Related papers: Multiview Differential Geometry of Curves

Reconstructing 3D scenes from multiple views has made impressive strides in recent years, chiefly by correlating isolated feature points, intensity patterns, or curvilinear structures. In the general setting - without controlled…

Multi-view image generation holds significant application value in computer vision, particularly in domains like 3D reconstruction, virtual reality, and augmented reality. Most existing methods, which rely on extending single images, face…

Obtaining complete information about the shape of an object by looking at it from a single direction is impossible in general. In this paper, we theoretically study obtaining differential geometric information of an object from orthogonal…

We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…

We address the problem of learning accurate 3D shape and camera pose from a collection of unlabeled category-specific images. We train a convolutional network to predict both the shape and the pose from a single image by minimizing the…

In recent years, 3D vision has become a crucial field within computer vision, powering a wide range of applications such as autonomous driving, robotics, augmented reality, and medical imaging. This field relies on accurate perception,…

We introduce a new formalism and a number of new results in the context of geometric computational vision. The classical scope of the research in geometric computer vision is essentially limited to static configurations of points and lines…

In this work, we address the problem of refining the geometry of local image features from multiple views without known scene or camera geometry. Current approaches to local feature detection are inherently limited in their keypoint…

Researchers have now achieved great success on dealing with 2D images using deep learning. In recent years, 3D computer vision and Geometry Deep Learning gain more and more attention. Many advanced techniques for 3D shapes have been…

This paper introduces a general approach to dynamic scene reconstruction from multiple moving cameras without prior knowledge or limiting constraints on the scene structure, appearance, or illumination. Existing techniques for dynamic scene…

The curvature regularities are well-known for providing strong priors in the continuity of edges, which have been applied to a wide range of applications in image processing and computer vision. However, these models are usually non-convex,…

Deep neural networks have achieved significant success in 3D point cloud classification while relying on large-scale, annotated point cloud datasets, which are labor-intensive to build. Compared to capturing data with LiDAR sensors and then…

The choice of data representation is a key factor in the success of deep learning in geometric tasks. For instance, DUSt3R recently introduced the concept of viewpoint-invariant point maps, generalizing depth prediction and showing that all…

DUSt3R has recently shown that one can reduce many tasks in multi-view geometry, including estimating camera intrinsics and extrinsics, reconstructing the scene in 3D, and establishing image correspondences, to the prediction of a pair of…

Generating consistent multiple views for 3D reconstruction tasks is still a challenge to existing image-to-3D diffusion models. Generally, incorporating 3D representations into diffusion model decrease the model's speed as well as…

In this paper, we address the problem of reconstructing an object's surface from a single image using generative networks. First, we represent a 3D surface with an aggregation of dense point clouds from multiple views. Each point cloud is…

Human has an incredible ability to effortlessly perceive the viewpoint difference between two images containing the same object, even when the viewpoint change is astonishingly vast with no co-visible regions in the images. This remarkable…

Multiview varieties are mathematical models for the set of image feature correspondences that can be produced by a given camera arrangement. They possess an invariant known as their Euclidean distance (ED) degree, which measures the…

Deep learning within the context of point clouds has gained much research interest in recent years mostly due to the promising results that have been achieved on a number of challenging benchmarks, such as 3D shape recognition and scene…

We introduce the Frenet theory of curves in dual space $\d^3$. After defining the curvature and the torsion of a curve, we classify all curves in dual plane with constant curvature. We also establish the fundamental theorem of existence in…