Related papers: Geometric dynamics of optimization
Recent research on accelerated gradient methods of use in optimization has demonstrated that these methods can be derived as discretizations of dynamical systems. This, in turn, has provided a basis for more systematic investigations,…
This paper describes a class of shape optimization problems for optical metamaterials comprised of periodic microscale inclusions composed of a dielectric, low-dimensional material suspended in a non-magnetic bulk dielectric. The shape…
We present HyperMorph, a learning-based strategy for deformable image registration that removes the need to tune important registration hyperparameters during training. Classical registration methods solve an optimization problem to find a…
Many optimization problems can be naturally represented as (hyper) graphs, where vertices correspond to variables and edges to tasks, whose cost depends on the values of the adjacent variables. Capitalizing on the structure of the graph,…
Optimization is an integral part of modern deep learning. Recently, the concept of learned optimizers has emerged as a way to accelerate this optimization process by replacing traditional, hand-crafted algorithms with meta-learned…
Lagrangian particle formulations of the large deformation diffeomorphic metric mapping algorithm (LDDMM) only allow for the study of a single shape. In this paper, we introduce and discuss both a theoretical and practical setting for the…
Image Processing, Optimization and Prediction of an Image play a key role in Computer Science. Image processing provides a way to analyze and identify an image .Many areas like medical image processing, Satellite images, natural images and…
Studying structural properties of linear dynamical systems through invariant subspaces is one of the key contributions of the geometric approach to system theory. In general, a model of the dynamics is required in order to compute the…
Two meta-evolutionary optimization strategies described in this paper accelerate the convergence of evolutionary programming algorithms while still retaining much of their ability to deal with multi-modal problems. The strategies, called…
Metamorphism is a recently introduced integral transform, which is useful in solving partial differential equations. Basic properties of metamorphism can be verified by direct calculations. In this paper we present metamorphism as a sort of…
For robots to handle the numerous factors that can affect them in the real world, they must adapt to changes and unexpected events. Evolutionary robotics tries to solve some of these issues by automatically optimizing a robot for a specific…
In this paper, we investigate two stochastic perturbations of the metamorphosis equations of image analysis, in the geometrical context of the Euler-Poincar\'e theory. In the metamorphosis of images, the Lie group of diffeomorphisms deforms…
This paper focuses on the statistical analysis of shapes of data objects called shape graphs, a set of nodes connected by articulated curves with arbitrary shapes. A critical need here is a constrained registration of points (nodes to…
This paper discusses the mathematical framework for designing methods of large deformation matching (LDM) for image registration in computational anatomy. After reviewing the geometrical framework of LDM image registration methods, a…
Time dependence is a universal phenomenon in nature, and a variety of mathematical models in terms of dynamical systems have been developed to understand the time-dependent behavior of real-world problems. Originally constructed to analyze…
We study relationships between dynamic programs by applying conjugacy methods from dynamical systems theory. When two dynamic programs are connected by an order isomorphism, we show that optimality properties transmit from one formulation…
We propose a PDE-constrained shape registration algorithm that captures the deformation and growth of biological tissue from imaging data. Shape registration is the process of evaluating optimum alignment between pairs of geometries through…
Metasurfaces have emerged as transformative electromagnetic structures for wireless communications, enabling the real-time control over wave propagation, yielding potential for improved data rates, privacy, energy efficiency and even…
Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…
We present a novel approach for the reconstruction of dynamic geometric shapes using a single hand-held consumer-grade RGB-D sensor at real-time rates. Our method does not require a pre-defined shape template to start with and builds up the…