Related papers: Supervised deep learning of elastic SRV distances …
The square root velocity transform is a powerful tool for the efficient computation of distances between curves. Also, after factoring out reparametrisations, it defines a distance between shapes that only depends on their intrinsic…
Of concern is the study of the space of curves in homogeneous spaces. Motivated by applications in shape analysis we identify two curves if they only differ by their parametrization and/or a rigid motion. For curves in Euclidean space the…
This paper focuses on the study of open curves in a Riemannian manifold M, and proposes a reparametrization invariant metric on the space of such paths. We use the square root velocity function (SRVF) introduced by Srivastava et al. to…
The square root velocity transformation provides a convenient and numerically efficient approach to functional and shape data analysis of curves. We study fundamental geometric properties of curves under this transformation. Moreover,…
The square root velocity function (SRVF), introduced by Srivastava et al, has proved to be an effective way to compare absolutely continuous curves in $R^N$ modulo reparametrization. Several computational papers have been published based on…
Shape analysis is ubiquitous in problems of pattern and object recognition and has developed considerably in the last decade. The use of shapes is natural in applications where one wants to compare curves independently of their…
How can one analyze detailed 3D biological objects, such as neurons and botanical trees, that exhibit complex geometrical and topological variation? In this paper, we develop a novel mathematical framework for representing, comparing, and…
Symmetric orthogonalization via SVD, and closely related procedures, are well-known techniques for projecting matrices onto $O(n)$ or $SO(n)$. These tools have long been used for applications in computer vision, for example optimal 3D…
The square root velocity framework is a method in shape analysis to define a distance between curves and functional data. Identifying two curves if they differ by a reparametrisation leads to the quotient space of unparametrised curves. In…
Deep Reinforcement Learning (DRL) has recently spread into a range of domains within physics and engineering, with multiple remarkable achievements. Still, much remains to be explored before the capabilities of these methods are well…
The aerodynamic optimization process of cars requires multiple iterations between aerodynamicists and stylists. Response Surface Modeling and Reduced-Order Modeling are commonly used to eliminate the overhead due to Computational Fluid…
Despite progress in the rapidly developing field of geometric deep learning, performing statistical analysis on geometric data--where each observation is a shape such as a curve, graph, or surface--remains challenging due to the…
We present learning-based implicit shape representations designed for real-time avatar collision queries arising in the simulation of clothing. Signed distance functions (SDFs) have been used for such queries for many years due to their…
Capturing the shape and spatially-varying appearance (SVBRDF) of an object from images is a challenging task that has applications in both computer vision and graphics. Traditional optimization-based approaches often need a large number of…
This work presents a novel physics-informed deep learning based super-resolution framework to reconstruct high-resolution deformation fields from low-resolution counterparts, obtained from coarse mesh simulations or experiments. We leverage…
Video super-resolution (VSR) aims to reconstruct a sequence of high-resolution (HR) images from their corresponding low-resolution (LR) versions. Traditionally, solving a VSR problem has been based on iterative algorithms that can exploit…
A main goal in the field of statistical shape analysis is to define computable and informative metrics on spaces of immersed manifolds, such as the space of curves in a Euclidean space. The approach taken in the elastic shape analysis…
High-quality 3D fetal brain MRI reconstruction from motion-corrupted 2D slices is crucial for clinical diagnosis. Reliable slice-to-volume registration (SVR)-based motion correction and super-resolution reconstruction (SRR) methods are…
Recent techniques have been successful in reconstructing surfaces as level sets of learned functions (such as signed distance fields) parameterized by deep neural networks. Many of these methods, however, learn only closed surfaces and are…
Recent advances in computer graphics and computer vision have found successful application of deep neural network models for 3D shapes based on signed distance functions (SDFs) that are useful for shape representation, retrieval, and…