TY - GEN
T1 - Hierarchical modeling of local image features through Lp-nested symmetric distributions
AU - Sinz, Fabian
AU - Simoncelli, Eero P.
AU - Bethge, Matthias
PY - 2009
Y1 - 2009
N2 - We introduce a new family of distributions, called Lp-nested symmetric distributions, whose densities are expressed in terms of a hierarchical cascade of Lp-norms. This class generalizes the family of spherically and Lp-spherically symmetric distributions which have recently been successfully used for natural image modeling. Similar to those distributions it allows for a nonlinear mechanism to reduce the dependencies between its variables. With suitable choices of the parameters and norms, this family includes the Independent Subspace Analysis (ISA) model as a special case, which has been proposed as a means of deriving filters that mimic complex cells found in mammalian primary visual cortex. Lp-nested distributions are relatively easy to estimate and allow us to explore the variety of models between ISA and the Lp-spherically symmetric models. By fitting the generalized Lp-nested model to 8 × 8 image patches, we show that the subspaces obtained from ISA are in fact more dependent than the individual filter coefficients within a subspace. When first applying contrast gain control as preprocessing, however, there are no dependencies left that could be exploited by ISA. This suggests that complex cell modeling can only be useful for redundancy reduction in larger image patches.
AB - We introduce a new family of distributions, called Lp-nested symmetric distributions, whose densities are expressed in terms of a hierarchical cascade of Lp-norms. This class generalizes the family of spherically and Lp-spherically symmetric distributions which have recently been successfully used for natural image modeling. Similar to those distributions it allows for a nonlinear mechanism to reduce the dependencies between its variables. With suitable choices of the parameters and norms, this family includes the Independent Subspace Analysis (ISA) model as a special case, which has been proposed as a means of deriving filters that mimic complex cells found in mammalian primary visual cortex. Lp-nested distributions are relatively easy to estimate and allow us to explore the variety of models between ISA and the Lp-spherically symmetric models. By fitting the generalized Lp-nested model to 8 × 8 image patches, we show that the subspaces obtained from ISA are in fact more dependent than the individual filter coefficients within a subspace. When first applying contrast gain control as preprocessing, however, there are no dependencies left that could be exploited by ISA. This suggests that complex cell modeling can only be useful for redundancy reduction in larger image patches.
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M3 - Conference contribution
AN - SCOPUS:84858738800
SN - 9781615679119
T3 - Advances in Neural Information Processing Systems 22 - Proceedings of the 2009 Conference
SP - 1696
EP - 1704
BT - Advances in Neural Information Processing Systems 22 - Proceedings of the 2009 Conference
PB - Neural Information Processing Systems
T2 - 23rd Annual Conference on Neural Information Processing Systems, NIPS 2009
Y2 - 7 December 2009 through 10 December 2009
ER -