Early Vision Optimization: Parametric Models, Parallelization and Curvature

Early vision is the process occurring before any semantic interpretation of an image takes place. Motion estimation, object segmentation and detection are all parts of early vision, but recognition is not. Many of these tasks are formulated as optimization problems and one of the key factors for the success of recent methods is that they seek to compute globally optimal solutions. This thesis is concerned with improving the efficiency and extending the applicability of the current state of the art. This is achieved by introducing new methods of computing solutions to image segmentation and other problems of early vision. The first part studies parametric problems where model parameters are estimated in addition to an image segmentation. For a small number of parameters these problems can still be solved optimally. In the second part the focus is shifted toward curvature regularization, i.e. when the commonly used length and area regularization is replaced by curvature in two and three dimensions. These problems can be discretized over a mesh and special attention is given to the mesh geometry. Specifically, hexagonal meshes are compared to square ones and a method for generating adaptive methods is introduced and evaluated. The framework is then extended to curvature regularization of surfaces. Thirdly, fast methods for finding minimal graph cuts and solving related problems on modern parallel hardware are developed and extensively evaluated. Finally, the thesis is concluded with two applications to early vision problems: heart segmentation and image registration

Recent Advances in Graph Partitioning

We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions

A massively parallel multi-level approach to a domain decomposition method for the optical flow estimation with varying illumination

We consider a variational method to solve the optical flow problem with varying illumination. We apply an adaptive control of the regularization parameter which allows us to preserve the edges and fine features of the computed flow. To reduce the complexity of the estimation for high resolution images and the time of computations, we implement a multi-level parallel approach based on the domain decomposition with the Schwarz overlapping method. The second level of parallelism uses the massively parallel solver MUMPS. We perform some numerical simulations to show the efficiency of our approach and to validate it on classical and real-world image sequences

Depth from Monocular Images using a Semi-Parallel Deep Neural Network (SPDNN) Hybrid Architecture

Deep neural networks are applied to a wide range of problems in recent years. In this work, Convolutional Neural Network (CNN) is applied to the problem of determining the depth from a single camera image (monocular depth). Eight different networks are designed to perform depth estimation, each of them suitable for a feature level. Networks with different pooling sizes determine different feature levels. After designing a set of networks, these models may be combined into a single network topology using graph optimization techniques. This "Semi Parallel Deep Neural Network (SPDNN)" eliminates duplicated common network layers, and can be further optimized by retraining to achieve an improved model compared to the individual topologies. In this study, four SPDNN models are trained and have been evaluated at 2 stages on the KITTI dataset. The ground truth images in the first part of the experiment are provided by the benchmark, and for the second part, the ground truth images are the depth map results from applying a state-of-the-art stereo matching method. The results of this evaluation demonstrate that using post-processing techniques to refine the target of the network increases the accuracy of depth estimation on individual mono images. The second evaluation shows that using segmentation data alongside the original data as the input can improve the depth estimation results to a point where performance is comparable with stereo depth estimation. The computational time is also discussed in this study.Comment: 44 pages, 25 figure

3D mesh processing using GAMer 2 to enable reaction-diffusion simulations in realistic cellular geometries

Recent advances in electron microscopy have enabled the imaging of single cells in 3D at nanometer length scale resolutions. An uncharted frontier for in silico biology is the ability to simulate cellular processes using these observed geometries. Enabling such simulations requires watertight meshing of electron micrograph images into 3D volume meshes, which can then form the basis of computer simulations of such processes using numerical techniques such as the Finite Element Method. In this paper, we describe the use of our recently rewritten mesh processing software, GAMer 2, to bridge the gap between poorly conditioned meshes generated from segmented micrographs and boundary marked tetrahedral meshes which are compatible with simulation. We demonstrate the application of a workflow using GAMer 2 to a series of electron micrographs of neuronal dendrite morphology explored at three different length scales and show that the resulting meshes are suitable for finite element simulations. This work is an important step towards making physical simulations of biological processes in realistic geometries routine. Innovations in algorithms to reconstruct and simulate cellular length scale phenomena based on emerging structural data will enable realistic physical models and advance discovery at the interface of geometry and cellular processes. We posit that a new frontier at the intersection of computational technologies and single cell biology is now open.Comment: 39 pages, 14 figures. High resolution figures and supplemental movies available upon reques