CN102938161B - A kind of 3D shape automatic division method based on Mean Shift - Google Patents

Abstract

The invention provides a kind of based on Mean? the 3D shape automatic division method of Shift, the local feature of each 3D shape grid is obtained by the distance on characterization summit, obtain the centre coordinate of its grid according to the apex coordinate of 3D shape grid, obtain four dimensional feature space combined; Do you adopt Mean? Shift algorithm carries out cluster calculation in aforementioned four dimensional feature space, obtains the unique point that cluster numbers and each cluster comprise; K arest neighbors sorting technique is adopted to carry out decision space modeling to cluster calculation result, local correction segmentation result; Adopt visualization technique that the segmentation result after local correction is carried out coloring treatment according to the mode of cluster attribute flags color, adopt the fiducial error of Princeton segmentation this dividing method of benchmark under difference is measured, thus carry out quantitatively evaluating.The present invention has that segmentation precision is high, automaticity is high, be suitable for the wide feature of 3D shape scope.

Description

A kind of 3D shape automatic division method based on Mean Shift

Technical field

The present invention relates to a kind of automatic division method of 3D shape.

Background technology

Mesh segmentation is the key element of Geometric Modeling and computer graphics study and application, and auxiliary its carries out parametrization, texture, form fit, distortion, many accuracy modelings, the operations such as compression and animation.The understanding of shape and the acquisition of semantic information that represents based on object are depended on to the extraction of the 3D grid characteristic sum structure representing these objects and shape.Become by three-dimensional surface grid auto Segmentation funtion part to be the underlying issue of computer graphics, segmentation can not only provide the semantic information of corresponding object, can also be used for instructing polytype Mesh Processing Algorithm.

In current disclosed document both at home and abroad, MarcoAttene, BiancaFalcidienoandmichelaSpagnuolo, " Hierarchicalmeshsegmentationbasedonfittingprimitives ", TheVisualComputer, propose the partitioning algorithm based on FittingPrimitives in 2006,3D shape is carried out to the segmentation of level.This algorithm completely automatically generates a cluster binary tree, the cluster of each node on behalf by a kind of basic figure as plane, cylinder or the matching of sphere institute.Each triangle surface in 3D shape represents a cluster, in the process of iterating by adjacent cluster to fusion, make the cluster after merging to better being generated new cluster by basic figure institute's matching.The Fusion of Clustering of the bottom-up recurrence of this algorithm, stops when reaching the Segmentation Number of definition.ShymonShlafman, AyelletTalandSagiKatz, " MetamorphosisofPolyhedralSurfacesusingDecomposition ' '; ComputerGraphicsForum, employs the destructing method similar to k-means clustering algorithm in 2002 when being out of shape polygon curved surface.K-means, after Segmentation Number k determines, first selects k seed patch grids as initial cluster center at body surface, then carries out recursive operation: 1) distributed to by all dough sheets from its nearest cluster centre; 2) calculate the average point of each cluster, initial cluster center is moved to average point, be used as new cluster centre; Until cluster centre and its average very close to time stop recurrence.K-means carries out cluster at feature space, and adopt Euclidean distance as similarity measurement, make the similarity in cluster between unique point the highest, the similarity of different cluster is minimum.By unique point and 3D shape polygonal mesh relation one to one, 3D shape is divided into significant funtion part.

But the dividing method of above-mentioned two kinds of 3D shapes has some not enough:

3D grid method for segmenting objects based on FittingPrimitives is only suitable for three-dimensional CAD model, segmentation number needs predefined, because algorithm uses the basic figure such as plane, curved surface to carry out matching to 3D shape, its error of fitting is comparatively large, and segmentation effect is bad.

Dividing method based on k-means needs artificial definition segmentation number, and when splitting multiple 3D shape, need to set gradually segmentation number, automaticity is low, and in addition, segmentation precision is low.

Summary of the invention

In order to overcome prior art robotization poor performance, the scope of application is little, segmentation precision is low deficiency, the invention provides a kind of 3D shape automatic division method based on meanshift, this dividing method can carry out auto Segmentation to the three-dimensional model of generic object and cad model.First, in order to obtain local attribute's characteristic sum geometric position feature of 3D shape, calculating shapediameter value and the centre coordinate of each patch grids in 3D shape respectively, forming four dimensional feature space of shapediameter and geometric coordinate combination.Then, use meanshift algorithm to carry out constrained clustering in four-dimensional assemblage characteristic space, obtained the segmentation of 3D shape by the corresponding relation of unique point and patch grids, cutting part mark is equal with cluster number.The present invention adopts k nearest neighbor classification to carry out local correction to segmentation result, then by visualized operation, abstract data is converted to 3-D view intuitively, then utilizes reference measures to carry out quantitatively evaluating.The present invention can carry out auto Segmentation to 3D shape, and splits number without the need to specifying in advance.

The technical solution adopted for the present invention to solve the technical problems comprises the following steps:

(1) obtained the local feature of each 3D shape grid by the distance on characterization summit, obtain the centre coordinate of its grid according to the apex coordinate of 3D shape grid, obtain four dimensional feature space combined;

(2) adopt Meanshift algorithm to carry out cluster calculation in aforementioned four dimensional feature space, obtain the unique point that cluster numbers and each cluster comprise;

(3) the cluster calculation result of K arest neighbors sorting technique to step (2) is adopted to carry out decision space modeling, local correction segmentation result;

(4) adopt visualization technique that the segmentation result after local correction is carried out coloring treatment according to the mode of cluster attribute flags color, adopt the fiducial error of Princeton segmentation this dividing method of benchmark under difference is measured, thus carry out quantitatively evaluating.

The invention has the beneficial effects as follows:

Present invention achieves a kind of automatic division method of 3D shape, the method can extract local attribute feature shapediameter and the geometric position feature of 3D shape, four dimensional feature space are combined into shapediameter after giving weight to centre coordinate, meanshift method uses k nearest neighbor classification to carry out local correction to segmentation result after feature space carries out constrained clustering, thus realizes the auto Segmentation of 3D shape.First, the 3D shape shapediameter feature that the present invention extracts can adapt to the rigid deformation of three-dimensional body and not change the non-rigid deformation of local volume, while the shortening feature extraction time, obtain good robustness; Secondly, the present invention introduces geometric properties at feature space, the parts that geometric position falls far short can be avoided to be segmented in situation together, greatly increase segmentation precision as space constraint; Again, the present invention adopts k nearest neighbor classification to carry out local correction to segmentation result, improves the slickness of partitioning boundary and the accuracy of segmentation result.Finally, the present invention adopts visualization technique and Princeton segmentation benchmark, and advantage is: 1) clearly show the 3D shape after segmentation, be convenient to carry out visual analysis; 2) calculate the error of the present invention under different measuring standard, make quantitative analysis have cogency and comparability; 3) by the combination of visual analysis and quantitatively evaluating, the performance of the method is made to obtain more clear specific description.Description of test, the three-dimensional automatic division method that the present invention proposes, have segmentation precision high, automaticity is high, is suitable for the feature that 3D shape scope is wide.

Accompanying drawing explanation

Fig. 1 is the general flow chart that this invention realizes;

Fig. 2 is calculating and the combination flow chart of feature;

Fig. 3 is the segmentation flow process based on meanshift;

Fig. 4 is the local correction process based on k arest neighbors;

Fig. 5 is the simple description of result visualization process;

Fig. 6 is the procedural representation of quantitatively evaluating.

Embodiment

The present invention includes following step:

(1) calculating of 3D shape local feature and geometric properties and combination.

The present invention obtains the local feature of each 3D shape grid by the distance on characterization summit, obtains the centre coordinate of its grid according to the apex coordinate of 3D shape, obtains four dimensional feature space combined.The present invention adopts the weighted mean of 3D grid summit spacing to obtain the local feature of 3D shape, local attribute shapediameter can not change along with the rigid transformation of three-dimensional body and the non-rigid deformation not changing shape local volume, can substantially by each for 3D shape parts separately, geometric properties combines as space constraint and shapediameter, makes cluster more accurate.

(2) adopt Meanshift algorithm in the cluster of feature space.

The present invention will carry out cluster calculation in aforementioned four dimensional feature space.Meanshift is a kind of unsupervised clustering, does not need to learn data and cluster number is determined automatically by algorithm.The present invention passes through the window size of gaussian radial basis function kernel function determination unique point, simultaneously using the Euclidean distance between unique point as measuring, for unique point gives different weight.Recursive calculation goes out the convergency value of each unique point, the unique point converging to identical value is gathered in a cluster.Recurrence terminates to obtain the unique point that the cluster numbers that generates and each cluster comprise.

(3) local correction of segmentation result.

The segmentation result of K arest neighbors sorting technique to step (2) is adopted to carry out decision space modeling.The cluster attribute of unique point corresponding to polygonal mesh is determined by the cluster attribute of k the unique point nearest with its Euclidean distance.Feature space cluster makes 3D shape obtain primary segmentation, and unique point is all marked as certain cluster, and in local correction process, unique point needs keeping original cluster and changing between new cluster making a policy.

(4) the visual and quantitatively evaluating of segmentation result.

The present invention adopts visualization technique that revised segmentation result is carried out coloring treatment according to the mode of cluster attribute flags color, makes abstract data with the display of concrete 3-D view, can observe its segmentation effect intuitively.In addition, the present invention introduces the fiducial error of Princeton segmentation this dividing method of benchmark under difference is measured, thus carries out quantitatively evaluating.

Below in conjunction with drawings and Examples, the present invention is further described.

As shown in Figure 1, the present invention realizes the main-process stream of 3D shape auto Segmentation, and this flow process contains each key step realizing auto Segmentation and evaluation.In the segmentation stage, a given Three Mesh, calculate the attributive character shapediameter of each patch grids of 3D shape and the geometric coordinate feature of grid element center, then give two kinds of Feature Combinations after optimal weight to geometric coordinate, by using meanshift, constrained clustering is carried out to unique point and 3D grid is divided into several funtion part, adopt k nearest neighbor classification to carry out local correction to result, obtain 3D shape and split more accurately.At evaluation phase, utilize visualization technique clearly to show segmentation result, adopt Princeton segmentation benchmark measurement error simultaneously, the performance of this dividing method is described from the angle of statistics.Therefore, the present invention can realize auto Segmentation to 3D shape and quantitatively evaluating.

By reference to the accompanying drawings, elaborate below concrete implementation step.

The calculating of attributive character and geometric properties and combination

The present invention supposes that 3D shape to be split is showed by polygonal mesh, and each grid is made up of according to topological relation summit, limit, polygon.The present invention obtains the local feature of each grid by the shapediameter on characterization summit, calculates each net center of a lattice geometric coordinate simultaneously.Shapediameter is local attribute's feature that the volume of partial 3 d shape and surface can be coupled together, all stable to the rigid transformation of whole mesh and the non-rigid transformation that do not change local shape, and there is calculating fast, the good feature of robustness.Launch one group of ray in the circular cone that Shapediameter is determined towards coning angle by vector reverse direction from grid vertex along this vertex scheme, this group ray is crossing with the inside surface of three-dimensional model, and every bar ray has intersection point p _iwith length r _i, ray length is this summit and intersection point p _ieuclidean distance.Obtain the average length r of this group ray _mand standard deviation sigma, obtain ray length scope weight is given to the every bar ray in scope, weight is the inverse of this ray and circular cone centerlines, the weighted mean value calculating these ray length obtains the shapediameter value on summit, is averaging to the polygon vertex shapediameter of composition 3D shape the local feature value obtaining each grid.Shapediameter value represents 3D shape local thickness characteristic, part thicker on larger shapediameter value corresponding three-dimensional object; Otherwise, then corresponding thinner part.

3D shape thickness may consistent but parts that geometric position differs greatly combine by independent employing shapediameter, make the segmentation effect of 3D shape undesirable, and geometric properties is as space constraint, can avoid above-mentioned situation well.Geometric properties is represented by the grid element center coordinate of 3D shape, and the position of each part of 3D shape can be clearly described, has vital role to the accurate segmentation of 3D shape.Grid element center coordinate, by acquisition of averaging to the summit of this grid of composition, calculates fast, consuming time few.

Widely, its geometrical construction is also not quite similar the 3D shape of current use.For the three-dimensional body of certain type, first the simple degree of accuracy adopting shapediameter segmentation is estimated by analyzing its geometrical property, then give certain weight to geometric properties the two is combined, by observing the weight of visual segmentation result amendment geometric properties, make segmentation effect best.Due to shapediameter have not with whole mesh rigid transformation and do not change the non-rigid transformation of local shape and the characteristic changed, for action or the slightly different isomorphism 3D shape of posture, the weights of geometric properties are substantially constant.

One, the cluster of feature space

Form four-dimensional assemblage characteristic space by step 1) calculating shapediameter value and centre coordinate, adopt meanshift to carry out constrained clustering to unique point.Identical with k-means, Meanshift is also non-Supervised Clustering Methods, and do not need to be come data manipulation by study, cluster has been come by iterative computation.Difference is, k-means is parametrization clustering algorithm, and algorithm needs given cluster number k before performing.And meanshift is imparametrization clustering algorithm, cluster number does not need to determine in advance, is automatically obtained by algorithm.Meanshift algorithm is an iterative process, to each unique point, first calculates the skew average of this point, this point is moved to its skew average place, continues mobile as new starting point, until skew average and current starting point very close to time stop.Then the unique point moving to same offset average is classified as one group, completes cluster.In addition, in algorithm, introduce kernel function, make unique point have different weight according to it from the Euclidean distance of current new starting point.By reference to the accompanying drawings 3, the cutting procedure based on meanshift method is described:

From a v, calculate the skew average of further feature point-to-point v, k is kernel function, and each point has different weights according to its distance to some v; W is weighting function, characterizes the importance of each unique point.

$m\left(x\right)=\frac{\mathrm{\Σk}(x-x_i)x_i\·w\left(x_i\right)}{\mathrm{\Σk}(x-x_i)w\left(x_i\right)}$

2) skew average and the difference e putting v is calculated:

e＝m(x)-x

If when e is less than threshold value θ, perform step 4); If when being greater than threshold value θ, perform step 3);

3), when mean distance current point of drifting about is far away, need to continue recursive calculation.M (x) is used as new starting point:

x←m(x)

Repeat step 1);

4) according to 3D shape vertex index order traversal unique point, whether judging characteristic point all calculates, if do not have, then regards the some p do not calculated as a some v, performs step 1); Otherwise algorithm terminates.

What cluster process obtained is is divided into the unique point of several groups, due to the grid one_to_one corresponding of unique point and 3D shape, in fact the grid of 3D shape be divide into several groups according to its shapediameter characteristic sum geometric relationship, namely 3D shape is split into several part, and each part represents a functional part of 3D shape.In addition, by giving the mode of each cluster distributing labels in cluster process, all unique points being marked, is convenient to carry out visualized operation to data point.

Introduce kernel function in Meanshift method, in the present invention, adopt gaussian radial basis function kernel function:

Xc represents that current signature point v, x represent other unique points, and Gaussian parameter σ is also referred to as bandwidth or window, and control the feature point number close with current signature point, conventional h represents.

Two, based on the local correction of k arest neighbors

By step 2) primary segmentation, unique point is divided into different clusters, now adopts k arest neighbors sorting algorithm to carry out local correction to segmentation result.For each grid f of 3D shape, according to the topological structure of model, first find out a ring neighborhood grid F of this grid ₁={ f _i, then by each grid f in calculating one ring Neighbourhood set _ia ring neighborhood grid F _i1={ f _ij, obtain the two ring Neighbourhood set F of this grid f ₂={ f _j.Set of computations F ₂the cluster of middle most of grid decides the cluster of grid f.Calculating due to grid two ring neighborhood is based upon on a ring neighborhood, suitable data structure need be adopted to store a ring adjacent region data, chained list is a kind of effective method: the grid of 3D shape represents with node, uses the forwarding pointer of node and backwarding pointer to be got up by all data cube computation.K nearest neighbor algorithm itself is simple is effectively a kind of lazylearning algorithm, and sorter does not need to use training set to train, therefore training time complexity is 0, and in computation complexity and training set, data point number is linear.

Primary segmentation is classified to each grid of 3D shape, when using k arest neighbors correction, calculates the two ring neighborhood F of grid f ₂={ f _j, in two ring neighborhoods, calculate the maximum cluster C of number _maxtimes N _maxand the cluster C after primary segmentation belonging to f _fat F ₂the times N of middle appearance _f.Grid f makes decisions between two cluster attributes: when occurring N _max> α N _ftime (α>=1), grid f belongs to cluster C _max; Otherwise grid f still belongs to cluster C _f.Wherein α artificially can determine according to actual conditions, and the sensitivity of local correction effect becomes inverse linear relationship with the size of α.

Another effect of K arest neighbors classification is smooth to 3D shape partitioning boundary.In 3D shape segmentation, dividing method operates for polygonal mesh, and cut-off rule connects along the limit of polygonal mesh, and due to the junction of the normally multiple funtion part in border, the probability of generation cluster mistake is very high.By using k arest neighbors, local correction is carried out to boundary grid and can avoid above-mentioned situation preferably, thus make partitioning boundary more smooth.

Three, segmentation result is visual

No matter be feature calculation, cluster computing or local correction are all process data, due to the abstractness of data, the result that above process performs just 3D shape be divide into several funtion part and polygonal mesh belongs to certain part, but intuitively cannot arrive segmentation result.Visualization technique is adopted to be shown by segmentation result: for the 3D shape split, its segmentation number and the shape belonging to each grid are determined, first by shape and color one_to_one corresponding, then according to the indexed sequential traversal grid of polygonal mesh in 3D shape, give each grid mark color according to segmentation result and show.Use grid element center point to replace polygonal mesh in the present invention, use visualization technique to be displayed by the segmentation result of three-dimensional model, flow process as shown in Figure 5.Visual abstract data is converted into image image shows out, make segmentation result very clear, make the identification of 3D shape and the visual evaluation of segmentation result be more prone to further.During visual evaluation, the segmentation result of 3D shape and artificial cognition are compared, the performance of this dividing method can be judged substantially.

Utilize clustering algorithm can obtain the tag types of cluster number and each unique point, therefore time painted to discrete polygonal mesh central point, in the set of whole unique point, recursively search the unique point being labeled as certain label, they are represented by certain color, until all unique points are all colored.When 3D shape is visual, with the geometric coordinate of each grid element center of reading in for base, give certain color by each grid element center.The geometric coordinate of grid element center obtains when step 1) feature calculation.

Four, the quantitatively evaluating of segmentation result

Step 4), having carried out visual evaluation to segmentation result is visual simultaneously, generally can estimate the performance of partitioning algorithm.When different dividing method is split identical 3D shape, can estimate according to visual evaluation the quality that two kinds of methods split this shape, but can not illustrate that the performance of two partitioning algorithms is good and bad; And use two kinds of dividing methods to split same shape data collection respectively, then the mode of carrying out visual comparison to evaluate two kinds of method performances is one by one then too loaded down with trivial details, it is very easy at this moment using certain evaluation to measure and comparing.The segmentation benchmark that Princeton University proposes is used in the present invention, meanshift dividing method is used to split the 3D shape in Princeton segmentation benchmark database, on this basis, calculate four measurement errors of this dividing method, the performance of this dividing method is described from the angle of statistics.

Princeton segmentation benchmark comprises shape database and calculates related data and the software of four measurement errors.What database comprised is 19 class 3D shapes, and each type comprises the identical but action of 20 kinds or the different 3D shape of local shape.Four tolerance are cutdiscrepancy (CD) criterion, hammingdistance (HD) criterion, randindex (RI) criterion and consistencyerror (CE) criterion respectively.Cutdiscrepancy criterion analyzes the close degree of the partitioning boundary that two kinds of algorithms obtain, and is the reference measures based on border; And hammingdistance, randindex and consistencyerror are the measuring standards based on region, measure the internal consistency of two kinds of algorithm gained segmentations.Also comprise the multiple artificial segmentation result of each model in pattern library, Standard Segmentation algorithm can be used as.When evaluating meanshift dividing method, for each 3D shape, itself and each artificial segmentation is substituted into calculate and just tries to achieve four fiducial error values respectively, calculate each mean value measuring lower fiducial error, obtain four measurement errors that the method splits this shape.Due to artificially segmentation be taken as benchmark segmentation, when meanshift dividing method and artificial ratio of division comparatively time, the less expression segmentation performance of measurement error is better.

In order to carry out quantitative estimation to meanshift partitioning algorithm, first this dividing method is used to split 19 class, 380 3D shapes in pattern library, afterwards 380 segmentation results are brought in software and calculate fiducial error value, owing to having multiple artificial dividing method for Arbitrary 3 D shape, therefore to each 3D shape, calculate four fiducial errors of meanshift partitioning algorithm relative to each artificial segmentation successively, in measuring often kind, multiple fiducial error is averaging, and finally obtains meanshift partitioning algorithm to four of this shape measurement errors.The measurement error of 380 3D shapes is obtained by interative computation.Its four metric averaging values of measuring lower 20 objects are asked respectively to every class 3D shape, the error amount of 19 type objects respectively under four measuring standards can be obtained.Then under four benchmark metric, 19 measurement errors are averaging, obtain the segmentation error of this dividing method in this three-dimensional shape data storehouse, very directly can carry out quantitative estimation to meanshift dividing method by these four measurement error values.

Effect of the present invention can be further illustrated by experiment below.Experimental data is from U.S. PrincetonUniversitySegmentationBenchmark, and this three-dimensional shape data collection comprises the 19 class universal models such as people, animal, machinery, the artwork altogether.Use meanshift dividing method to split rear substitution software to the 3D shape of 380 in database and calculate acquisition four measurement errors, successively four fiducial errors are averaging by bottom-up, obtain the measurement error of this dividing method to this 3D shape pattern library.Equally, the dividing method based on fittingprimitives and the dividing method based on k-means is used to split these 380 shapes respectively, obtain measurement error by iterative computation, utilization measure error amount carries out quantification to three kinds of dividing methods and compares, as table 1.

	CD	HD	RI	CE
					Fitting primitives	0.340	0.230	0.203	0.140
k-means	0.405	0.265	0.230	0.160
					Mean shift	0.340	0.225	0.233	0.113

Table 1 the present invention compares with the quantification of other dividing methods

Quantize relatively as can be seen from table 1, the quantization error of the 3D shape automatic division method that the present invention proposes is less than the quantization error of other two kinds of dividing methods, this partitioning algorithm that the present invention is proposed has certain superiority, there is good segmentation performance, in addition, this invention does not need the number of specifying segmentation before segmentation is carried out, and has higher automatism.The preferred embodiment of the present invention described in above entirety, those skilled in the art under the premise without departing from the principles of the invention, can make some improvement, comprise the kernel function etc. changing meanshift, scope of the present invention is by appended claims and equivalency thereof.

Claims (1)

1., based on a 3D shape automatic division method of MeanShift, it is characterized in that comprising the steps:

(1) obtained the local shape thickness feature of each 3D shape grid by the distance on characterization summit, obtain the centre coordinate of its grid according to the apex coordinate of 3D shape grid, obtain the four-dimensional assemblage characteristic space of weighting;

(2) adopt Meanshift algorithm to carry out cluster calculation in the four-dimensional assemblage characteristic space of aforementioned weighting, obtain the unique point that cluster numbers and each cluster comprise; Wherein Meanshift algorithm adopts gaussian radial basis function kernel function: x _crepresent that current signature point v, x represent other unique points, Gaussian parameter σ, also referred to as bandwidth or window, controls the feature point number close with current signature point;

(3) the cluster calculation result of K arest neighbors sorting technique to step (2) is adopted to carry out decision space modeling, local correction segmentation result;

(4) adopt visualization technique that the segmentation result after local correction is carried out coloring treatment according to the mode of cluster attribute flags color, adopt the fiducial error of Princeton segmentation this dividing method of benchmark under difference is measured, thus carry out quantitatively evaluating.