Related papers: Deep Regression on Manifolds: A 3D Rotation Case S…

In this article we present the basics of manifold relevance determination (MRD) as introduced in \cite{mrd}, and some applications where the technology might be of particular use. Section 1 acts as a short tutorial of the ideas developed in…

Neural implicit representations have become a popular choice for modeling surfaces due to their adaptability in resolution and support for complex topology. While previous works have achieved impressive reconstruction quality by training on…

Whereas recovery of the manifold from data is a well-studied topic, approximation rates for functions defined on manifolds are less known. In this work, we study a regression problem with inputs on a $d^*$-dimensional manifold that is…

We introduce a neural implicit framework that exploits the differentiable properties of neural networks and the discrete geometry of point-sampled surfaces to approximate them as the level sets of neural implicit functions. To train a…

Embedding 3D morphable basis functions into deep neural networks opens great potential for models with better representation power. However, to faithfully learn those models from an image collection, it requires strong regularization to…

To have a superior generalization, a deep learning neural network often involves a large size of training sample. With increase of hidden layers in order to increase learning ability, neural network has potential degradation in accuracy.…

Rotation estimation of known rigid objects is important for robotic applications such as dexterous manipulation. Most existing methods for rotation estimation use intermediate representations such as templates, global or local feature…

Current work on human-machine alignment aims at understanding machine-learned latent spaces and their correspondence to human representations. G{\"a}rdenfors' conceptual spaces is a prominent framework for understanding human…

The success of deep neural networks hinges on our ability to accurately and efficiently optimize high-dimensional, non-convex functions. In this paper, we empirically investigate the loss functions of state-of-the-art networks, and how…

Predicting the pose of objects from a single image is an important but difficult computer vision problem. Methods that predict a single point estimate do not predict the pose of objects with symmetries well and cannot represent uncertainty.…

Uncertainty quantification for deep learning is a challenging open problem. Bayesian statistics offer a mathematically grounded framework to reason about uncertainties; however, approximate posteriors for modern neural networks still…

How to effectively represent camera pose is an essential problem in 3D computer vision, especially in tasks such as camera pose regression and novel view synthesis. Traditionally, 3D position of the camera is represented by Cartesian…

Recently, regression-based methods have dominated the field of 3D human pose and shape estimation. Despite their promising results, a common issue is the misalignment between predictions and image observations, often caused by minor joint…

Many computer vision challenges require continuous outputs, but tend to be solved by discrete classification. The reason is classification's natural containment within a probability $n$-simplex, as defined by the popular softmax activation…

Embedding of large but redundant data, such as images or text, in a hierarchy of lower-dimensional spaces is one of the key features of representation learning approaches, which nowadays provide state-of-the-art solutions to problems once…

A complete representation of 3D objects requires characterizing the space of deformations in an interpretable manner, from articulations of a single instance to changes in shape across categories. In this work, we improve on a prior…

Differentiable render is widely used in optimization-based 3D reconstruction which requires gradients from differentiable operations for gradient-based optimization. The existing differentiable renderers obtain the gradients of rendering…

In this paper, we analyze deep learning from a mathematical point of view and derive several novel results. The results are based on intriguing mathematical properties of high dimensional spaces. We first look at perturbation based…

The diagnosis of prostate cancer faces a problem with overdiagnosis that leads to damaging side effects due to unnecessary treatment. Research has shown that the use of multi-parametric magnetic resonance images to conduct biopsies can…

Omnidirectional images and spherical representations of $3D$ shapes cannot be processed with conventional 2D convolutional neural networks (CNNs) as the unwrapping leads to large distortion. Using fast implementations of spherical and…