Coded aperture imaging

This thesis studies the coded aperture camera, a device consisting of a conventional camera with a modified aperture mask, that enables the recovery of both depth map and all-in-focus image from a single 2D input image. Key contributions of this work are the modeling of the statistics of natural images and the design of efficient blur identification methods in a Bayesian framework. Two cases are distinguished: 1) when the aperture can be decomposed in a small set of identical holes, and 2) when the aperture has a more general configuration. In the first case, the formulation of the problem incorporates priors about the statistical variation of the texture to avoid ambiguities in the solution. This allows to bypass the recovery of the sharp image and concentrate only on estimating depth. In the second case, the depth reconstruction is addressed via convolutions with a bank of linear filters. Key advantages over competing methods are the higher numerical stability and the ability to deal with large blur. The all-in-focus image can then be recovered by using a deconvolution step with the estimated depth map. Furthermore, for the purpose of depth estimation alone, the proposed algorithm does not require information about the mask in use. The comparison with existing algorithms in the literature shows that the proposed methods achieve state-of-the-art performance. This solution is also extended for the first time to images affected by both defocus and motion blur and, finally, to video sequences with moving and deformable objects

Anisotropy Across Fields and Scales

This open access book focuses on processing, modeling, and visualization of anisotropy information, which are often addressed by employing sophisticated mathematical constructs such as tensors and other higher-order descriptors. It also discusses adaptations of such constructs to problems encountered in seemingly dissimilar areas of medical imaging, physical sciences, and engineering. Featuring original research contributions as well as insightful reviews for scientists interested in handling anisotropy information, it covers topics such as pertinent geometric and algebraic properties of tensors and tensor fields, challenges faced in processing and visualizing different types of data, statistical techniques for data processing, and specific applications like mapping white-matter fiber tracts in the brain. The book helps readers grasp the current challenges in the field and provides information on the techniques devised to address them. Further, it facilitates the transfer of knowledge between different disciplines in order to advance the research frontiers in these areas. This multidisciplinary book presents, in part, the outcomes of the seventh in a series of Dagstuhl seminars devoted to visualization and processing of tensor fields and higher-order descriptors, which was held in Dagstuhl, Germany, on October 28–November 2, 2018

The Shallow and the Deep:A biased introduction to neural networks and old school machine learning

The Shallow and the Deep is a collection of lecture notes that offers an accessible introduction to neural networks and machine learning in general. However, it was clear from the beginning that these notes would not be able to cover this rapidly changing and growing field in its entirety. The focus lies on classical machine learning techniques, with a bias towards classification and regression. Other learning paradigms and many recent developments in, for instance, Deep Learning are not addressed or only briefly touched upon.Biehl argues that having a solid knowledge of the foundations of the field is essential, especially for anyone who wants to explore the world of machine learning with an ambition that goes beyond the application of some software package to some data set. Therefore, The Shallow and the Deep places emphasis on fundamental concepts and theoretical background. This also involves delving into the history and pre-history of neural networks, where the foundations for most of the recent developments were laid. These notes aim to demystify machine learning and neural networks without losing the appreciation for their impressive power and versatility