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Summary: To appear in ACM Transactions on Graphics (Special Issue of SIGGRAPH 2005)
Out-of-Core Tensor Approximation of
Multi-Dimensional Matrices of Visual Data
Hongcheng Wang Qing Wu Lin Shi Yizhou Yu Narendra Ahuja
University of Illinois at Urbana-Champaign
Abstract
Tensor approximation is necessary to obtain compact multilinear
models for multi-dimensional visual datasets. Traditionally, each
multi-dimensional data item is represented as a vector. Such a
scheme flattens the data and partially destroys the internal structures
established throughout the multiple dimensions. In this paper, we
retain the original dimensionality of the data items to more effec-
tively exploit existing spatial redundancy and allow more efficient
computation. Since the size of visual datasets can easily exceed
the memory capacity of a single machine, we also present an out-
of-core algorithm for higher-order tensor approximation. The basic
idea is to partition a tensor into smaller blocks and perform tensor-
related operations blockwise. We have successfully applied our
techniques to three graphics-related data-driven models, including
6D bidirectional texture functions, 7D dynamic BTFs and 4D vol-
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