相关论文: 4D Atlas: Statistical Analysis of the Spatiotempor…

This paper introduces a novel approach to statistics and data analysis, departing from the conventional assumption of data residing in Euclidean space to consider a Riemannian Manifold. The challenge lies in the absence of vector space…

Modelling deformation of anatomical objects observed in medical images can help describe disease progression patterns and variations in anatomy across populations. We apply a stochastic generalisation of the Large Deformation Diffeomorphic…

Objects that undergo non-rigid deformation are common in the real world. A typical and challenging example is the human faces. While various techniques have been developed for deformable shape registration and classification, benchmarks…

Reconstructing dynamic 3D scenes from 2D images and generating diverse views over time is challenging due to scene complexity and temporal dynamics. Despite advancements in neural implicit models, limitations persist: (i) Inadequate Scene…

Spatiotemporal Traffic Data (STTD) measures the complex dynamical behaviors of the multiscale transportation system. Existing methods aim to reconstruct STTD using low-dimensional models. However, they are limited to data-specific…

We introduce a stochastic model of diffeomorphisms, whose action on a variety of data types descends to stochastic evolution of shapes, images and landmarks. The stochasticity is introduced in the vector field which transports the data in…

Non-Rigid Structure-from-Motion (NRSfM) problem aims to recover 3D geometry of a deforming object from its 2D feature correspondences across multiple frames. Classical approaches to this problem assume a small number of feature points and,…

In this paper, we propose a novel space-time geometric representation of human landmark configurations and derive tools for comparison and classification. We model the temporal evolution of landmarks as parametrized trajectories on the…

Given data, deep generative models, such as variational autoencoders (VAE) and generative adversarial networks (GAN), train a lower dimensional latent representation of the data space. The linear Euclidean geometry of data space pulls back…

While classical data analysis has addressed observations that are real numbers or elements of a real vector space, at present many statistical problems of high interest in the sciences address the analysis of data that consist of more…

As a core step in structure-from-motion and SLAM, robust feature detection and description under challenging scenarios such as significant viewpoint changes remain unresolved despite their ubiquity. While recent works have identified the…

Exploring variations of 3D shapes is a time-consuming process in traditional 3D modeling tools. Deep generative models of 3D shapes often feature continuous latent spaces that can, in principle, be used to explore potential variations…

Many econometric analyses involve spatio--temporal data. A considerable amount of literature has addressed spatio--temporal models, with Spatial Dynamic Panel Data (SDPD) being widely investigated and applied. In real data applications,…

This paper addresses the task of dense non-rigid structure-from-motion (NRSfM) using multiple images. State-of-the-art methods to this problem are often hurdled by scalability, expensive computations, and noisy measurements. Further, recent…

Topological data analysis is becoming a popular way to study high dimensional feature spaces without any contextual clues or assumptions. This paper concerns itself with one popular topological feature, which is the number of…

Parametric spatial transformation models have been successfully applied to image registration tasks. In such models, the transformation of interest is parameterized by a fixed set of basis functions as for example B-splines. Each basis…

We introduce a novel, data-driven approach for reconstructing temporally coherent 3D motion from unstructured and potentially partial observations of non-rigidly deforming shapes. Our goal is to achieve high-fidelity motion reconstructions…

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…

In the study of shapes of human organs using computational anatomy, variations are found to arise from inter-subject anatomical differences, disease-specific effects, and measurement noise. This paper introduces a stochastic model for…

Estimating the pose of an object from a monocular image is an inverse problem fundamental in computer vision. The ill-posed nature of this problem requires incorporating deformation priors to solve it. In practice, many materials do not…