Related papers: Shape theory via SVD decomposition I
Spatial transcriptomics has revolutionized tissue analysis by simultaneously mapping gene expression, spatial topography, and histological context across consecutive tissue sections, enabling systematic investigation of spatial…
This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \& S\"uli [SIAM J.\ Numer.\ Anal.\…
We develop a mathematical and numerical framework to solve state estimation problems for applications that present variations in the shape of the spatial domain. This situation arises typically in a biomedical context where inverse problems…
In biomedical imaging reliable segmentation of objects (e.g. from small cells up to large organs) is of fundamental importance for automated medical diagnosis. New approaches for multi-scale segmentation can considerably improve performance…
The molecular rearrangements of most fluids under flow and deformation do not directly follow the macroscopic strain field. In this work, we describe a phenomenological method for characterizing such non-affine deformation via the…
We investigate how thin structures change their shape in response to non-mechanical stimuli that can be interpreted as variations in the structure's natural curvature. Starting from the theory of non-Euclidean plates and shells, we derive…
The problem of finding elliptical shapes in an image will be considered. We discuss the solution which uses cross-entropy clustering. The proposed method allows the search for ellipses with predefined sizes and position in the space.…
We introduce the first completely unsupervised correspondence learning approach for deformable 3D shapes. Key to our model is the understanding that natural deformations (such as changes in pose) approximately preserve the metric structure…
Bayes spaces were initially designed to provide a geometric framework for the modeling and analysis of distributional data. It has recently come to light that this methodology can be exploited to provide an orthogonal decomposition of…
We introduce a variational multiscale closure modeling strategy for the numerical stabilization of proper orthogonal decomposition reduced-order models of convection-dominated equations. As a first step, the new model is analyzed and tested…
We propose elliptical graphical models based on conditional uncorrelatedness as a general- ization of Gaussian graphical models by letting the population distribution be elliptical instead of normal, allowing the fitting of data with…
This invited paper proposes and discusses several Bayesian attempts at nonparametric and semiparametric density estimation. The main categories of these ideas are as follows: 1) Build a nonparametric prior around a given parametric model.…
This paper introduces an extended tensor decomposition (XTD) method for model reduction. The proposed method is based on a sparse non-separated enrichment to the conventional tensor decomposition, which is expected to improve the…
In this work, we consider methods for large-scale and nonconvex unconstrained optimization. We propose a new trust-region method whose subproblem is defined using a so-called "shape-changing" norm together with densely-initialized…
Estimating correspondences between pairs of deformable shapes remains a challenging problem. Despite substantial progress, existing methods lack broad generalization capabilities and require category-specific training data. To address these…
The question of representation of 3D geometry is of vital importance when it comes to leveraging the recent advances in the field of machine learning for geometry processing tasks. For common unstructured surface meshes state-of-the-art…
We study the structure of the set of all possible affine hyperplane sections of a convex polytope. We present two different cell decompositions of this set, induced by hyperplane arrangements. Using our decomposition, we bound the number of…
We present a new class of particle methods with deformable shapes that converge in the uniform norm without requiring remappings, extended overlapping or vanishing moments for the particles. The crux of the method is to use polynomial…
To date, the comparison of Statistical Shape Models (SSMs) is often solely performance-based, carried out by means of simplistic metrics such as compactness, generalization, or specificity. Any similarities or differences between the actual…
Diffusion models, which convert noise into new data instances by learning to reverse a diffusion process, have become a cornerstone in contemporary generative modeling. In this work, we develop non-asymptotic convergence theory for a…