CN100552722C - Method for extracting multi-dimension curvature characteristic on triangle gridding - Google Patents

Abstract

A kind of method for extracting multi-dimension curvature characteristic on triangle gridding belongs to technical field of digital media, and this method is operated according to following process step: the multiple dimensioned net point principal curvature information of a. is estimated; B. the structure of local grid surface geometry descriptor under the particular dimensions; C. grid curvature Feature Extraction under the particular dimensions.This analytical approach is estimated multiple dimensioned net point principal curvature information on the grid, thereby can be extracted the curvature feature that is rich in geological information on the grid model under the particular dimensions ideally by facing the territory principal component analysis.

Description

Method for extracting multi-dimension curvature characteristic on triangle gridding

Technical field

The invention belongs to technical field of digital media, specially refer to the intellectuality that is used for visual media and handle, for multi-dimension curvature feature extracting methods on a kind of triangle gridding.

Background technology

In Digital Media, triangle gridding is a kind of the most common form in the three-dimensional geometry numeral expression.Have benefited from the progress of three-dimensional data acquisition methods such as three-dimensional laser measuring technique, after the eighties of last century DAB of the seventies, the digital picture of the eighties, the digital video of the nineties, from the beginning of this century, digital geometry is as the appearance of a kind of new Digital Media and obtain increasingly extensive application.Compare with the modeling of traditional employing cad technique, use three-dimensional to obtain technology and can obtain high-quality three-dimensional geometry data fast, and do not need the operator to have advanced professional knowledge and complicated operations, greatly promoted popularizing of three-dimensional geometry data, three-dimensional geometry quantitatively still all is greatly improved on the scale.In the discrete expression form of digital geometry for continuous curve surface, triangle gridding is the most general a kind of form, is widely used in aspects such as video display amusement, 3D recreation, virtual reality, cultural heritage protection.Along with continuous advancement in technology is obtained in scanning, having the material object that enriches geometric properties can obtain and modeling by scanning, is converted to triangle grid model, the analysis of geometric properties has wherein been attracted more and more researchers' concern.Its result can be applied in the various fields based on inherent geological information, the fields such as model simplification that for example content-based model index, Model Matching, feature keep.Analysis for grid model curvature feature, it is the focus of foreign study in recent years, but existing method is in the process of extracting feature, do not consider the dimensional properties of curvature, there is not clear and definite division for minutia and coarseness feature, cause the understanding of model comprehensively inadequately, the result of feature extraction can not reflect the geological information that model contains fully.

Summary of the invention

The technical issues that need to address of the present invention are, at in prior art, the analysis of network model curvature feature is not considered the dimensional properties of curvature information, clearly do not divide for minutia and coarseness feature, cause model is understood comprehensive inadequately, feature result extracts many weak points such as undesirable, in order to overcome these deficiencies, just need seek new analytical approach, the object of the present invention is to provide a kind of method for extracting multi-dimension curvature characteristic on triangle gridding.

Also promptly need be based on a kind of multiple dimensioned mesh shape analytical approach, this method can be extracted the grid curvature feature of particular dimensions, as the main description of grid geometry under this yardstick, thereby sets up comprehensive representation to the grid geological information.

For solving the problems of the technologies described above, purpose of the present invention realizes that by the following technical solutions a kind of method for extracting multi-dimension curvature characteristic on triangle gridding is characterized in that: operate according to following process step:

The multiple dimensioned net point principal curvature information of step a. is estimated: by the territory principal component analysis is faced in the part under the grid vertex particular dimensions, obtain principal component information, and estimate principal curvature information according to the progressive analytic relationship of principal component information and curvature;

A1. do convolution with spheric function and derivative function thereof and grid indicative function;

A2. obtain principal component and the anti-principal curvatures of asking by principal component analysis;

A3. obtain the principal curvature information under particular dimensions, calculate Gaussian curvature information by principal curvature information again;

The structure of local grid surface geometry descriptor under the step b. particular dimensions:

B1. with grid vertex according to the descending ordering of Gaussian curvature;

B2. to each grid vertex, make up local frame according to its curvature direction and normal direction;

B3. in local frame, make up the close curved surface of local secondary according to principal curvatures, and extraction and the close curved surface of secondary agree with good local grid surface geometry descriptor;

Grid curvature Feature Extraction under the step c particular dimensions:

C1. to each local grid surface geometry descriptor computation curvature fundamental function value;

C2. the descriptor from curvature fundamental function value maximum begins to carry out the breadth First cluster, obtains the curvature feature of grid model under the particular dimensions.

Based on said method, can carry out shape analysis by the multiple dimensioned curvature feature of extracting, carry out tagsort and feature editor.

Based on said method, can carry out multiple dimensioned Model Matching by the comparison of curvature feature between different models.

Put it briefly, the present invention at first estimates multiple dimensioned net point principal curvature information on the grid by the method for facing the territory principal component analysis; Thereby obtain under particular dimensions and the irrelevant intrinsic geometry amount of rotation translation.Traditional grid Curvature Estimation method is discrete differential method of geometry and local approximating method, and these two kinds of methods all do not have the dimensional properties determined, and the present invention according to a kind of based on the method for facing the territory principal component analysis, estimate the curvature information under the particular dimensions.Obtaining on the basis of curvature information, former grid is resolved into the set of the feature descriptor that can express the local geometric shape, this feature descriptor be the grid part for quadric a kind of form of agreeing with, obtain according to the pass series structure of local curvature constraint.After having constructed grid local feature description symbol, the present invention is by definition curvature fundamental function, and the tangible local geometric features descriptor of aggregation features obtains the curvature feature that grid model under the particular dimensions is rich in geological information.

The invention has the beneficial effects as follows that this analytical approach is estimated multiple dimensioned net point principal curvature information on the grid by facing the territory principal component analysis, thereby can extract the curvature feature that grid model under the particular dimensions is rich in geological information ideally.

Description of drawings

The present invention is further detailed explanation below in conjunction with the drawings and specific embodiments:

Fig. 1 is an extracting method process flow diagram of the present invention.

Fig. 2 is for estimating the synoptic diagram of the curvature information that grid is multiple dimensioned among the present invention.

Fig. 3 shows that the part agrees with the curve form of error.

Embodiment

With reference to Fig. 1, represent extracting method process flow diagram of the present invention.The input data are triangle griddings of arbitrary topology to be analyzed.The present invention is at first by facing the method for territory principal component analysis, and the multiple dimensioned grid curvature information of a estimates, a1 does convolution with spheric function and derivative function thereof and grid indicative function; A2 obtains principal component and the anti-principal curvatures of asking by principal component analysis; A3 calculates Gaussian curvature information based on multiple dimensioned principal curvatures; B is by the constraint type of Gaussian curvature on quadric surface, makes up the grid feature descriptor set of satisfying the local secondary surface constraint, b1 with grid vertex according to the descending ordering of Gaussian curvature; B2 makes up local frame to each grid vertex according to its curvature direction and normal direction; B3 makes up the close curved surface of local secondary according to principal curvatures in local frame, and extraction and the close curved surface of secondary agree with good local grid surface geometry descriptor; According to the curvature fundamental function of definition, the evident characteristic descriptor is carried out polymerization at last; C obtains grid curvature Feature Extraction under the particular dimensions; C1 is to each local grid surface geometry descriptor computation curvature fundamental function value; C2 begins to carry out the breadth First cluster from the descriptor of curvature fundamental function value maximum, obtains the curvature feature of grid model under the particular dimensions.

With reference to the synoptic diagram of Fig. 2 for estimating among the present invention that grid multi-dimension curvature information is estimated.The present invention is by being that the ball at center faces territory (21) and grid interior zone and asks to hand over and obtain the net point part and face territory (22) with the net point.Obtain reflecting that by principal component analysis the part faces the principal component of territory global shape (23) again.And estimate multiple dimensionedly to go up the principal curvature information principal component of grid model and the progressive restriction relation of principal curvatures is by the progressive restriction relation of principal component and principal curvatures:

$M_{b1}^r=\frac{2\mathrm{\π}}{15}{r}^5-\frac{\mathrm{\π}}{48}(3k_1+k_2)r^6+O\left(r^7\right),$

$M_{b2}^r=\frac{2\mathrm{\π}}{15}{r}^5-\frac{\mathrm{\π}}{48}(k_1+{3k}_2)r^6+O\left(r^7\right).$

Make up among the present invention in the expression way of multiple dimensioned grid local feature description symbol set.At first calculate Gaussian curvature information according to the principal curvature information of estimating, the size according to grid vertex Gaussian curvature absolute value makes up the close curved surface of local secondary successively then.

With reference to Fig. 3, represent that each quadric surface agrees with error according to calculating Gaussian curvature with estimation Gaussian curvature measurement part, this error is expressed as the difference of Gaussian curvature between P, the S curve in Yp, Xp coordinate domain, by cumulative errors and interceptive value is set, obtain agreeing with the good grid local feature description symbol of degree with quadric surface.Form a structure that local feature description's symbol of original mesh is covered at last.

The Gaussian curvature computing formula is:

${\hat{K}}_G^q=\frac{k_1{k}_2}{[1+{\left(k_1{q}_x\right)}^2+{\left(k_2{q}_y\right)}^2{]}^2}$

After the feature descriptor covered structure of grid generated, its characterizing definition was the cluster of feature descriptor, and whether feature significantly defines by following curvature fundamental function:

$S\left(F\right)=\underset{d\∈F}{\mathrm{\Σ}}{W}_1\mathrm{Area}\left(d\right)\mathrm{Curu}{\left(d\right)}^3+W_{2}N\left(F\right)\mathrm{Var}\left(F\right)$

By the tangible local geometric features descriptor of aggregation features, obtain the curvature feature of grid model under the particular dimensions, the curvature feature of small scale has reflected the minutia of grid model, the curvature feature of large scale has reflected the coarseness feature of grid model, this yardstick effect has met people and has observed object different feeling from the close-by examples to those far off, and can react the feature of object on different scale, be that three-dimensional feature is more comprehensively explained.

Claims (3)

1. method for extracting multi-dimension curvature characteristic on triangle gridding is characterized in that: according to following process step operation:

A. multiple dimensioned net point principal curvature information is estimated: by the territory principal component analysis is faced in the part under the grid vertex particular dimensions, obtain principal component information, and estimate principal curvature information according to the progressive analytic relationship of principal component information and curvature:

A1. do convolution with spheric function and derivative function thereof and grid indicative function;

A2. obtain principal component and the anti-principal curvatures of asking by principal component analysis;

A3. obtain the principal curvature information under particular dimensions, calculate Gaussian curvature information by principal curvature information again;

B. the structure of local grid surface geometry descriptor under the particular dimensions:

B1. with grid vertex according to the descending ordering of Gaussian curvature;

B2. to each grid vertex, make up local frame according to its curvature direction and normal direction;

B3. in local frame, make up the close curved surface of local secondary according to principal curvatures, and extraction and the close curved surface of secondary agree with good local grid surface geometry descriptor;

C. grid curvature Feature Extraction under the particular dimensions:

C1. to each local grid surface geometry descriptor computation curvature fundamental function value;

C2. the descriptor from curvature fundamental function value maximum begins to carry out the breadth First cluster, obtains the curvature feature of grid model under the particular dimensions.

2. method for extracting multi-dimension curvature characteristic on triangle gridding according to claim 1 is characterized in that: carry out shape analysis by the multiple dimensioned curvature feature of extracting, carry out tagsort and feature editor.

3. method for extracting multi-dimension curvature characteristic on triangle gridding according to claim 1 is characterized in that: by the comparison of curvature feature, carry out multiple dimensioned Model Matching between different models.

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