Multiresolution Banded Refinement to Accelerate Surface Reconstruction from Polygons

We propose a method for constructing a tiling between a pair of planar polygons. Our technique uses multiresolution: tilings of lower resolution polygons are used to construct a tiling for the full resolution polygons. The tilings are constructed using banded refinement, by restricted dynamic programming, in roughly linear time and space. By contrast, the optimal dynamic programming method requires quadratic time and space. In our empirical study of surface reconstruction of brain contours our algorithm exhibited significant speedup over the optimal dynamic program, yet nearly always found an optimal reconstruction. Our approach appears to be generalizable to other geometric problems solvable by dynamic programming, and flexible enough to be tuned for varying data set characteristics. 1 Introduction A typical subproblem of many surface reconstruction algorithms is the fitting of a surface to a set of parallel contours. This problem arises, for example, in medical visualization applic..

Stereological techniques for synthesizing solid textures from images of aggregate materials

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, February 2005.Includes bibliographical references (leaves 121-130).When creating photorealistic digital scenes, textures are commonly used to depict complex variation in surface appearance. For materials that have spatial variation in three dimensions, such as wood or marble, solid textures offer a natural representation. Unlike 2D textures, which can be easily captured with a photograph, it can be difficult to obtain a 3D material volume. This thesis addresses the challenge of extrapolating tileable 3D solid textures from images of aggregate materials, such as concrete, asphalt, terrazzo or granite. The approach introduced here is inspired by and builds on prior work in stereology--the study of 3D properties of a material based on 2D observations. Unlike ad hoc methods for texture synthesis, this approach has rigorous mathematical foundations that allow for reliable, accurate material synthesis with well-defined assumptions. The algorithm is also driven by psychophysical constraints to insure that slices through the synthesized volume have a perceptually similar appearance to the input image. The texture synthesis algorithm uses a variety of techniques to independently solve for the shape, distribution, and color of the embedded particles, as well as the residual noise. To approximate particle shape, I consider four methods-including two algorithms of my own contribution. I compare these methods under a variety of input conditions using automated, perceptually-motivated metrics as well as a carefully controlled psychophysical experiment. In addition to assessing the relative performance of the four algorithms, I also evaluate the reliability of the automated metrics in predicting the results of the user study. To solve for the particle distribution, I apply traditional stereological methods.(cont.) I first illustrate this approach for aggregate materials of spherical particles and then extend the technique to apply to particles of arbitrary shapes. The particle shape and distribution are used in conjunction to create an explicit 3D material volume using simulated annealing. Particle colors are assigned using a stochastic method, and high-frequency noise is replicated with the assistance of existing algorithms. The data representation is suitable for high-fidelity rendering and physical simulation. I demonstrate the effectiveness of the approach with side-by-side comparisons of real materials and their synthetic counterparts derived from the application of these techniques.by Robert Carl Jagnow.Ph.D