Narrow Results

We review Monte Carlo simulations of the Ising model and similar models in three dimensions that were performed in the last decade. Only recently, Monte Carlo simulations provide more accurate results for critical exponents than field theoretic methods, such as the ∊-expansion. These results were obtained with finite size scaling and "improved actions". In addition, we summarize Monte Carlo results for universal amplitude ratios, the interface tension, and the dimensional crossover from three to two dimensions.

Analysis of the dermo-epidermal surface in three-dimensions has great value in evaluating cosmetics. One approach is based on the active contour model, which is used extensively in computer vision and image processing applications, particularly for local object boundaries with closed curve form. The dermo-epidermal surface, however, is a plane with open form. We have developed a method of automatically extracting the dermo-epidermal surface from volumetric confocal microscopic images, as well as constructing a 3D visual model of the surface by using the geometric information contained in the control points. Our method is a 3D extension of the active contour model, so we call it the active open surface model (AOSM). The initial surface for AOSM is an open curve plane, guided by a 3D internal force, a 3D external constraint force, and a 3D image force, which pull it towards the objective surface. The proposed tecnique has been applied to extract actual dermo-epidermal surface in the given volumetric confocal microscopic images.