Stochastic
Medial Axis and Gestalt Laws in Markov Random Field

Some of the observed shapes as training examples, from which some shape statistics are extracted along the contour (co-linearity and co-circularity) and cross the medial axis for (proximity, parallelism, and symmetry). These are the popular Gestalt features. Then histograms of these features are accumulated across the data set. |

By maximum entropy, we construct a shape model which reproduces the observed statistics. This figure shows three stages of the Markov chain sampling of this descriptive shape model. At the beginning, the sample (left) is very irregular. After adding the contour-based statistics, the sampled shape (middel) becomes smooth but bloby. After further adding the region-based statistics, the sample shape (right) has symmetric and elongated limes, just like the natural shapes. This descriptive model does not know parts or joints. |

More examples from the Markov chain random walks, look, how much they resemble the spirit of those animal shapes in the training set ! |

The previous FORMS project is a generative shape model. Motivated by the success of texture modeling, we made the second attempt to modeling shape by a descriptive (Gibbs model). Two papers reported this project

1. S. C. Zhu , "Stochastic
Jump-Diffusion process for computing Medial Axes in Markov Random Fields",
IEEE Trans. on PAMI, Vol. 21, No.11, pp1158-1169, Nov, 1999.

2. S. C. Zhu, "Embedding Gestalt Laws
in Markov Random Fields -- A theory for shape modeling and perceptual organization",
IEEE Trans. on PAMI , Vol. 21, No.11, Nov, pp1170-1187, 1999.