Diego Macrini

Retrieving articulated 3-d models using medial surfaces and their graph spectra

We consider the use of medial surfaces to represent symmetries of 3-D objects. This allows for a qualitative abstraction based on a directed acyclic graph of components and also a degree of invariance to a variety of transformations including the articulation and deformation of parts. We demonstrate the use of this representation for both indexing and matching 3-D object models. Our formulation uses the geometric information associated with each node along with an eigenvalue labeling of the adjacency matrix of the subgraph rooted at that node. We present comparative results against the techniques of shape distributions [17] and harmonic spheres [12] on a database of 320 models representing 13 object classes. The results demonstrate that medial surface based graph matching significantly outperforms these techniques for objects with articulating parts.

View-based 3-D object recognition using shock graphs

The shock graph is an emerging shape representation for object recognition, in which a 2-D silhouette is decomposed into a set of qualitative parts, captured in a directed acyclic graph. Although a number of approaches have been proposed for shock graph matching, these approaches do not address the equally important indexing problem. We extend our previous work in both shock graph matching and hierarchical structure indexing to propose the first unified framework for view-based 3-D object recognition using shock graphs. The heart of the framework is an improved spectral characterization of shock graph structure that not only drives a powerful indexing mechanism (to retrieve similar candidates from a large database), but also drives a matching algorithm that can accommodate noise and occlusion. We describe the components of our system and evaluate its performance using both unoccluded and occluded queries. The large set of recognition trials (over 25,000) from a large database (over 1400 views) represents one of the most ambitious shock graph-based recognition experiments conducted to date.

Canonical Skeletons for Shape Matching

Skeletal representations of 2-D shape, including shock graphs, have become increasingly popular for shape matching and object recognition. However, it is well known that skeletal structure can be unstable under minor boundary deformation, part articulation, and minor shape deformation (due to, for example, small changes in viewpoint). As a result, two very similar shapes may yield two significantly different skeletal representations which, in turn, will induce a large matching distance. Such instability occurs both at external branches as well as internal branches of the skeleton. We present a framework for the structural simplification of a shapes skeleton which balances, in an optimization framework, the desire to reduce a skeletons complexity by minimizing the number of branches, with the desire to maximize the skeletons ability to accurately reconstruct the original shape. This optimization yields a canonical skeleton whose increased stability yields significantly improved recognition performance

The representation and matching of categorical shape

We present a framework for categorical shape recognition. The coarse shape of an object is captured by a multiscale blob decomposition, representing the compact and elongated parts of an object at appropriate scales. These parts, in turn, map to nodes in a directed acyclic graph, in which edges encode both semantic relations (parent/child) as well as geometric relations. Given two image descriptions, each represented as a directed acyclic graph, we draw on spectral graph theory to derive a new algorithm for computing node correspondence in the presence of noise and occlusion. In computing correspondence, the similarity of two nodes is a function of their topological (graph) contexts, their geometric (relational) contexts, and their node contents. We demonstrate the approach on the domain of view-based 3-D object recognition.

Many-to-Many Feature Matching in Object Recognition

One of the bottlenecks of current recognition (and graph matching) systems is their assumption of one-to-one feature (node) correspondence. This assumption breaks down in the generic object recognition task where, for example, a collection of features at one scale (in one image) may correspond to a single feature at a coarser scale (in the second image). Generic object recognition therefore requires the ability to match features many-to-many. In this paper, we will review our progress on three independent object recognition problems, each formulated as a graph matching problem and each solving the many-to-many matching problem in a different way. First, we explore the problem of learning a 2-D shape class prototype (represented as a graph) from a set of object exemplars (also represented as graphs) belonging to the class, in which there may be no one-to-one correspondence among extracted features. Next, we define a low-dimensional, spectral encoding of graph structure and use it to match entire subgraphs whose size can be different. Finally, in very recent work, we embed graphs into geometric spaces, reducing the many-to-many graph matching problem to a weighted point matching problem, for which efficient many-to-many matching algorithms exist.

Object categorization and the need for many-to-many matching

Object recognition systems have their roots in the AI community, and originally addressed the problem of object categorization. These early systems, however, were limited by their inability to bridge the representational gap between low-level image features and high-level object models, hindered by the assumption of one-to-one correspondence between image and model features. Over the next thirty years, the mainstream recognition community moved steadily in the direction of exemplar recognition while narrowing the representational gap. The community is now returning to the categorization problem, and faces the same representational gap as its predecessors did. We review the evolution of object recognition systems and argue that bridging this representational gap requires an ability to match image and model features many-to-many. We review three formulations of the many-to-many matching problem as applied to model acquisition and object recognition.

Spectral Methods for View-Based 3-D Object Recognition Using Silhouettes

The shockg raph is an emerging shape representation for object recognition, in which a 2-D silhouette is decomposed into a set of qualitative parts, captured in a directed acyclic graph. Although a number of approaches have been proposed for shock graph matching, these approaches do not address the equally important indexing problem. We extend our previous workin both shock graph matching and hierarchical structure indexing to propose the first unified framework for view-based 3-D object recognition using shock graphs. The heart of the framework is an improved spectral characterization of shock graph structure that not only drives a powerful indexing mechanism (to retrieve similar candidates from a large database), but also drives a matching algorithm that can accommodate noise and occlusion. We describe the components of our system and evaluate its performance using both unoccluded and occluded queries. The large set of recognition trials (over 25,000) from a large database (over 1400 views) represents one of the most ambitious shockg raph-based recognition experiments conducted to date. This paper represents an expanded version of [12].

3D Model Retrieval Using Medial Surfaces

Graphs derived from medial representations have been used for 2D object matching and retrieval with considerable success (Pelillo et al., 1999; Siddiqi et al., 1999b; Sebastian et al., 2001). In this chapter we consider consider the use of graphs derived from medial surfaces for 3D object matching and retrieval. The medial reprsentation allows for a qualitative abstraction based on a directed acyclic graph of components and also a degree of invariance to a variety of transformations including the articulation of parts. The formulation discussed in this chapter uses the geometric information associated with each node along with an eigenvalue labeling of the adjacency matrix of the subgraph rooted at that node. Comparative retrieval results are presented against the techniques of shape distributions (Osada et al., 2002) and harmonic spheres (Kazhdan et al., 2003b) on 425 models representing 19 object classes. These results demonstrate that medial surface based graph matching outperforms these techniques for objects with articulating parts.