Leonidas J. Guibas

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We investigate the properties of a metric between two distributions, the Earth Mover's Distance (EMD), for content-based image retrieval. The EMD is based on the minimal cost that must be paid to transform one distribution into the other, in a precise sense, and was first proposed for certain vision problems by Peleg, Werman, and Rom. For image retrieval,(More)
Proceedings of the 1998 IEEE International Conference on Computer Vision, Bombay, India We introduce a new distance between two distributions that we call the Earth Mover’s Distance (EMD), which reflects the minimal amount of work that must be performed to transform one distribution into the other by moving “distribution mass” around. This is a special case(More)
We propose a novel point signature based on the properties of the heat diffusion process on a shape. Our signature, called the Heat Kernel Signature (or HKS), is obtained by restricting the well-known heat kernel to the temporal domain. Remarkably we show that under certain mild assumptions, HKS captures all of the information contained in the heat kernel,(More)
Light transport algorithms generate realistic images by simulating the emission and scattering of light in an artificial environment. Applications include lighting design, architecture, and computer animation, while related engineering disciplines include neutron transport and radiative heat transfer. The main challenge with these algorithms is the high(More)
We discuss the following problem: given <italic>n</italic> points in the plane (the &#8220;sites&#8221;), and an arbitrary query point <italic>q</italic>, find the site that is closest to <italic>q</italic>. This problem can be solved by constructing the Voronoi diagram of the given sites, and then locating the query point in one of its regions. We give two(More)
Computer systems commonly cache the values of variables to gain efficiency. In applications where the goal is to track attributes of a continuously moving or deforming physical system over time, caching relations between variables works better than caching individual values. The reason is that, as the system evolves, such relationships are more stable than(More)
Monte Carlo integration is a powerful technique for the evaluation of difficult integrals. Applications in rendering include distribution ray tracing, Monte Carlo path tracing, and form-factor computation for radiosity methods. In these cases variance can often be significantly reduced by drawing samples from several distributions, each designed to sample(More)
Many algorithms for routing in sensor networks exploit greedy forwarding strategies to get packets to their destinations. In this paper we study a fundamental difficulty such strategies face: the “local minimum phenomena” that can cause packets to get stuck. We give a definition of stuck nodes where packets may get stuck in greedy multi-hop forwarding, and(More)
Given a triangulation of a simple polygonP, we present linear-time algorithms for solving a collection of problems concerning shortest paths and visibility withinP. These problems include calculation of the collection of all shortest paths insideP from a given source vertexS to all the other vertices ofP, calculation of the subpolygon ofP consisting of(More)