Probabilistic Relaxation and Hierarchical Relaxation

Probabilistic relaxation has been shown to be a powerful method for extracting features from images [5, 6]. Because the ltering process is basically independent of the relaxation itself, probabilistic relaxation can be used to extract edges or ridges simply by choosing an edge lter or a line lter. In this report, we describe an hierarchical approach to probabilistic relaxation. There are two main ideas in this work. Firstly, we use multiresolution constraints for the extraction of major line features. Secondly, we partition the dictionary items according to the angle formed by the labels in each of the dictionary items to reduce the processing time for traversing the dictionary. The relaxation process is performed on the low resolution copy of the input image and the output is used to guide a modi ed relaxation process applied to the original image by controlling the number of dictionary items being searched at each pixel. The new method is proved to be more e cient than the original method and it also produces a more re ned ridge map. In the report, we also describe in detail our implementation of the hierarchical relaxation which includes the choice of lters, the partition of the label dictionary and some re nements of the hierarchical relaxation method. We also show some of our experimental results of hierarchical relaxation method applied to aerial infra-red images.