Isometry Invariant Shape Priors for Variational Image Segmentation

Variational methods play a fundamental role in mathematical image analysis as a bridge between models and algorithms. A major challenge is to formulate a given model as a feasible optimization problem. There has been a huge leap in that respect concerning local data models in the framework of convex relaxation. But non-local concepts such as the shape of a sought-after object are still difficult to implement. In this thesis we study mathematical representations for shapes and develop shape prior functionals for object segmentation based thereon. A particular focus is set on the isometry invariance of the functionals and the compatibility with existing convex functionals for image labelling. Optimal transport is used as a central modelling and computational tool to compute registrations between different shapes as a basis for a shape similarity measure. This point of view leads to a link between the two somewhat dual representations of a shape by the region it occupies and its outline, allowing to combine their respective strengths. Naively the computational complexity implied by the derived functionals is unfeasible. Therefore suitable hierarchical optimization methods are developed

A survey on generative adversarial networks for imbalance problems in computer vision tasks

Any computer vision application development starts off by acquiring images and data, then preprocessing and pattern recognition steps to perform a task. When the acquired images are highly imbalanced and not adequate, the desired task may not be achievable. Unfortunately, the occurrence of imbalance problems in acquired image datasets in certain complex real-world problems such as anomaly detection, emotion recognition, medical image analysis, fraud detection, metallic surface defect detection, disaster prediction, etc., are inevitable. The performance of computer vision algorithms can significantly deteriorate when the training dataset is imbalanced. In recent years, Generative Adversarial Neural Networks (GANs) have gained immense attention by researchers across a variety of application domains due to their capability to model complex real-world image data. It is particularly important that GANs can not only be used to generate synthetic images, but also its fascinating adversarial learning idea showed good potential in restoring balance in imbalanced datasets. In this paper, we examine the most recent developments of GANs based techniques for addressing imbalance problems in image data. The real-world challenges and implementations of synthetic image generation based on GANs are extensively covered in this survey. Our survey first introduces various imbalance problems in computer vision tasks and its existing solutions, and then examines key concepts such as deep generative image models and GANs. After that, we propose a taxonomy to summarize GANs based techniques for addressing imbalance problems in computer vision tasks into three major categories: 1. Image level imbalances in classification, 2. object level imbalances in object detection and 3. pixel level imbalances in segmentation tasks. We elaborate the imbalance problems of each group, and provide GANs based solutions in each group. Readers will understand how GANs based techniques can handle the problem of imbalances and boost performance of the computer vision algorithms

Trends in Mathematical Imaging and Surface Processing

Motivated both by industrial applications and the challenge of new problems, one observes an increasing interest in the field of image and surface processing over the last years. It has become clear that even though the applications areas differ significantly the methodological overlap is enormous. Even if contributions to the field come from almost any discipline in mathematics, a major role is played by partial differential equations and in particular by geometric and variational modeling and by their numerical counterparts. The aim of the workshop was to gather a group of leading experts coming from mathematics, engineering and computer graphics to cover the main developments

Mathematical Imaging and Surface Processing

Within the last decade image and geometry processing have become increasingly rigorous with solid foundations in mathematics. Both areas are research fields at the intersection of different mathematical disciplines, ranging from geometry and calculus of variations to PDE analysis and numerical analysis. The workshop brought together scientists from all these areas and a fruitful interplay took place. There was a lively exchange of ideas between geometry and image processing applications areas, characterized in a number of ways in this workshop. For example, optimal transport, first applied in computer vision is now used to define a distance measure between 3d shapes, spectral analysis as a tool in image processing can be applied in surface classification and matching, and so on. We have also seen the use of Riemannian geometry as a powerful tool to improve the analysis of multivalued images. This volume collects the abstracts for all the presentations covering this wide spectrum of tools and application domains

Universal consistency of Wasserstein kk-NN classifier

The Wasserstein distance provides a notion of dissimilarities between probability measures, which has recent applications in learning of structured data with varying size such as images and text documents. In this work, we analyze the $k$-nearest neighbor classifier ($k$-NN) under the Wasserstein distance and establish the universal consistency on families of distributions. Using previous known results on the consistency of the $k$-NN classifier on infinite dimensional metric spaces, it suffices to show that the families is a countable union of finite dimensional components. As a result, we are able to prove universal consistency of $k$-NN on spaces of finitely supported measures, the space of finite wavelet series and the spaces of Gaussian measures with commuting covariance matrices.Comment: 12 page

Score-based Diffusion Models for Generating Liquid Argon Time Projection Chamber Images

For the first time, we show high-fidelity generation of LArTPC-like data using a generative neural network. This demonstrates that methods developed for natural images do transfer to LArTPC-produced images, which, in contrast to natural images, are globally sparse but locally dense. We present the score-based diffusion method employed. We evaluate the fidelity of the generated images using several quality metrics, including modified measures used to evaluate natural images, comparisons between high-dimensional distributions, and comparisons relevant to LArTPC experiments