From Scaling Laws of Natural Images to Regimes of Statistical Models

Song-Chun Zhu

In this talk, I will present a primal sketch model that integrates Markov random field theory (statistical physics) and sparse image coding theory under a common framework. I will start with empirical observations that image statistics changes over scales. When we down scaling an image, the entropy rate will increase, and so does the perceptual uncertainty. Consequently our perception experiences quantum jumps over scales and the corresponding statistical models change dimensions. For example, the image coding model will have much more variables for image structures with low entropy rate, in contrast, the Markov random field models have very short representation for image textures with high entropy. The two types of models work on different entropy regimes.

Then in the second half of my talk, I will show various high-order image structures as image primitives specified by photometric, geometric, dynamic and topologic parameters. These primitives then form low dimensional manifolds in the image space.

Presentation (PDF File)

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