Next: 3 Multiscale Probabilistic Relaxation Up: Multi-Level Probabilistic Relaxation Previous: 1 Introduction

2 Literature Survey

  Probabilistic relaxation has been used by a few researchers in multi-resolution representations of data. A major reason for adopting such an approach has been to reduce the computational load through a faster convergence. Glazer [ 2 ] applied ``multi-level'' relaxation to the Gauss-Seidel method of iterative solution of a finite-difference approximation for optic flow analysis. He used a multi-resolution pyramid representation of the input image. The iterative relaxation was effectively applied by formulating problems in low level vision as partial differential or finite difference equations. In a similar vain, Terzopoulos [ 11 ] developed multi-resolution iterative algorithms for other image analysis tasks, such as shape from shading, which are put forward mathematically as variational principles or as partial differential equations. Zhang et al. [ 13 ] applied a relaxation technique for edge detection on a multi-resolution hierarchical representation of the input image.

Hancock et al. [ 3 ] presented a probabilistic relaxation method for more consistent edge labelling but using a multi-resolution, hierarchical representation of the edge map. In this scheme, the probabilistic relaxation approach is applied to each level of resolution as if it were the single level approach, with the only difference that the ``prior probabilities'' of the labels at each level are adjusted to be consistent with the priors of the previous level as extracted from the dictionaries. Our scheme differs in the sense that it applies across different levels and it uses the same dictionary of allowable label configurations at all levels. Furthermore, we have a tower of images smoothed at different scales rather than a pyramid where the physical dimensions of the image are reduced.

Such multiscale approaches for texture analysis are few and far between. Unser and Eden [ 12 ] extracted texture energy measures form the image and smoothed the output of the extraction filter bank using Gaussian smoothing at different scales. The features in these multiscale planes are reduced, by diagonalising scatter matrices evaluated at two different spatial resolutions, and thresholded to yield texture segmentation. Matalas et al. [ 5 ], used a B-spline transform in order to obtain images at several smoothing levels to calculate vector dispersion and gradient orientation at different scales. A small disparity function was then applied to segment textures.



Next: 3 Multiscale Probabilistic Relaxation Up: Multi-Level Probabilistic Relaxation Previous: 1 Introduction

Dr. Majid Mirmehdi
Wed Jul 2 18:24:08 BST 1997