Related papers: The fshape framework for the variability analysis …
Shape information is crucial for human perception and cognition, and should therefore also play a role in cognitive AI systems. We employ the interdisciplinary framework of conceptual spaces, which proposes a geometric representation of…
The field-theoretic wavefunction has received renewed attention with the goal of better understanding observables at the boundary of de Sitter spacetime and studying the interior of Minkowski or general FLRW spacetime. Understanding the…
For manifold learning, it is assumed that high-dimensional sample/data points are embedded on a low-dimensional manifold. Usually, distances among samples are computed to capture an underlying data structure. Here we propose a metric…
We adapt concepts, methodology, and theory originally developed in the areas of multidimensional scaling and dimensionality reduction for multivariate data to the functional setting. We focus on classical scaling and Isomap -- prototypical…
In affine formation control problems, the construction of the framework with universal rigidity and affine localizability is a critical prerequisite, but it has not yet been well addressed, especially when additional agents join the…
Deep networks for image classification often rely more on texture information than object shape. While efforts have been made to make deep-models shape-aware, it is often difficult to make such models simple, interpretable, or rooted in…
We propose a framework for the design and analysis of optimization algorithms in variational quantum Monte Carlo, drawing on geometric insights into the corresponding function space. The framework translates infinite-dimensional…
Problems of flexible mechanical metamaterials, and highly deformable porous solids in general, are rich and complex due to nonlinear mechanics and nontrivial geometrical effects. While numeric approaches are successful, analytic tools and…
A critical step in data analysis for many different types of experiments is the identification of features with theoretically defined shapes in N-dimensional datasets; examples of this process include finding peaks in multi-dimensional…
Analytic methods are emerging in solid and configuration modeling, while providing new insights into a variety of shape and motion related problems by exploiting tools from group morphology, convolution algebras, and harmonic analysis.…
Over the last decade, nonparametric methods have gained increasing attention for modeling complex data structures due to their flexibility and minimal structural assumptions. In this paper, we study a general multivariate nonparametric…
The persistence diagram is an increasingly useful tool from Topological Data Analysis, but its use alongside typical machine learning techniques requires mathematical finesse. The most success to date has come from methods that map…
Wombling methods, first introduced in 1951, have been widely applied to detect boundaries and variations across spatial domains, particularly in biological, public health and meteorological studies. Traditional applications focus on…
A pedagogical but concise overview of fiber bundles and their connections is provided, in the context of gauge theories in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing…
Bundle adjustment (BA) is a technique for refining sensor orientations of satellite images, while adjustment accuracy is correlated with feature matching results. Feature match-ing often contains high uncertainties in weak/repeat textures,…
We address the problem of merging graph and feature-space information while learning a metric from structured data. Existing algorithms tackle the problem in an asymmetric way, by either extracting vectorized summaries of the graph…
These notes on Riemannian geometry use the bases bundle and frame bundle, as in Geometry of Manifolds, to express the geometric structures. It has more problems and omits the background material. It starts with the definition of Riemannian…
Real-life man-made objects often exhibit strong and easily-identifiable structure, as a direct result of their design or their intended functionality. Structure typically appears in the form of individual parts and their arrangement.…
The shapelets method for image analysis is based upon the decomposition of localised objects into a series of orthogonal components with convenient mathematical properties. We extend the "Cartesian shapelet" formalism from earlier work, and…
Any procedure applied to data, and any quantity derived from data, is required to respect the nature and symmetries of the data. This axiom applies to refinement procedures and multiresolution transforms as well as to more basic operations…