As the number of 3D models available on the Web grows, there is an increasing need for a search engine to help people find them. Unfortunately, traditional text-based search techniques are not always effective for 3D data. In this paper, we investigate new shape-based search methods. The key challenges are to develop query methods simple enough for novice users and matching algorithms robust enough to work for arbitrary polygonal models. We present a web-based search engine system that supports queries based on 3D sketches, 2D sketches, 3D

Measuring the similarity between 3D shapes is a fundamental problem, with applications in computer vision, molecular biology, computer graphics, and a variety of other fields. A challenging aspect of this problem is to find a suitable shape signature that can be constructed and compared quickly, while still discriminating between similar and dissimilar shapes. In this paper, we propose and analyze a method for computing shape signatures for arbitrary (possibly degenerate) 3D polygonal models. The key idea is to represent the signature of an object as a shape distribution sampled from a shape function measuring global geometric properties of an object. The primary motivation for this approach is to reduce the shape matching problem to the comparison of probability distributions, which is a simpler problem than the comparison of 3D surfaces by traditional shape matching methods that require pose registration, feature correspondence, or model fitting. We find that the dissimilarities be...

this paper, we propose and analyze a method for computing shape signatures for arbitrary (possibly degenerate) 3D polygonal models. The key idea is to represent the signature of an object as a shape distribution sampled from a shape function measuring global geometric properties of an object. The primary motivation for this approach is to reduce the shape matching problem to the comparison of probability distributions, which is simpler than traditional shape matching methods that require pose registration, feature correspondence, or model fitting

Computing reflective symmetries of 2D and 3D shapes is a classical problem in computer vision and computational geometry. Most prior work has focused on finding the main axes of symmetry, or determining that none exists. In this paper we introduce a new reflective symmetry descriptor that represents a measure of reflective symmetry for an arbitrary 3D model for all planes through the model’s center of mass (even if they are not planes of symmetry). The main benefits of this new shape descriptor are that it is defined over a canonical parameterization (the sphere) and describes global properties of a 3D shape. We show how to obtain a voxel grid from arbitrary 3D shapes and, using Fourier methods, we present an algorithm that computes the symmetry descriptor in O(N 4 log N) time for an N × N × N voxel grid and computes a multiresolution approximation in O(N 3 log N) time. In our initial experiments, we have found that the symmetry descriptor is insensitive to noise and stable under point sampling. We have also found that it performs well in shape matching tasks, providing a measure of shape similarity that is orthogonal to existing methods.

In geometric pattern matching, we are given two sets of points P and Q in d dimensions, and the problem is to determine the rigid transformation that brings P closest to Q, under some distance measure. More generally, each point can be modelled as a ball of small radius, and we may wish to nd a transformation approximating the closest distance between P and Q. This problem has many applications in domains such as computer vision and computational chemistry In this paper we present improved algorithms for this problem, by allowing the running time of our algorithms to depend not only on n, (the number of points in the sets), but also on, the diameter of the point set. The dependence on also allows us to e ectively process point sets that occur in practice, where diameters tend to be small ([EVW94]). Our algorithms are also simple to implement, in contrast to much of the earlier work. To obtain the above-mentioned results, we introduce a novel discretization technique to reduce geometric pattern matching to combinatorial pattern matching. In addition, we address various generalizations of the classical problem rst posed by Erdos: \Given a set of n points in the plane, how many pairs of points can be exactly a unit distance apart?". The combinatorial bounds we prove enable us to obtain improved results for geometric pattern matching and may have other applications.

This document contains the draft version of the following paper: A. Cardone, S.K. Gupta, and M. Karnik. A survey of shape similarity assessment algorithms for product design and manufacturing applications. ASME Journal of

Vehicle tracking data is an essential “raw ” material for a broad range of applications such as traffic management and control, routing, and navigation. An important issue with this data is its accuracy. The method of sampling vehicular movement using GPS is affected by two error sources and consequently produces inaccurate trajectory data. To become useful, the data has to be related to the underlying road network by means of map matching algorithms. We present three such algorithms that consider especially the trajectory nature of the data rather than simply the current position as in the typical map-matching case. An incremental algorithm is proposed that matches consecutive portions of the trajectory to the road network, effectively trading accuracy for speed of computation. In contrast, the two global algorithms compare the entire trajectory to candidate paths in the road network. The algorithms are evaluated in terms of (i) their running time and (ii) the quality of their matching result. Two novel quality measures utilizing the Fréchet distance are introduced and subsequently used in an experimental evaluation to assess the quality of matching real tracking data to a road network. 1

Hausdorff metrics are used in geometric settings for measuring the distance between sets of points. They

This paper describes a randomized approach for finding invariants in a set of flexible ligands (drug molecules) that underlies an integrated software system called RAPID currently under development. An invariant is a collection of features embedded in < 3 which is present in one or more of the possible low-energy conformations of each ligand. Such invariants of chemically distinct molecules are useful for computational chemists since they may represent candidate pharmacophores. A pharmacophore contains the parts of the ligand that are primarily responsible for its interaction and binding with a specific receptor. It is regarded as an inverse image of a receptor and is used as a template for building more effective pharmaceutical drugs. The identification of pharmacophores is crucial in drug design since the structure of the targeted receptor is frequently unknown, but a number of molecules that interact with the receptor have been discovered by experiments. It is expected that our techniques and the results produced by our system will prove useful in other applications such as molecular database screening and comparative molecular field analysis.

... of 3D models, the need for retrieval of models has gained prominence in the graphics and vision communities. A variety of methods have been proposed that enable the efficient querying of model repositories for a desired 3D shape. Many of these methods use a 3D model as a query and attempt to retrieve models from the database that have a similar shape. In this paper