Surface reconstruction based on relaxation refinement

Probabilistic relaxation is a powerful method for extracting features form images. Because the filtering process is basically independent of the relaxation process itself, probabilistic relaxation can be used to extract edges or ridges simply by choosing s suitable edge filter or line filter. Our recent work in hierarchical relaxation further improves the relaxation technique. Firstly, we use hierarchical constraints for the extraction of major features. Secondly, we partition the dictionary items according to the angle formed by the label sin each of the dictionary items to reduce the processing time for traversing the dictionary. The advantages of this hierarchical relaxation method are that it produces a more refined feature map and it improves the efficiency of the relaxation process by passing constraints from a low resolution relaxation process to a higher one. In this paper, we extend the idea of hierarchical relaxation to extracting 3D surfaces from volumetric data such as MRI data. Given a set of MRI images representing an object, we perform the relaxation process on each of the images to extract the contours of the object in the image. This relaxation process is constrained by the results of the same process applied to nearby images. A 3D geometric description of the object in the form of a polygon mesh can then be generated from the set of 2D contour curves. Results of the new method will also be demonstrated in this paper.