25,519 research outputs found
Finding Non-overlapping Clusters for Generalized Inference Over Graphical Models
Graphical models use graphs to compactly capture stochastic dependencies
amongst a collection of random variables. Inference over graphical models
corresponds to finding marginal probability distributions given joint
probability distributions. In general, this is computationally intractable,
which has led to a quest for finding efficient approximate inference
algorithms. We propose a framework for generalized inference over graphical
models that can be used as a wrapper for improving the estimates of approximate
inference algorithms. Instead of applying an inference algorithm to the
original graph, we apply the inference algorithm to a block-graph, defined as a
graph in which the nodes are non-overlapping clusters of nodes from the
original graph. This results in marginal estimates of a cluster of nodes, which
we further marginalize to get the marginal estimates of each node. Our proposed
block-graph construction algorithm is simple, efficient, and motivated by the
observation that approximate inference is more accurate on graphs with longer
cycles. We present extensive numerical simulations that illustrate our
block-graph framework with a variety of inference algorithms (e.g., those in
the libDAI software package). These simulations show the improvements provided
by our framework.Comment: Extended the previous version to include extensive numerical
simulations. See http://www.ima.umn.edu/~dvats/GeneralizedInference.html for
code and dat
Connectivity Compression for Irregular Quadrilateral Meshes
Applications that require Internet access to remote 3D datasets are often
limited by the storage costs of 3D models. Several compression methods are
available to address these limits for objects represented by triangle meshes.
Many CAD and VRML models, however, are represented as quadrilateral meshes or
mixed triangle/quadrilateral meshes, and these models may also require
compression. We present an algorithm for encoding the connectivity of such
quadrilateral meshes, and we demonstrate that by preserving and exploiting the
original quad structure, our approach achieves encodings 30 - 80% smaller than
an approach based on randomly splitting quads into triangles. We present both a
code with a proven worst-case cost of 3 bits per vertex (or 2.75 bits per
vertex for meshes without valence-two vertices) and entropy-coding results for
typical meshes ranging from 0.3 to 0.9 bits per vertex, depending on the
regularity of the mesh. Our method may be implemented by a rule for a
particular splitting of quads into triangles and by using the compression and
decompression algorithms introduced in [Rossignac99] and
[Rossignac&Szymczak99]. We also present extensions to the algorithm to compress
meshes with holes and handles and meshes containing triangles and other
polygons as well as quads
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