Deformable Surface Reconstruction Through Optimization-Based Techniques

Abstract

In this thesis, we address the problem of estimating the 3D structure of non-rigid surfaces that deform in a natural way. The deformation could take two general forms, that is, inextensible and extensible. The main goal of this thesis is to make signi cant contributions to the context of deformable surface reconstruction. For this purpose, we closely investigate the problem and propose innovative ideas and solutions. To be precise, we tackle the reconstruction problem aiming to obtain and report ndings and conclusions that positively a ect the relevant eld. The focus of the work is on the development of e cient approaches based on novel problem formulations that lead to less complex models and simultaneously to more accurate results. Although the thesis is mostly concentrated on specialized approaches for the reconstruction of inextensible or extensible surfaces, however we develop our work toward general formulations so that consistent modeling of both deformation types can be derived. The entire work is an organized e ort to accomplish the thesis objectives in a 3-stage research program. Each stage is assigned to one task and we deal with the reconstruction problem in various ways. In fact, certain algorithms have been designed in accordance with the elements de ned in the reconstruction problem in each task. These elements include the camera type, deformation type, deformation model, the surface representation, etc. As a result, three general ideas have been proposed in order to perform the surface reconstruction. Brie y, each idea relies on a particular basis, namely the use of Time-of-Flight camera, combination of deformation constraints or deformation modeling using surface transformations. As an outcome, we seek to achieve a reliable comparison between the three ideas with respect to performance and applicability, by evaluating the strengths and weaknesses of the relevant approaches. For this purpose, a comprehensive set of experiments and evaluations are performed on both real and synthetic video sequences capturing several variants of non-rigid surfaces.

Nesta tese, lidamos com o problema de estimar a estrutura 3D de super cies nao rigidas que deformam de forma natural. A deformacao pode assumir duas formas gerais, nao extensivel e extensivel. O objetivo principal desta tese e fazer contribuicoes signi cativas para o contexto da reconstrucao de super cies deformaveis. Para esse m, investigamos rigorosamente o problema e propomos ideias e solucoes inovadoras. Para ser mais preciso, nos resolvemos o problema de reconstrucao com o objetivo de obtermos e divulgarmos os resultados e as conclusoes que afetam positivamente o dominio em causa. O foco da obra e no desenvolvimento de algoritmos com base em formulacoes e cazes do problema que levam a modelos menos complexos e, em simultaneo, a resultados mais precisos. Embora a tese e principalmente concentrado em algoritmos especializadas para a reconstrucao de super cies nao extensiveis ou extensiveis, no entanto, desenvolvemos o nosso trabalho para formulacoes gerais de tal forma que a modelagem consistente de ambos os tipos de deformacao possam ser derivados. O trabalho inteiro e um esforco organizado para atingir os objetivos de tese em um programa de investigacao de 3 estagios. Cada estagio e atribuido a uma tarefa e nos lidamos com o problema de reconstrucao de varias maneiras. Na verdade, certos algoritmos foram concebidas de acordo com os elementos de nidos na problema de reconstrucao em cada tarefa. Estes elementos incluem o tipo de camara, tipo de deformacao, modelo de deformacao, a representacao da super cie, etc. Como resultado, tres ideias gerais tem sido propostos a m de executar a reconstrucao da super cie. Resumidamente, cada ideia conta com uma base especial, nomeadamente a utilizacao de camara de Time-of-Flight, combinacao de restricoes de deformacao ou modelagem de deformacao usando transformacoes de super cie. Como resultado, procuramos alcancar uma comparacao avel entre as tres ideias em relacao ao desempenho e aplicabilidade, atraves da avaliacao dos pontos fortes e fracos das algoritmos relevantes. Para este efeito, um conjunto compreensivo de experimentos e avaliacoes sao realizadas em ambas as sequencias de video reais e sinteticos que capturam varias variantes de super cie nao rigida.