Feature Lines for Illustrating Medical Surface Models: Mathematical Background and Survey

This paper provides a tutorial and survey for a specific kind of illustrative visualization technique: feature lines. We examine different feature line methods. For this, we provide the differential geometry behind these concepts and adapt this mathematical field to the discrete differential geometry. All discrete differential geometry terms are explained for triangulated surface meshes. These utilities serve as basis for the feature line methods. We provide the reader with all knowledge to re-implement every feature line method. Furthermore, we summarize the methods and suggest a guideline for which kind of surface which feature line algorithm is best suited. Our work is motivated by, but not restricted to, medical and biological surface models.Comment: 33 page

On the beneficial effect of noise in vertex localization

A theoretical and experimental analysis related to the effect of noise in the task of vertex identication in unknown shapes is presented. Shapes are seen as real functions of their closed boundary. An alternative global perspective of curvature is examined providing insight into the process of noise- enabled vertex localization. The analysis reveals that noise facilitates in the localization of certain vertices. The concept of noising is thus considered and a relevant global method for localizing Global Vertices is investigated in relation to local methods under the presence of increasing noise. Theoretical analysis reveals that induced noise can indeed help localizing certain vertices if combined with global descriptors. Experiments with noise and a comparison to localized methods validate the theoretical results

Fast Spheres, Shadows, Textures, Transparencies, and Image Enhancements in Pixel-Planes

Pixel-planes is a logic-enhanced memory system for raster graphics and imaging. Although each pixel-memory is enhanced with a one-bit ALU, the system's real power comes from a tree of one-bit address that can evaluate linear expressions Ax + By + C for every pixel (x,y) simultaneously, as fast as the ALUs and the memory circuits can accept the results. The development of a variety of algorithms that exploit this fast linear expression evaluation capability has started. The paper reports some of those results. Illustrated in this paper is a sample image from a small working prototype of the Pixel- planes hardware and a variety of images from simulations of a full-scale system. Timing estimates indicate that 30,000 smooth shaded triangles can be generated per second, or 21, 000 smooth-shaded and shadowed triangles can be generated per second, or over 25,000 shaded spheres can be generated per second. Image-enhancement by adaptive histogram equalization can be performed within 4 seconds on a 512 x 512 image

Brain image analysis using spherical splines

Abstract. We propose a novel technique based on spherical splines for brain surface representation and analysis. This research is strongly inspired by the fact that, for brain surfaces, it is both necessary and natural to employ spheres as their natural domains. We develop an automatic and efficient algorithm, which transforms a brain surface to a single spherical spline whose maximal error deviation from the original data is less than the user-specified tolerance. Compared to the discrete mesh-based representation, our spherical spline offers a concise (low storage requirement) digital form with high continuity (C n−1 continuity for a degree n spherical spline). Furthermore, this representation enables the accurate evaluation of differential properties, such as curvature, principal direction, and geodesic, without the need for any numerical approximations. Thus, certain shape analysis procedures, such as segmentation, gyri and sulci tracing, and 3D shape matching, can be carried out both robustly and accurately. We conduct several experiments in order to demonstrate the efficacy of our approach for the quantitative measurement and analysis of brain surfaces.