Deep Structured Layers for Instance-Level Optimization in 2D and 3D Vision

The approach we present in this thesis is that of integrating optimization problems as layers in deep neural networks. Optimization-based modeling provides an additional set of tools enabling the design of powerful neural networks for a wide battery of computer vision tasks. This thesis shows formulations and experiments for vision tasks ranging from image reconstruction to 3D reconstruction. We first propose an unrolled optimization method with implicit regularization properties for reconstructing images from noisy camera readings. The method resembles an unrolled majorization minimization framework with convolutional neural networks acting as regularizers. We report state-of-the-art performance in image reconstruction on both noisy and noise-free evaluation setups across many datasets. We further focus on the task of monocular 3D reconstruction of articulated objects using video self-supervision. The proposed method uses a structured layer for accurate object deformation that controls a 3D surface by displacing a small number of learnable handles. While relying on a small set of training data per category for self-supervision, the method obtains state-of-the-art reconstruction accuracy with diverse shapes and viewpoints for multiple articulated objects. We finally address the shortcomings of the previous method that revolve around regressing the camera pose using multiple hypotheses. We propose a method that recovers a 3D shape from a 2D image by relying solely on 3D-2D correspondences regressed from a convolutional neural network. These correspondences are used in conjunction with an optimization problem to estimate per sample the camera pose and deformation. We quantitatively show the effectiveness of the proposed method on self-supervised 3D reconstruction on multiple categories without the need for multiple hypotheses

Image coding using wavelets, interval wavelets and multi- layered wedgelets

Ph.DDOCTOR OF PHILOSOPH

Efficient fast Fourier transform-based solvers for computing the thermomechanical behavior of applied materials

The mechanical behavior of many applied materials arises from their microstructure. Thus, to aid the design, development and industrialization of new materials, robust computational homogenization methods are indispensable. The present thesis is devoted to investigating and developing FFT-based micromechanics solvers for efficiently computing the (thermo)mechanical response of nonlinear composite materials with complex microstructures

Efficient fast Fourier transform-based solvers for computing the thermomechanical behavior of applied materials

The mechanical behavior of many applied materials arises from their microstructure. Thus, to aid the design, development and industrialization of new materials, robust computational homogenization methods are indispensable. The present thesis is devoted to investigating and developing FFT-based micromechanics solvers for efficiently computing the (thermo)mechanical response of nonlinear composite materials with complex microstructures