Poligonização de Superfícies Implícitas por Amostragem Baseada num Corrector de Newton

A maioria dos algoritmos para amostragem de superfícies implícitas baseia-se no Teorema do Valor Intermédio. Isto é, assume-se que existe variação de sinal da função que representa a superfície. Acontece que nem sempre é assim, ou seja, nem sempre existe variação de sinal da função na vizinhança da superfície. Introduz-se assim um novo algoritmo baseado num Corrector de Newton capaz de efectuar a amostragem de superfícies implícitas quer exista ou não variação de sinal da função na vizinhança da superfície.Most algorithms for sampling implicit surfaces are based on the Intermediate Value Theorem. That is, it is assumed that the function that describes a surface changes sign in the neighborhood of each point of it. It happens that not all functions describing implicit surfaces change sign in the neighborhood of each surface point. We introduce a new Newton-Corrector based algorithm capable of sampling implicit surfaces, regardless whether there exists sign changes near the surface or not

Feature-Based Models for Three-Dimensional Data Fitting.

There are numerous techniques available for fitting a surface to any supplied data set. The feature-based modeling technique takes advantage of the known, geometric shape of the data by deforming a model having this generic shape to approximate the data. The model is constructed as a rational B-spline surface with characteristic features superimposed on its definition. The first step in the fitting process is to align the model with a data set using the center of mass, principal axes and/or landmarks. Using this initial orientation, the position, rotation and scale parameters are optimized using a Newton-type optimization of a least squares cost function. Once aligned, features embedded within the model, corresponding to pertinent characteristics of the shape, are used to improve the fit of the model to the data. Finally, the control vertex weights and positions of the rational B-spline model are optimized to approximate the data to within a specified tolerance. Since the characteristic features are defined within the model a creation, important measures are easily extracted from a data set, once fit. The feature-based modeling approach is demonstrated in two-dimensions by the fitting of five facial, silhouette profiles and in three-dimensions by the fitting of eleven human foot scans. The algorithm is tested for sensitivity to data distribution and structure and the extracted measures are tested for repeatability and accuracy. Limitations within the current implementation, future work and potential applications are also provided

Extracting Depth Information From Photographs of Faces

Recently new methods of recovering the 3D appearance of objects, like stereo- imaging sensors, laser scanners, and range-imaging sensors provide automatic tools for obtaining the 3D appearance of an object but they require the presence of the object. When only photographic images are available, it is still possible to reconstruct the 3D appearance of the object if there is also a model which can be referenced. The human face is very popular with researchers who try to solve the problems including facial recognition, animation, composition, or modelling. However it is rare to find attempts to reconstruct shape from single photographic images of human faces, although there are numerous methods to solve the shape-from-shading (SFS) problem to date. This thesis describes a novel geometrical approach to reconstructing the original face from a very impoverished facial model1 and a single Lambertian image. This thesis also introduces a different approach to the SFS problem in the sense that it uses prior knowledge of the object, the so-called shape-from-prior-knowledge approach, and addresses the question of what degree of impoverishment is sufficient to compromise the reconstruction. Most recovered surfaces using conventional SFS methods suffer from flattening so that we cannot view them in other directions. We believe that this flatness is due to the lack of geometric knowledge of the subject to be recovered. In this thesis, it is also argued that our approach improves upon existing SFS techniques, because a reconstructed face looks correct even when it is turned to a different orientation from the one in the input image