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Many generic prior models have been widely used in computer vision ranging from
image and surface reconstruction to motion analysis, and these models presume
that surfaces of objects be smooth, and adjacent pixels in images have similar
intensity values. However, there is little rigorous theory to guide the
construction and selection of prior models for a given application.
Furthermore, images are often observed at arbitrary scales, but none of the
existing prior models are scale-invariant. Motivated by these problems, this
article chooses general natural images as a domain of application, and
proposes a theory for learning prior models from a set of observed natural
images. Our theory is based on a maximum entropy principle, and the learned
prior models are of Gibbs distributions.
A novel information criterion is proposed for model selection by minimizing a
Kullback-Leibler information distance. We also investigate scale invariance
in the statistics of natural images and study a prior model which has scale
invariant property. In this paper, in contrast with all existing prior models,
negative potentials in Gibbs distribution are first reported. The learned
prior models are verified in two ways. Firstly images are sampled from the
prior distributions to demonstrate what typical images they stand for.
Secondly they are compared with existing prior models in experiments of
image restoration. |
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| A learn prior model on the image pyramid,
which is scale invariant at 4 levels, and
can be used for both denoising and enhancement.
The inverted potential function observed |
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