T, S represents the source patch set, D (T)i,Sj) Representing a target patch TiAnd source patch SjBy the error after rigid registration, S (T)i) Representing a target patch TiA corresponding candidate set of similar source patches. It should be noted that in the rigid registration process, the most similar point pair in the anisotropic heat transfer relationship values corresponding to the vertex in the whole time domain is searched as the matching point pair in registration.
Through the above description of the descriptor definition and the similar patch finding process, the similarity matching result as shown in fig. 3 can be obtained. In fig. 3, only the central vertices of the patches are shown and the target hole area is indicated by the shaded portion in the left image and the corresponding similarity matching area calculated by similarity matching is indicated by the shaded portion in the right image. As can be seen from fig. 3, the defined descriptors can get good similarity matching results.
After finding out similar source patches, geometric detail migration and full-frequency model editing at different scale levels need to migrate geometric detail information to target patches. The method of the present invention has been described above, without the need for copying and pasting the source patch, but with the aid of the EEMD decomposition algorithm for the migration of details. In the step (1), the model is subjected to the EEMD decomposition, and geometric Information (IMFs) and signal margins of the model under different scales are obtained, so that only the IMFs information of the source patch needs to be migrated to the target patch, and then surface reconstruction is performed according to a new surface signal formed after migration, so that migration of geometric details is realized. Meanwhile, in the process of IMFs migration, the effect of a full frequency boundary is achieved by controlling the weight of each scale IMF. The invention will give a detailed description of how to implement the migration of geometric details and full frequency editing.
From the equation of the EEMD decomposition in step (1), the EEMD decomposition defined on the target patch can be obtained:
wherein, gTRepresents a function, i.e. a signal, defined on the target patch; t denotes a target patch. Migrating the IMFs of the source patch to the target patch according to the similarity matching result obtained in the step (2), so as to obtain a new signal defined on the surface of the model:
wherein,to form new signals, fk SIMF information, ω, for similar source patcheskIs the weight of the corresponding scale information.
The method described in section (1) will be used to reconstruct the mesh model from the new signal. However, in the reconstruction process, dimensions of the laplacian matrix, the IMFS and the signal margin are all consistent with the number of vertices of the model, the model is initially repaired before the dimension is consistent with the number of vertices of the model, the number of vertices is changed, the IMFS obtained through the EEMD decomposition in the step (1), the signal margin and the laplacian matrix need to be reconstructed, and the signal margin and the laplacian matrix are consistent with the current model. And for the relevant information of the internal vertex of the model, the relevant information is still kept unchanged, and only the information corresponding to the boundary vertex and the newly-added vertex for hole repair needs to be reconstructed.
Definition of LNFor a new laplacian matrix after the initial patch,the components of the matrix corresponding to the vertices inside the model,is the component corresponding to the vertex of the boundary,for adding the component corresponding to the vertex, the following formula is provided,
constructing a new Laplace matrixThe components of the initial laplacian matrix corresponding to the vertices inside the model. And (3) performing surface reconstruction by using the Laplace energy minimization method introduced in the step (1) according to the newly constructed signal, and simultaneously realizing the effect of full-frequency editable by changing the weight of the IMF. Fig. 4 and 5 show the results after migration from the original model to the initial patch and then to the geometric details, wherein (a), (b), (c) and (d) represent the repair results after migration of the original model, the model hole, the initial patch smooth patch and the geometric details, respectively. FIG. 6 shows the effect of full frequency editing, in which (a) represents the initial model, and (b) to (f) represent the weights ω corresponding to three IMFs1,ω2，ω3And taking different repairing effects corresponding to different values.
As shown in the following table, the weight assignment conditions of different editing and repairing results of the bunny model are shown.
| Result \ weight | ω1 | ω2 | ω3 |
| b | 1.0 | 1.0 | 1.0 |
| c | 2.0 | 3.0 | 14.0 |
| d | 3.0 | 3.0 | 3.0 |
| e | 3.0 | 10.0 | 10.0 |
| f | 10.0 | 3.0 | 3.0 |
As is clear from the above table, five different repairing results, b, c, d, e, f in FIG. 6, correspond to different ω1,ω2，ω3Combining weights, known by adjusting weightsAnd the size can obtain diversified repairing effects, so that the repairing of the triangular mesh model can be edited according to different requirements.
It will be understood that modifications and variations can be made by persons skilled in the art in light of the above teachings and all such modifications and variations are intended to be included within the scope of the invention as defined in the appended claims.
Claims (5)
1. A full-frequency detail restoration method for a geometric model is characterized by comprising the following steps: comprises the following implementation steps of the method,
in the step (1), full-frequency detail decomposition of a geometric model, average curvature is used as an input signal of self-adaptive decomposition of a triangular mesh model, and the signal is decomposed to obtain full-frequency geometric detail information comprising a group of intrinsic mode functions and signal margins;
in the patch model optimal matching stage, based on the adjacent structural features of the damaged region of the model, full-frequency features determined by anisotropic heat transfer relationship weighted values in different time domains are used for model matching; by defining a statistical information descriptor related to adjacent structural features of a damaged region of the model, extending an anisotropic descriptor from a vertex descriptor to a descriptor of a patch, effectively searching a similarity patch which is most matched with a target patch, and storing a matching result;
in the stage of geometrical structure information transmission and full-frequency model restoration, full-frequency geometrical detail information obtained in the step (1) is migrated to a target patch from the similarity patch according to the matching result obtained in the step (2); in the migration process, adjusting the weights of intrinsic mode functions in different scales to obtain different signals; and respectively reconstructing the grid model aiming at each signal to obtain different geometric detail repairing results, so that the model can be edited.
2. The full-frequency detail restoration method for the geometric model according to patent claim 1, characterized in that: in the step (1), decomposing the adaptive decomposition input signal of the triangular mesh model based on Ensemble Empirical Mode Decomposition (EEMD);
function g defined on the surface of the triangular mesh model: m → R, M denotes a mesh model, R denotes a set of real numbers,
wherein f iskDenotes the kth IMFs, k 1, N denotes the total number of intrinsic mode functions, rNRepresenting the corresponding signal margin;
the decomposition process is as follows,
first, the extreme point is defined, for the function g, if g (v)i) Satisfies the following conditions: g (v)i)≥g(vj) J ∈ N (i) or g (v)i)≤g(vj) J ∈ N (i), then v is callediA maximum point or minimum point of g;
secondly, finding out extreme points according to the definition of the extreme points in the previous step, constructing upper and lower envelopes by the extreme points, solving the envelopes by using double harmonic interpolation calculation, wherein the double harmonic interpolation is the expansion of spline interpolation on a three-dimensional curved surface and is realized by an energy function defined on a potential manifold curved surface M where a minimized triangular mesh model is positioned,
∫M(ΔMφ)2dV.
the corresponding Lagrange equation isWherein ΔMIs the Laplace-Beltrami operator of the surface M, in particular, for a given interpolation point and corresponding value { (v)i,g(vi) I ∈ C }, and the interpolation function Φ ═ phi (v) }1),φ(v2),...,φ(vn) Can be found by solving the following n × n linear system:
L2·φ＝0,s.t.,φ(vi)＝g(vi),i∈C,
wherein, C is an interpolation set, and L is an n multiplied by n Laplace matrix of a triangular mesh model;
finally, after calculating (whether to delete the word; the convergence standard of the screening is to judge whether the signal after the screening is an intrinsic mode function or not; the end process is to see if the standard deviation SD is less than a given threshold, the standard deviation SD is calculated using two adjacent screening results, the standard deviation SD is formulated as follows,
3. the full-frequency detail restoration method for the geometric model according to patent claim 1, characterized in that: in the step (2), a similarity matching result for the patch is obtained by defining a statistical information descriptor related to adjacent structural features of the damaged region of the model;
given a potential manifold surface M, the following equation exists:
wherein HTAs a thermodynamic operator, ht(x, y) the amount of heat transferred from point x to y at time t;
the matching process is as follows,
firstly, performing characteristic decomposition on thermonuclear to obtain a statistical information descriptor related to adjacent structural characteristics of a model damaged area:
wherein, λ itAnd ΩiRespectively corresponding eigenvalue and sum eigenfunction of Laplace-Bellameter operator, and satisfying equation delta M omegai＝λitΩiAdding the local structure information into the Laplace matrix construction;
secondly, according to the anisotropic heat transfer relationship weight value of the vertex calculated in the previous step, a statistical information descriptor related to the adjacent structural features of the model damage area is defined as follows,
wherein, [0,1 ]]Denotes normalization to the interval [0,1 ]]Selecting a plurality of time domain descriptors, namely each patch corresponds to a plurality of descriptors; in the time domainSampling 100 time points as an anisotropic heat transfer relationship weight vector of one point;
finally, calculating a matching result between patches according to a statistical information descriptor related to adjacent structural features of a defined model damaged area, calculating the distance between patch descriptors by adopting an Euclidean distance standard, and selecting k nearest and most similar source patches as candidate patches for each target patch;
the formula for the match error between the defined patches is,
wherein N isTThe number of patches in the target patch set T, D (T)i,Sj) Representing a target patch TiAnd source patch SjError after rigid registration;
and selecting the patch with the minimum matching error from the candidate patches as a matching result according to the formula.
4. The geometric model full-frequency detail restoration method according to claim 1, characterized in that: in the step (3), the intrinsic mode function information of the similarity patch is transferred to the corresponding target patch, so that the transfer of the geometric details is realized; meanwhile, full-frequency restoration of the model is implemented by adjusting the weights of the intrinsic mode functions in different layers;
the set of empirical mode decomposition equations defined over the target patch is,
wherein, gTRepresents a function, i.e. a signal, defined on the target patch; t represents a target patch;
comprises the following implementation steps of the following steps of,
firstly, migrating the intrinsic mode function of a source patch to a target patch according to the matching result of the step (2) and the intrinsic mode function information obtained in the step (1) to obtain a new signal defined on the surface of the model;
wherein,to form new signals, fk SBuilt-in modal function information, omega, for similar source patcheskAs a weight corresponding to the scale information, rN TSignal margin for the target patch;
secondly, while generating new signals in the previous step, the Laplace matrix is reconstructed to define LNIs the new laplacian matrix after the initial patch,the components of the matrix corresponding to the vertices inside the model,is the component corresponding to the vertex of the boundary,for newly adding the corresponding component of the vertex, i.e.The constructed new Laplace matrixThe components corresponding to the original Laplace matrix and the internal vertexes of the model are obtained;
and finally, reconstructing a three-dimensional grid model by adopting a Laplace minimum energy method according to the newly constructed signal and the new Laplace matrix, and obtaining different repairing effects, namely the editing effect of the model by adjusting the weight of the intrinsic mode function.
5. The geometric model full-frequency detail restoration method according to patent claim 2, characterized in that: the threshold value is 0.1.
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110070096A (en) * | 2019-05-31 | 2019-07-30 | 中国科学院自动化研究所 | Sub- generation method and device are described for the matched local frequency domain of non-rigid shape |
| CN110363759A (en) * | 2019-07-22 | 2019-10-22 | 国家超级计算天津中心 | Three-dimensional mould tuning parameter determines method and device |
| CN110889893A (en) * | 2019-10-25 | 2020-03-17 | 中国科学院计算技术研究所 | Three-dimensional model representation method and system for expressing geometric details and complex topology |
| CN118003031A (en) * | 2024-04-09 | 2024-05-10 | 中国长江电力股份有限公司 | Self-adaptive machining method for material-adding repairing bearing bush |
| TWI847355B (en) * | 2022-10-06 | 2024-07-01 | 杜宇威 | Reconstruction method of three dimensional model and computing apparatus |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101877148A (en) * | 2009-11-13 | 2010-11-03 | 北京航空航天大学 | Method for repairing three-dimensional grid model based on global structure |
| CN105427252A (en) * | 2015-11-06 | 2016-03-23 | 北京航空航天大学 | Mesh model multi-scale geometric detail repair method based on empirical mode decomposition |
| CN108230452A (en) * | 2017-12-18 | 2018-06-29 | 华侨大学 | A kind of model filling-up hole method based on textures synthesis |
| CN108470018A (en) * | 2018-02-22 | 2018-08-31 | 中国铁道科学研究院 | Smoothing method and device based on the intrinsic mode functions that empirical mode decomposition decomposes |
-
2018
- 2018-09-07 CN CN201811043106.4A patent/CN109118589A/en active Pending
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101877148A (en) * | 2009-11-13 | 2010-11-03 | 北京航空航天大学 | Method for repairing three-dimensional grid model based on global structure |
| CN105427252A (en) * | 2015-11-06 | 2016-03-23 | 北京航空航天大学 | Mesh model multi-scale geometric detail repair method based on empirical mode decomposition |
| CN108230452A (en) * | 2017-12-18 | 2018-06-29 | 华侨大学 | A kind of model filling-up hole method based on textures synthesis |
| CN108470018A (en) * | 2018-02-22 | 2018-08-31 | 中国铁道科学研究院 | Smoothing method and device based on the intrinsic mode functions that empirical mode decomposition decomposes |
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110070096A (en) * | 2019-05-31 | 2019-07-30 | 中国科学院自动化研究所 | Sub- generation method and device are described for the matched local frequency domain of non-rigid shape |
| CN110070096B (en) * | 2019-05-31 | 2021-01-12 | 中国科学院自动化研究所 | Local frequency domain descriptor generation method and device for non-rigid shape matching |
| CN110363759A (en) * | 2019-07-22 | 2019-10-22 | 国家超级计算天津中心 | Three-dimensional mould tuning parameter determines method and device |
| CN110889893A (en) * | 2019-10-25 | 2020-03-17 | 中国科学院计算技术研究所 | Three-dimensional model representation method and system for expressing geometric details and complex topology |
| TWI847355B (en) * | 2022-10-06 | 2024-07-01 | 杜宇威 | Reconstruction method of three dimensional model and computing apparatus |
| CN118003031A (en) * | 2024-04-09 | 2024-05-10 | 中国长江电力股份有限公司 | Self-adaptive machining method for material-adding repairing bearing bush |
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