The techniques of a posteriori image restoration and iterative image feature extraction are described and compared. Image feature extraction methods known as graduated nonconvexity (GNC); variable conductance diffusion (VCD), anisotropic diffusion, and biased anisotropic diffusion (BAD), which extract edges from noisy images, are compared with a restoration/feature extraction method known as mean field annealing (MFA). All are shown to be performing the same basic operation: image relaxation. This equivalence shows the relationship between energy minimization methods and spatial analysis methods and between their respective parameters of temperature and scale. As a result of the equivalence, VCD is demonstrated to minimize a cost function, and that cost is specified explicitly. Furthermore, operations over scale space are shown to be a method of avoiding local minima.>

Motion artifacts due to heart motion and blood flow within the heart chambers are a significant barrier to accurate interpretation of cardiac magnetic resonance images (MRI). The post-processing techniques of Wiener filtering, alternating projections onto convex sets (POCS), and mean field annealing (MFA) to remove these artifacts are studied. Removal of noise from the images is accomplished with MFA by setting up a restoration problem whose objective function encapsulates both data-dependent and a priori knowledge about the image. Two important aspects of MFA are the use of a penalty rather than a constraint, and the fact that it converges twenty times as rapidly as normal simulated annealing. Images of the results of Wiener filtering and MFA are shown, and the methods of POCS and MFA are briefly explained.>

The problem of pose determination of a surface in a range image is described as a six-degree-of-freedom optimization problem, where the surface is expressed by a quadratic equation. The tree annealing algorithm, a general-purpose technique for finding minima of functions of continuously valued variables, is presented. The technique is applied to the pose determination of analytic surfaces and is shown to be quite effective even in the presence of considerable amounts of noise in the images.>