3D Classification Via Structural Prototypes
We describe a 3D shape classification framework, and discuss the performance of selective and creative prototypes extracted from structural descriptors.
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Abstract. We describe a 3D shape classification framework, and discuss the performance of selective and creative prototypes extracted from structural descriptors.
1
Introduction
Shape classification methods establish the membership of an unknown query shape in one of a set of classes, thus inferring semantic information about the query model. In this paper, we discuss the role of 3D prototypes for shape classification. Prototypes are embedded in a general, dissimilarity-based classification framework. The flow is illustrated in Fig. 1. For each class, a small set of prototypes is defined (a); a query is classified at run-time by matching its descriptor vs. the subset of prototypes (b), thus reducing the search space. Prototypes can be defined in either a selective or a creative manner. In the first case, one or a few class members are chosen to represent the whole class. In the second case, new descriptors are generated. We focus on testing and comparing selective and creative prototypes; in particular, we discuss the creative prototypes in [1].
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Dissimilarity Based 3D Shape Classification
Given a database D with n models classified in disjoint classes, we compute a descriptor Si for each model and consider a dissimilarity measure d between
(a)
(b) Fig. 1. Classification using prototypes extracted from structural descriptors B. Falcidieno et al. (Eds.): SAMT 2007, LNCS 4816, pp. 140–143, 2007. c Springer-Verlag Berlin Heidelberg 2007
3D Classification Via Structural Prototypes
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˜ so descriptors [2]. d is used to derive a query-to-class membership measure d, ˜ that a query is classified by selecting the class which minimizes d. We analyze two classification schemes. The first is based on the Nearest Neighbor (NN) rule. Let N = {1, . . . , n}, and let Nk ⊂ N be the set of in˜ Ck ) is then: dices corresponding to the models in a class Ck . The distance d(Q, ˜ d(Q, Ck ) = mini∈Nk d(SQ , Si ). The second rule uses a set R of t shape prototypes {Pi }, i = 1, . . . , t, with t 1 prototypes are considered: d(Q, k with Tk the set of indices of the t prototypes of the class Ck .
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Selective and Creative Prototypes
We choose selective prototypes according to their degree of similarity to other models, called eccentricity. For each descriptor S ∈ Ck , the eccentricity is: avgCk (S) =
d(S,SR )
, with |Nk | the number of objects in Ck . We can choose as selective prototypes either those minimizing this value (inner models), or those maximizing it (boundary models), or average models, see Sec. 4. Creative prototypes summarize, in a new descriptor, the relevant shape features of a class. The creative prototypes used in this paper (cfr. [1] for details) are extracted from structural descriptors coded as attributed graphs, in our case Extended Reeb Graphs (ERGs) with the geodesic function [3]. For each class, we select a seed model and match it against the remaining class members. We store the resulting editing operations, and apply a subset of them to the seed, that is transformed in a new descriptor (the creative prototype
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