Topic
Epipolar geometry
About: Epipolar geometry is a research topic. Over the lifetime, 4224 publications have been published within this topic receiving 135847 citations.
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Proceedings Article•
31 Dec 1993TL;DR: Results from constrained optimization some results from algebraic geometry differential geometry are shown.
Abstract: Projective geometry modelling and calibrating cameras edge detection representing geometric primitives and their uncertainty stereo vision determining discrete motion from points and lines tracking tokens over time motion fields of curves interpolating and approximating three-dimensional data recognizing and locating objects and places answers to problems. Appendices: constrained optimization some results from algebraic geometry differential geometry.
2,744 citations
21 Jul 2017
TL;DR: In this article, the authors propose a novel training objective that enables CNNs to learn to perform single image depth estimation, despite the absence of ground truth depth data, by generating disparity images by training their network with an image reconstruction loss.
Abstract: Learning based methods have shown very promising results for the task of depth estimation in single images. However, most existing approaches treat depth prediction as a supervised regression problem and as a result, require vast quantities of corresponding ground truth depth data for training. Just recording quality depth data in a range of environments is a challenging problem. In this paper, we innovate beyond existing approaches, replacing the use of explicit depth data during training with easier-to-obtain binocular stereo footage. We propose a novel training objective that enables our convolutional neural network to learn to perform single image depth estimation, despite the absence of ground truth depth data. Ex-ploiting epipolar geometry constraints, we generate disparity images by training our network with an image reconstruction loss. We show that solving for image reconstruction alone results in poor quality depth images. To overcome this problem, we propose a novel training loss that enforces consistency between the disparities produced relative to both the left and right images, leading to improved performance and robustness compared to existing approaches. Our method produces state of the art results for monocular depth estimation on the KITTI driving dataset, even outperforming supervised methods that have been trained with ground truth depth.
2,239 citations
TL;DR: A robust approach to image matching by exploiting the only available geometric constraint, namely, the epipolar constraint, is proposed and a new strategy for updating matches is developed, which only selects those matches having both high matching support and low matching ambiguity.
1,574 citations
15 Sep 1995
TL;DR: An image-based rendering system based on sampling, reconstructing, and resampling the plenoptic function is presented and a novel visible surface algorithm and a geometric invariant for cylindrical projections that is equivalent to the epipolar constraint defined for planar projections are introduced.
Abstract: Image-based rendering is a powerful new approach for generating real-time photorealistic computer graphics. It can provide convincing animations without an explicit geometric representation. We use the “plenoptic function” of Adelson and Bergen to provide a concise problem statement for image-based rendering paradigms, such as morphing and view interpolation. The plenoptic function is a parameterized function for describing everything that is visible from a given point in space. We present an image-based rendering system based on sampling, reconstructing, and resampling the plenoptic function. In addition, we introduce a novel visible surface algorithm and a geometric invariant for cylindrical projections that is equivalent to the epipolar constraint defined for planar projections.
1,555 citations
TL;DR: A complete review of the current techniques for estimating the fundamental matrix and its uncertainty is provided, and a well-founded measure is proposed to compare these techniques.
Abstract: Two images of a single scene/object are related by the epipolar geometry, which can be described by a 3×3 singular matrix called the essential matrix if images‘ internal parameters are known, or the fundamental matrix otherwise. It captures all geometric information contained in two images, and its determination is very important in many applications such as scene modeling and vehicle navigation. This paper gives an introduction to the epipolar geometry, and provides a complete review of the current techniques for estimating the fundamental matrix and its uncertainty. A well-founded measure is proposed to compare these techniques. Projective reconstruction is also reviewed. The software which we have developed for this review is available on the Internet.
1,217 citations