the synthesis and analysis of motion data tractable, we present a low-dimensional motion space in which high-dimensional human motion can be effectively visualized, synthesized, edited, parameterized, and interpolated in both spatial and temporal domains. Our system allows users to create and edit the motion

We present several approximation algorithms for the problem of embedding metric spaces into a line, and into the two-dimensional plane. We give an O ( √ n)approximation algorithm for the problem of finding a line embedding of a metric induced by a given unweighted graph, that minimizes

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This paper presents two models of audio key finding: a template based correlational model and a template based model that uses a low-dimensional tonal representation. The first model uses a confidence weighted correlation to find the most probable key. The second model is distance based and employs

, that minimizes the (standard)multiplicative distortion. We give an improved ~ O(n1/3)approximation for the case of metrics generated by unweighted trees. This is the first result of this type. 1 Introduction Embedding distance matrices into geometric spaces(most notably, into low-dimensional spaces) is a

is highly desirable. In this paper, we investigate various statistical distance measures from the point of view of discovering low distortion embeddings into low-dimensional spaces. More specifically, we consider the Mahalanobis distance measure, the Bhattacharyya class of divergences and the Kullback

2 Approximation Algorithms for Low-Distortion Embeddings

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This paper proposes a two-level 3D human pose tracking method for a specific action captured by several cameras. The generation of pose estimates relies on fitting a 3D articulated model on a Visual Hull generated from the input images. First, an initial pose estimate is constrained by a low

A new motion planning method for robots in static workspaces is presented. This method proceeds in two phases: a learning phase and a query phase. In the learning phase, a probabilistic roadmap is constructed and stored as a graph whose nodes correspond to collision-free configurations and whose edges correspond to feasible paths between these configurations. These paths are computed using a simple and fast local planner. In the query phase, any given start and goal configurations of the robot are connected to two nodes of the roadmap; the roadmap is then searched for a path joining these two nodes. The method is general and easy to implement. It can be applied to virtually any type of holonomic robot. It requires selecting certain parameters (e.g., the duration of the learning phase) whose values depend on the scene, that is the robot and its workspace. But these values turn out to be relatively easy to choose, Increased efficiency can also be achieved by tailoring some components of the method (e.g., the local planner) to the considered robots. In this paper the method is applied to planar articulated robots with many degrees of freedom. Experimental results show that path planning can be done in a fraction of a second on a contemporary workstation (=150 MIPS), after learning for relatively short periods of time (a few dozen seconds)