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

Super-resolution of Point Set Surfaces using Local Similarities

International audience3D scanners provide a virtual representation of object surfaces at some given precision that depends on many factors such as the object material, the quality of the laser-ray or the resolution of the camera. This precision may even vary over the surface, depending for example on the distance to the scanner which results in uneven and unstructured point sets, with an uncertainty on the coordinates. To enhance the quality of the scanner output, one usually resorts to local surface interpolation between measured points. However, object surfaces often exhibit interesting statistical features such as repetitive geometric textures. Building on this property, we propose a new approach for surface super-resolution that detects repetitive patterns or self-similarities and exploits them to improve the scan resolution by aggregating scattered measures. In contrast with other surface super-resolution methods, our algorithm has two important advantages. First, when handling multiple scans, it does not rely on surface registration. Second, it is able to produce super-resolution from even a single scan. These features are made possible by a new local shape description able to capture differential properties of order above 2. By comparing those descriptors, similarities are detected and used to generate a high-resolution surface. Our results show a clear resolution gain over state-of-the-art interpolation methods

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

MorphoGraphX:A platform for quantifying morphogenesis in 4D

Morphogenesis emerges from complex multiscale interactions between genetic and mechanical processes. To understand these processes, the evolution of cell shape, proliferation and gene expression must be quantified. This quantification is usually performed either in full 3D, which is computationally expensive and technically challenging, or on 2D planar projections, which introduces geometrical artifacts on highly curved organs. Here we present MorphoGraphX (www.MorphoGraphX.org), a software that bridges this gap by working directly with curved surface images extracted from 3D data. In addition to traditional 3D image analysis, we have developed algorithms to operate on curved surfaces, such as cell segmentation, lineage tracking and fluorescence signal quantification. The software’s modular design makes it easy to include existing libraries, or to implement new algorithms. Cell geometries extracted with MorphoGraphX can be exported and used as templates for simulation models, providing a powerful platform to investigate the interactions between shape, genes and growth.DOI: http://dx.doi.org/10.7554/eLife.05864.001Author keywordsResearch organis

Understanding Errors in Approximating Principal Direction Vectors

Suppose we are given only a surface mesh of vertices and polygons approximating some unknown smooth surface. There have been many methods proposed for approximating principal directions of the underlying surface. In this paper we will examine a few of the known methods, showing how well they can work for some surfaces and how miserably they can fail for others. In particular we will show that very tiny approximation errors can be magnified into large directional errors. We also introduce a new method that we believe performs significantly better than the others. In section I, we will outline the basic mathematics behind computing principal directions, stating the necessary formulas for the Weingarten curvature matrix and for its use in computing normal curvature in a given direction. In section II we describe in detail three methods each of which approximates the Weingarten curvature matrix at a vertex of the mesh. In section III we apply each method to some surfaces using a number of different mesh schemes and examine the direction errors. In section IV we develop some mathematical relationships between surface approximation errors and errors in principal directions

FIBRE MAPS AND INCOMPRESSIBILITY.

Abstract not availabl

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