Ali Shokoufandeh

Object Recognition as Many-to-Many Feature Matching

Object recognition can be formulated as matching image features to model features. When recognition is exemplar-based, feature correspondence is one-to-one. However, segmentation errors, articulation, scale difference, and within-class deformation can yield image and model features which don’t match one-to-one but rather many-to-many. Adopting a graph-based representation of a set of features, we present a matching algorithm that establishes many-to-many correspondences between the nodes of two noisy, vertex-labeled weighted graphs. Our approach reduces the problem of many-to-many matching of weighted graphs to that of many-to-many matching of weighted point sets in a normed vector space. This is accomplished by embedding the initial weighted graphs into a normed vector space with low distortion using a novel embedding technique based on a spherical encoding of graph structure. Many-to-many vector correspondences established by the Earth Mover’s Distance framework are mapped back into many-to-many correspondences between graph nodes. Empirical evaluation of the algorithm on an extensive set of recognition trials, including a comparison with two competing graph matching approaches, demonstrates both the robustness and efficacy of the overall approach.

REEB GRAPH BASED SHAPE RETRIEVAL FOR CAD

Our recent work has described a framework for matching solid of mechanical artifacts models based on scale-space feature decomposition. In this work we adopt a method of comparing solid models based on Multiresolutional Reeb Graphs (MRG) similarity computations. This method was originally proposed by Hilaga et al. in [1]. Reeb Graph technique applies MRG structure to comparisons of approximate models found in the graphics community, such as polygonal meshes, faceted representation and Virtual Reality Modeling Language (VRML) models. First, we provide a brief review of shape matching using Multiresolutional Reeb Graphs and present an approach to matching solid models. Second, we show the performance of the Reeb Graph technique when handling primitive CAD models, such as cubes and spheres; then we perform experiments with more complex models, such as LEGO models and mechanical parts, and we discuss Reeb Graph technique’s performance on complex CAD models. Third, we emphasize several problems with the existing technique. Finally, we conclude with discussion of future work.

Sentiment classification based on supervised latent n-gram analysis

In this paper, we propose an efficient embedding for modeling higher-order (n-gram) phrases that projects the n-grams to low-dimensional latent semantic space, where a classification function can be defined. We utilize a deep neural network to build a unified discriminative framework that allows for estimating the parameters of the latent space as well as the classification function with a bias for the target classification task at hand. We apply the framework to large-scale sentimental classification task. We present comparative evaluation of the proposed method on two (large) benchmark data sets for online product reviews. The proposed method achieves superior performance in comparison to the state of the art.

The Regularity Lemma and Its Applications in Graph Theory

Szemeredis Regularity Lemma is an important tool in discrete mathematics. It says that, in some sense, all graphs can be approximated by random-looking graphs. Therefore the lemma helps in proving theorems for arbitrary graphs whenever the corresponding result is easy for random graphs. In the last few years more and more new results were obtained by using the Regularity Lemma, and Mso some new variants and generalizations appeared. Komlos and Simonovits have written a survey on the topic [96]. The present survey is, in a sense, a continuation of the earlier survey. Here we describe some sample applications and generalizations. To keep the paper self-contained we decided to repeat (sometimes in a shortened form) parts of the first survey, but the emphasis is on new results.

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.

Landmark Selection for Vision-Based Navigation

Recent work in the object recognition community has yielded a class of interest-point-based features that are stable under significant changes in scale, viewpoint, and illumination, making them ideally suited to landmark-based navigation. Although many such features may be visible in a given view of the robots environment, only a few such features are necessary to estimate the robots position and orientation. In this paper, we address the problem of automatically selecting, from the entire set of features visible in the robots environment, the minimum (optimal) set by which the robot can navigate its environment. Specifically, we decompose the world into a small number of maximally sized regions, such that at each position in a given region, the same small set of features is visible. We introduce a novel graph theoretic formulation of the problem, and prove that it is NP-complete. Next, we introduce a number of approximation algorithms and evaluate them on both synthetic and real data. Finally, we use the decompositions from the real image data to measure the localization performance versus the undecomposed map

Computer-Aided Design of Porous Artifacts

Abstract Heterogeneous structures represent an important new frontier for 21st century engineering. Human tissues, composites, ‘smart’ and multi-material objects are all physically manifest in the world as three-dimensional (3D) objects with varying surface, internal and volumetric properties and geometries. For instance, a tissue engineered structure, such as bone scaffold for guided tissue regeneration, can be described as a heterogeneous structure consisting of 3D extra-cellular matrices (made from biodegradable material) and seeded donor cells and/or growth factors. The design and fabrication of such heterogeneous structures requires new techniques for solid models to represent 3D heterogeneous objects with complex material properties. This paper presents a representation of model density and porosity based on stochastic geometry. While density has been previously studied in the solid modeling literature, porosity is a relatively new problem. Modeling porosity of bio-materials is critical for developing replacement bone tissues. The paper uses this representation to develop an approach to modeling of porous, heterogeneous materials and provides experimental data to validate the approach. The authors believe that their approach introduces ideas from the stochastic geometry literature to a new set of engineering problems. It is hoped that this paper stimulates researchers to find new opportunities that extend these ideas to be more broadly applicable for other computational geometry, graphics and computer-aided design problems.

Local feature extraction and matching partial objects

Abstract A primary shortcoming of existing techniques for hree-dimensional (3D) model matching is the reliance on global information of the model’s structure. Models are matched in their entirety, depending on overall topology and geometry information. A currently open challenge is how to perform partial matching. Partial matching is important for finding similarities across part models with different global shape properties and for the segmentation and matching of data acquired from 3D scanners. This paper presents a Scale–Space feature extraction technique based on recursive decomposition of polyhedral surfaces into surface patches. The experimental results presented in this paper suggest that this technique can potentially be used to perform matching based on local model structure. In our previous work, Scale–Space decomposition has been used successfully to extract features from mechanical artifacts. Scale–Space techniques can be parameterized to generate decompositions that correspond to manufacturing, assembly or surface features relevant to mechanical design. One application of these technique is to support matching and content-based retrieval of solid models. This paper shows how a Scale–Space technique can extract features that are invariant with respect to the global structure of the model as well as small perturbations that 3D laser scanning process introduce. In order to accomplish this, we introduce a new distance function defined on triangles instead of points. We believe this technique offers a new way to control the feature decomposition process, which results in the extraction of features that are more meaningful from an engineering viewpoint. The new technique is computationally practical for use in indexing large models. Examples are provided that demonstrate effective feature extraction on 3D laser scanned models. In addition, a simple sub-graph isomorphism algorithm was used to show that the feature adjacency graphs, obtained through feature extraction, are meaningful descriptors of 3D CAD objects. All of the data used in the experiments for this work is freely available at: http://www.designrepository.org/datasets/ .

Many-to-many graph matching via metric embedding

Graph matching is an important component in many object recognition algorithms. Although most graph matching algorithms seek a one-to-one correspondence between nodes, it is often the case that a more meaningful correspondence exists between a cluster of nodes in one graph and a cluster of nodes in the other. We present a matching algorithm that establishes many-to-many correspondences between nodes of noisy, vertex-labeled weighted graphs. The algorithm is based on recent developments in efficient low-distortion metric embedding of graphs into normed vector spaces. By embedding weighted graphs into normed vector spaces, we reduce the problem of many-to-many graph matching to that of computing a distribution-based distance measure between graph embeddings. We use a specific measure, the earth movers distance, to compute distances between sets of weighted vectors. Empirical evaluation of the algorithm on an extensive set of recognition trials demonstrates both the robustness and efficiency of the overall approach.

Scale-space representation of 3D models and topological matching

Reeb graphs have been shown to be effective for topology matching of 3D objects. Their effectiveness breaks down, however, when the individual models become very geometrically and topologically detailed---as is the case for complex machined parts. The result is that Reeb graph techniques, as developed for matching general shape and computer graphics models, produce poor results when directly applied to create engineering databases.This paper presents a framework for shape matching through scale-space decomposition of 3D models. The algorithm is based on recent developments in efficient hierarchical decomposition of metric data using its spectral properties. Through spectral decomposition, we reduce the problem of matching to that of computing a mapping and distance measure between vertex-labeled rooted trees. We use a dynamic programming scheme to compute distances between trees corresponding to solid models. Empirical evaluation of the algorithm on an extensive set of 3D matching trials demonstrates both robustness and efficiency of the overall approach.