相关论文: A cortical-inspired sub-Riemannian model for Pogge…
Quantifying hemodynamics in the curved segments of the intracranial internal carotid artery is a core challenge in diagnosing vascular stenosis. Conventional full-field imaging, such as 4D Flow MRI, is costly and difficult to widely…
Coarse-grained modeling in molecular simulations serves not only to extend accessible time and length scales beyond atomistic limits, but also to reduce high-dimensional chemical data to low-dimensional representations that expose the…
Euclidean representations distort data with intrinsic non-Euclidean structure. While Riemannian representation learning offers a solution by embedding data onto matching manifolds, it typically relies on an encoder to estimate densities on…
Recent progress in brain-guided image generation has improved the quality of fMRI-based reconstructions; however, fundamental challenges remain in preserving object-level structure and semantic fidelity. Many existing approaches overlook…
In vision science, cascades of Linear+Nonlinear transforms are very successful in modeling a number of perceptual experiences [Carandini&Heeger12]. However, the conventional literature is usually too focused on only describing the…
Anatomically guided PET reconstruction using MRI information has been shown to have the potential to improve PET image quality. However, these improvements are limited to PET scans with paired MRI information. In this work we employed a…
In this paper, we tackle a critical issue in nonparametric inference for systems of interacting particles on Riemannian manifolds: the identifiability of the interaction functions. Specifically, we define the function spaces on which the…
This paper advocates a novel framework for segmenting a dataset in a Riemannian manifold $M$ into clusters lying around low-dimensional submanifolds of $M$. Important examples of $M$, for which the proposed clustering algorithm is…
Decoding visual representations from brain signals has attracted significant attention in both neuroscience and artificial intelligence. However, the degree to which brain signals truly encode visual information remains unclear. Current…
Interpreting computations in the visual cortex as learning and inference in a generative model of the environment has received wide support both in neuroscience and cognitive science. However, hierarchical computations, a hallmark of visual…
This paper presents a novel framework for visual object recognition using infinite-dimensional covariance operators of input features in the paradigm of kernel methods on infinite-dimensional Riemannian manifolds. Our formulation provides…
Image reconstruction for positron emission tomography (PET) is challenging because of the ill-conditioned tomographic problem and low counting statistics. Kernel methods address this challenge by using kernel representation to incorporate…
Recent advances in implicit neural representations and differentiable rendering make it possible to simultaneously recover the geometry and materials of an object from multi-view RGB images captured under unknown static illumination.…
We present a computational approach to general hyperelliptic Riemann surfaces in Weierstrass normal form. The surface is either given by a list of the branch points, the coefficients of the defining polynomial or a system of cuts for the…
The state-of-the-art facial image inpainting methods achieved promising results but face realism preservation remains a challenge. This is due to limitations such as; failures in preserving edges and blurry artefacts. To overcome these…
Neuromorphic Computing promises orders of magnitude improvement in energy efficiency compared to traditional von Neumann computing paradigm. The goal is to develop an adaptive, fault-tolerant, low-footprint, fast, low-energy intelligent…
The problem of linking functional connectomics to behavior is extremely challenging due to the complex interactions between the two distinct, but related, data domains. We propose a coupled manifold optimization framework which projects…
We obtain upper bounds for the estimation error of Kernel Ridge Regression (KRR) for all non-negative regularization parameters, offering a geometric perspective on various phenomena in KRR. As applications: 1. We address the multiple…
Recent advances in brain-vision decoding have driven significant progress, reconstructing with high fidelity perceived visual stimuli from neural activity, e.g., functional magnetic resonance imaging (fMRI), in the human visual cortex. Most…
We extend the diffusion-map formalism to data sets that are induced by asymmetric kernels. Analytical convergence results of the resulting expansion are proved, and an algorithm is proposed to perform the dimensional reduction. In this work…