Related papers: The Local Dimension of Deep Manifold

Due to the abundance of 2D product images from the Internet, developing efficient and scalable algorithms to recover the missing depth information is central to many applications. Recent works have addressed the single-view depth estimation…

We consider the problems of classification and intrinsic dimension estimation on image data. A new subspace based classifier is proposed for supervised classification or intrinsic dimension estimation. The distribution of the data in each…

Learning-based multi-view stereo (MVS) methods deal with predicting accurate depth maps to achieve an accurate and complete 3D representation. Despite the excellent performance, existing methods ignore the fact that a suitable depth…

Dense depth perception is critical for autonomous driving and other robotics applications. However, modern LiDAR sensors only provide sparse depth measurement. It is thus necessary to complete the sparse LiDAR data, where a synchronized…

Stochastic gradient descent (SGD) is widely used in deep learning due to its computational efficiency, but a complete understanding of why SGD performs so well remains a major challenge. It has been observed empirically that most…

The manifold hypothesis asserts that data of interest in high-dimensional ambient spaces, such as image data, lies on unknown low-dimensional submanifolds. Diffusion models (DMs) -- which operate by convolving data with progressively larger…

Deep neural networks have been widely used in image denoising during the past few years. Even though they achieve great success on this problem, they are computationally inefficient which makes them inappropriate to be implemented in mobile…

Recently, deep learning methods have been proposed for quantitative susceptibility mapping (QSM) data processing: background field removal, field-to-source inversion, and single-step QSM reconstruction. However, the conventional padding…

Increasing depth of convolutional neural networks (CNNs) is a highly promising method of increasing the accuracy of the (CNNs). Increased CNN depth will also result in increased layer count (parameters), leading to a slow backpropagation…

High-dimensional data are ubiquitous in contemporary science and finding methods to compress them is one of the primary goals of machine learning. Given a dataset lying in a high-dimensional space (in principle hundreds to several thousands…

Estimating a depth map from a single RGB image has been investigated widely for localization, mapping, and 3-dimensional object detection. Recent studies on a single-view depth estimation are mostly based on deep Convolutional neural…

Deep neural networks progressively transform their inputs across multiple processing layers. What are the geometrical properties of the representations learned by these networks? Here we study the intrinsic dimensionality (ID) of…

Depth estimation is of critical interest for scene understanding and accurate 3D reconstruction. Most recent approaches in depth estimation with deep learning exploit geometrical structures of standard sharp images to predict corresponding…

Our formal understanding of the inductive bias that drives the success of convolutional networks on computer vision tasks is limited. In particular, it is unclear what makes hypotheses spaces born from convolution and pooling operations so…

Deep convolutional neural networks (ConvNets) of 3-dimensional kernels allow joint modeling of spatiotemporal features. These networks have improved performance of video and volumetric image analysis, but have been limited in size due to…

Deep Neural Networks (DNNs) have encountered an emerging deployment challenge due to large and expensive memory and computation requirements. In this paper, we present a new Adaptive-Rank Singular Value Decomposition (ARSVD) method that…

Despite their empirical success, pushing Transformer architectures to extreme depth often leads to a paradoxical failure: representations become increasingly redundant, lose rank, and ultimately collapse. Existing explanations largely…

Matrix factorizations in dual number algebra, a hypercomplex system, have been applied to kinematics, mechanisms, and other fields recently. We develop an approach to identify spatiotemporal patterns in the brain such as traveling waves…

The concept of dimension is essential to grasp the complexity of data. A naive approach to determine the dimension of a dataset is based on the number of attributes. More sophisticated methods derive a notion of intrinsic dimension (ID)…

Depth estimation from a single image is an important task that can be applied to various fields in computer vision, and has grown rapidly with the development of convolutional neural networks. In this paper, we propose a novel structure and…