Detecting, modeling and rendering complex configurations of curvilinear features

Curvilinear features act as a basis in description and representation of a variety of real world patterns spanning from simple regular patterns like honeycomb tiling or text glyphs to very complicated random patterns like networks of furrows on the surface of the human skin, webs of cracks and fissure patterns on dry soil, clay, or old paintings, networks of blood microvessels, and planar maps of linear fault zones. In this work we have developed a set of methods and new data representations for solving key problems related to curvilinear features, which include (1) robust detection of intricate networks of curvilinear features from digital images, (2) GPU-based sharp rendering of fields with curvilinear features, and (3) a parametric synthesis approach to generate systems of curvilinear features with desirable local configurations and global control.;Existing edge-detection and image segmentation techniques for detecting features from digital images may underperform in the presence of inevitable noise, usually do not link the detected edge points into chains, often fail on complex structures and weakly presented curves, heavily depend on initial guess, or/and assume significant manual phase. We have developed a technique based on active contours, or snakes, which avoids laborious manual initial positioning of the snakes, does not require user interaction during optimization, and can detect large networks of curves with complex junctions.;The standard bilinear interpolation of piecewise continuous fields defined on regular grids results in unwanted smoothing along the curvilinear discontinuities, which is common during rendering of surfaces with small detail features like creases, wrinkles, and dents. In many cases, spatially varying features are best represented as a function of the distance to the discontinuity curves and its gradient, like the normal field near the creases along curves. We have presented a real-time, GPU-based method for unsigned distance function field and its gradient field interpolation which preserves discontinuity feature curves. The discontinuities are represented by a set of quadratic Bezier curves, with minimal restriction on their topology.;Detail features are very important visual clues which make computer-generated imagery look less artificial. Sample-based synthesis has become ubiquitous technique in generating arbitrary size textures of a high quality which locally resemble a given small reference texture. However, it shows inferior performance on textures with well structured patterns producing gaps in features or breaking feature coherency. Control on the pattern specification is very limited and often requires exhaustive ad-hoc search for the right parameters, yet not intuitive. We have explored an alternative approach of generating features using random fibre process. Existing mathematical models of random fibres---stochastic processes of networks of curves and lines --- model only completely random, stationary, and isotropic curve arrangements in the plane. We have developed a Gibbs-type random process of linear fibres based on local fibre interactions. It allows generating non-stationary curvilinear networks with some degree of regularity, and provides an intuitive set of parameters which directly defines fibre local configurations and global pattern of fibres.;For random systems of linear fibres which approximately form two dominant orientation fields, mutually orthogonal at each point, we have adapted a streamline placement algorithm which converts such systems into overlapping random sets of coherent smooth curves.