Optimization appears in many computer vision and image processing problems such as image restoration (denoising, inpainting, compressed sensing), multi-view reconstruction, shape from X, object detection, image segmentation, optical flow, matching, and network training. While there are formulations allowing for global optimal optimization, e.g. using convex objectives or exact combinatorial algorithms, many problems in computer vision and image processing require efficient approximation methods.

Optimization methods that are widely used range from graph-based techniques and convex relaxations to greedy approaches (e.g. gradient descent). Each method has different efficiency and optimality guarantees. The goal of this workshop is a broad discussion of mathematical models (objectives and constraints) and robust efficient optimization methods (exact or approximate, discrete or continuous) addressing existing issues and advancing the state of the art.

Computational imaging involves the use of mathematical models and computational methods as part of imaging systems. Algorithms for image reconstruction have important applications, including in medical image analysis and imaging for the physical sciences. Classical approaches often involve solving large inverse problems using a variety of regularization methods and numerical algorithms.

Current research includes the development of new cameras and imaging methods, where the hardware system and the computational techniques used for image reconstruction are co-designed. New developments have been influenced by the introduction of novel techniques for compressed sensing and sparse reconstruction. The use of machine learning methods for designing a new generation of imaging systems has also been increasingly important.

Specific topics that will be discussed include: image reconstruction, computational photography, compressed sensing, machine learning methods, numerical optimization,... (more)

A long-standing problem in quantum topology is to find a function, more precisely a q-series with integer coefficients, such that its limiting values at primitive roots of unity yield invariants of Witten and Reshetikhin-Turaev. In other words, such a function would be to 3-manifolds what the Jones polynomial is to knots. Somewhat surprisingly, recent physics developments suggest that, in order to solve this problem, one must associate to a 3-manifold not a single function (q-series), but rather a collection of functions. Very recently, based on both physical intuition and explicit computations, it was suggested that these 3-manifold invariants display (modified) modularity properties of various types and are related to number theoretic objects including mock and false theta functions and quantum modular forms. This workshop will bring experts from the fields of topology, physics and number theory together, with the goal of combining knowledge and computational skills and furthering... (more)

Building systems that can understand visual concepts and describe them coherently in natural language is fundamental to artificial intelligence. Advances in machine learning have had profound impact on computer vision and natural language processing. There has been interesting progress in recent years at the intersection of these two fields, producing systems that describe (eg., caption) images and videos captured by personal cameras in ordinary scenes and street views. Much work remains in this and a host of related problems, including that of building natural language descriptions of commercial overhead imagery and videos, where automation is greatly needed: "If we were to attempt to manually exploit the commercial satellite imagery we expect to have over the next 20 years, we would need eight million imagery analysts" [Robert Cardillo, NGA Director, GEOINT Symposium 2017]. This workshop brings together researchers in machine learning, computer vision, natural language processing... (more)

Recent advances in machine learning have had a profound impact on computer vision. Simultaneously, success in computer vision applications has rapidly increased our understanding of some machine learning techniques, especially their applicability. This workshop will bring together researchers who are building a stronger theoretical understanding of the foundations of machine learning with computer vision researchers who are advancing our understanding of machine learning in practice.

Much of the recent growth in the use of machine learning in computer vision has been spurred by advances in deep neural networks. At the same time, new advances in other areas of machine learning, including reinforcement learning, generative models, and optimization methods, hold great promise for future impact. These raise important fundamental questions, such as understanding what influences the ability of learning algorithms to generalize, understanding what causes optimization in learning to converge... (more)

Computer vision is an inter-disciplinary topic crossing boundaries between computer science, statistics, mathematics, engineering and cognitive science.

Research in computer vision involves the development and evaluation of computational methods for image analysis. This includes the design of new theoretical models and algorithms, and practical implementation of these algorithms using a variety of computer architectures and programming languages. The methods under consideration are often motivated by generative mathematical models of the world and the imaging process. Recent approaches also rely heavily on machine learning techniques and discriminative models such as deep neural networks.

Problems that will be considered in the program include image restoration, image segmentation, object recognition and 3D reconstruction. Current approaches to address these problems draw on a variety of mathematical and computational topics such as stochastic models, statistical methods,... (more)

This will be a hands-on workshop focused on a specific computational problem: enumerating all isomorphism classes of abelian varieties of dimension g over a finite field of cardinality q, for a suitable range of integers g and q. Isogeny classes of abelian varieties over finite fields have been previously classified by Weil polynomials and can be found in the L-functions and Modular Form Database. The goal of this workshop is to refine this to the level of isomorphism classes, and, whenever possible, to construct explicit representatives for each isomorphism class. By exploiting recent theoretical and computational advances and assembling an appropriate team of experts, we hope to make rapid and substantial progress during this short, focused workshop and to have results available in advance of the conference on the Arithmetic of Low-dimensional Abelian Varieties that will take place at ICERM in June.

This is a closed workshop that will not be accepting applications.(more)

Note: At this time, ICERM is no longer accepting applications for this workshop as we are at capacity. Talks will be live streamed and recorded for viewing.

The machine learning revolution is already having a significant impact across the social sciences and business, but it is also beginning to change computational science and engineering in fundamental and very varied ways.

We are experiencing the rise of new and simpler data-driven methods based on techniques from machine learning such as deep learning. This revolution allows for the development of radical new techniques to address problems known to be very challenging with traditional methods and suggests the potential dramatic enhancement of existing methods through data informed parameter selection, both in static and dynamic modes of operation. Techniques are emerging that allows us to produce realistic solutions from non-sterilized computational problems in diverse physical sciences.

However, the urgent and... (more)

Causal and mathematical models are widely used for decision making and policy evaluation at both the micro and macro levels. For example, causal models using large datasets are used to evaluate treatment efficacy in HIV; mathematical models are used to simulate the effects of prevention or policy measures to improve health outcomes or reduce the spread of infectious diseases. Entities such as the World Health Organization and UNAIDS rely on these models to set wide-ranging and high-impact policy related to treatment and prevention of infectious disease.

Causal models tend to rely on large-scale cohort data, while mathematical models in many ways represent evidence synthesis. Important methodologic issues in the development, application, and interpretation of these models include the role of untestable assumptions, transportability of findings to specific populations of interest, model calibration and validation, and uncertainty quantification. The datasets used to develop these... (more)