Beyond Gr\"obner Bases: Basis Selection for Minimal Solvers

Many computer vision applications require robust estimation of the underlying geometry, in terms of camera motion and 3D structure of the scene. These robust methods often rely on running minimal solvers in a RANSAC framework. In this paper we show how we can make polynomial solvers based on the action matrix method faster, by careful selection of the monomial bases. These monomial bases have traditionally been based on a Gr\"obner basis for the polynomial ideal. Here we describe how we can enumerate all such bases in an efficient way. We also show that going beyond Gr\"obner bases leads to more efficient solvers in many cases. We present a novel basis sampling scheme that we evaluate on a number of problems

Calibrated and Partially Calibrated Semi-Generalized Homographies

In this paper, we propose the first minimal solutions for estimating the semi-generalized homography given a perspective and a generalized camera. The proposed solvers use five 2D-2D image point correspondences induced by a scene plane. One of them assumes the perspective camera to be fully calibrated, while the other solver estimates the unknown focal length together with the absolute pose parameters. This setup is particularly important in structure-from-motion and image-based localization pipelines, where a new camera is localized in each step with respect to a set of known cameras and 2D-3D correspondences might not be available. As a consequence of a clever parametrization and the elimination ideal method, our approach only needs to solve a univariate polynomial of degree five or three. The proposed solvers are stable and efficient as demonstrated by a number of synthetic and real-world experiments

Procedures for condition mapping using 360° images

The identification of deterioration mechanisms and their monitoring over time is an essential phase for conservation. This work aimed at developing a novel approach for deterioration mapping and monitoring based on 360° images, which allows for simple and rapid data collection. The opportunity to capture the whole scene around a 360° camera reduces the number of images needed in a condition mapping project, resulting in a powerful solution to document small and narrow spaces. The paper will describe the implemented workflow for deterioration mapping based on 360° images, which highlights pathologies on surfaces and quantitatively measures their extension. Such a result will be available as standard outputs as well as an innovative virtual environment for immersive visualization. The case of multi-temporal data acquisition will be considered and discussed as well. Multiple 360° images acquired at different epochs from slightly different points are co-registered to obtain pixel-to-pixel correspondence, providing a solution to quantify and track deterioration effects

Computational Methods for Computer Vision : Minimal Solvers and Convex Relaxations

Robust fitting of geometric models is a core problem in computer vision. The most common approach is to use a hypothesize-and-test framework, such as RANSAC. In these frameworks the model is estimated from as few measurements as possible, which minimizes the risk of selecting corrupted measurements. These estimation problems are called minimal problems, and they can often be formulated as systems of polynomial equations. In this thesis we present new methods for building so-called minimal solvers or polynomial solvers, which are specialized code for solving such systems. On several minimal problems we improve on the state-of-the-art both with respect to numerical stability and execution time.In many computer vision problems low rank matrices naturally occur. The rank can serve as a measure of model complexity and typically a low rank is desired. Optimization problems containing rank penalties or constraints are in general difficult. Recently convex relaxations, such as the nuclear norm, have been used to make these problems tractable. In this thesis we present new convex relaxations for rank-based optimization which avoid drawbacks of previous approaches and provide tighter relaxations. We evaluate our methods on a number of real and synthetic datasets and show state-of-the-art results

Tele-immersive display with live-streamed video.

Tang Wai-Kwan.Thesis (M.Phil.)--Chinese University of Hong Kong, 2001.Includes bibliographical references (leaves 88-95).Abstracts in English and Chinese.Abstract --- p.iAcknowledgement --- p.iiiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Applications --- p.3Chapter 1.2 --- Motivation and Goal --- p.6Chapter 1.3 --- Thesis Outline --- p.7Chapter 2 --- Background and Related Work --- p.8Chapter 2.1 --- Panoramic Image Navigation --- p.8Chapter 2.2 --- Image Mosaicing --- p.9Chapter 2.2.1 --- Image Registration --- p.10Chapter 2.2.2 --- Image Composition --- p.12Chapter 2.3 --- Immersive Display --- p.13Chapter 2.4 --- Video Streaming --- p.14Chapter 2.4.1 --- Video Coding --- p.15Chapter 2.4.2 --- Transport Protocol --- p.18Chapter 3 --- System Design --- p.19Chapter 3.1 --- System Architecture --- p.19Chapter 3.1.1 --- Video Capture Module --- p.19Chapter 3.1.2 --- Video Streaming Module --- p.23Chapter 3.1.3 --- Stitching and Rendering Module --- p.24Chapter 3.1.4 --- Display Module --- p.24Chapter 3.2 --- Design Issues --- p.25Chapter 3.2.1 --- Modular Design --- p.25Chapter 3.2.2 --- Scalability --- p.26Chapter 3.2.3 --- Workload distribution --- p.26Chapter 4 --- Panoramic Video Mosaic --- p.28Chapter 4.1 --- Video Mosaic to Image Mosaic --- p.28Chapter 4.1.1 --- Assumptions --- p.29Chapter 4.1.2 --- Processing Pipeline --- p.30Chapter 4.2 --- Camera Calibration --- p.33Chapter 4.2.1 --- Perspective Projection --- p.33Chapter 4.2.2 --- Distortion --- p.36Chapter 4.2.3 --- Calibration Procedure --- p.37Chapter 4.3 --- Panorama Generation --- p.39Chapter 4.3.1 --- Cylindrical and Spherical Panoramas --- p.39Chapter 4.3.2 --- Homography --- p.41Chapter 4.3.3 --- Homography Computation --- p.42Chapter 4.3.4 --- Error Minimization --- p.44Chapter 4.3.5 --- Stitching Multiple Images --- p.46Chapter 4.3.6 --- Seamless Composition --- p.47Chapter 4.4 --- Image Mosaic to Video Mosaic --- p.49Chapter 4.4.1 --- Varying Intensity --- p.49Chapter 4.4.2 --- Video Frame Management --- p.50Chapter 5 --- Immersive Display --- p.52Chapter 5.1 --- Human Perception System --- p.52Chapter 5.2 --- Creating Virtual Scene --- p.53Chapter 5.3 --- VisionStation --- p.54Chapter 5.3.1 --- F-Theta Lens --- p.55Chapter 5.3.2 --- VisionStation Geometry --- p.56Chapter 5.3.3 --- Sweet Spot Relocation and Projection --- p.57Chapter 5.3.4 --- Sweet Spot Relocation in Vector Representation --- p.61Chapter 6 --- Video Streaming --- p.65Chapter 6.1 --- Video Compression --- p.66Chapter 6.2 --- Transport Protocol --- p.66Chapter 6.3 --- Latency and Jitter Control --- p.67Chapter 6.4 --- Synchronization --- p.70Chapter 7 --- Implementation and Results --- p.71Chapter 7.1 --- Video Capture --- p.71Chapter 7.2 --- Video Streaming --- p.73Chapter 7.2.1 --- Video Encoding --- p.73Chapter 7.2.2 --- Streaming Protocol --- p.75Chapter 7.3 --- Implementation Results --- p.76Chapter 7.3.1 --- Indoor Scene --- p.76Chapter 7.3.2 --- Outdoor Scene --- p.78Chapter 7.4 --- Evaluation --- p.78Chapter 8 --- Conclusion --- p.83Chapter 8.1 --- Summary --- p.83Chapter 8.2 --- Future Directions --- p.84Chapter A --- Parallax --- p.8