Detecting shadows and low-lying objects in indoor and outdoor scenes using homographies

Many computer vision applications apply background suppression techniques for the detection and segmentation of moving objects in a scene. While these algorithms tend to work well in controlled conditions they often fail when applied to unconstrained real-world environments. This paper describes a system that detects and removes erroneously segmented foreground regions that are close to a ground plane. These regions include shadows, changing background objects and other low-lying objects such as leaves and rubbish. The system uses a set-up of two or more cameras and requires no 3D reconstruction or depth analysis of the regions. Therefore, a strong camera calibration of the set-up is not necessary. A geometric constraint called a homography is exploited to determine if foreground points are on or above the ground plane. The system takes advantage of the fact that regions in images off the homography plane will not correspond after a homography transformation. Experimental results using real world scenes from a pedestrian tracking application illustrate the effectiveness of the proposed approach

Acquiring 3D scene information from 2D images

In recent years, people are becoming increasingly acquainted with 3D technologies such as 3DTV, 3D movies and 3D virtual navigation of city environments in their daily life. Commercial 3D movies are now commonly available for consumers. Virtual navigation of our living environment as used on a personal computer has become a reality due to well-known web-based geographic applications using advanced imaging technologies. To enable such 3D applications, many technological challenges such as 3D content creation, 3D displaying technology and 3D content transmission need to tackled and deployed at low cost. This thesis concentrates on the reconstruction of 3D scene information from multiple 2D images, aiming for an automatic and low-cost production of the 3D content. In this thesis, two multiple-view 3D reconstruction systems are proposed: a 3D modeling system for reconstructing the sparse 3D scene model from long video sequences captured with a hand-held consumer camcorder, and a depth reconstruction system for creating depth maps from multiple-view videos taken by multiple synchronized cameras. Both systems are designed to compute the 3D scene information in an automated way with minimum human interventions, in order to reduce the production cost of 3D contents. Experimental results on real videos of hundreds and thousands frames have shown that the two systems are able to accurately and automatically reconstruct the 3D scene information from 2D image data. The findings of this research are useful for emerging 3D applications such as 3D games, 3D visualization and 3D content production. Apart from designing and implementing the two proposed systems, we have developed three key scientific contributions to enable the two proposed 3D reconstruction systems. The first contribution is that we have designed a novel feature point matching algorithm that uses only a smoothness constraint for matching the points, which states that neighboring feature points in images tend to move with similar directions and magnitudes. The employed smoothness assumption is not only valid but also robust for most images with limited image motion, regardless of the camera motion and scene structure. Because of this, the algorithm obtains two major advan- 1 tages. First, the algorithm is robust to illumination changes, as the employed smoothness constraint does not rely on any texture information. Second, the algorithm has a good capability to handle the drift of the feature points over time, as the drift can hardly lead to a violation of the smoothness constraint. This leads to the large number of feature points matched and tracked by the proposed algorithm, which significantly helps the subsequent 3D modeling process. Our feature point matching algorithm is specifically designed for matching and tracking feature points in image/video sequences where the image motion is limited. Our extensive experimental results show that the proposed algorithm is able to track at least 2.5 times as many feature points compared with the state-of-the-art algorithms, with a comparable or higher accuracy. This contributes significantly to the robustness of the 3D reconstruction process. The second contribution is that we have developed algorithms to detect critical configurations where the factorization-based 3D reconstruction degenerates. Based on the detection, we have proposed a sequence-dividing algorithm to divide a long sequence into subsequences, such that successful 3D reconstructions can be performed on individual subsequences with a high confidence. The partial reconstructions are merged later to obtain the 3D model of the complete scene. In the critical configuration detection algorithm, the four critical configurations are detected: (1) coplanar 3D scene points, (2) pure camera rotation, (3) rotation around two camera centers, and (4) presence of excessive noise and outliers in the measurements. The configurations in cases (1), (2) and (4) will affect the rank of the Scaled Measurement Matrix (SMM). The number of camera centers in case (3) will affect the number of independent rows of the SMM. By examining the rank and the row space of the SMM, the abovementioned critical configurations are detected. Based on the detection results, the proposed sequence-dividing algorithm divides a long sequence into subsequences, such that each subsequence is free of the four critical configurations in order to obtain successful 3D reconstructions on individual subsequences. Experimental results on both synthetic and real sequences have demonstrated that the above four critical configurations are robustly detected, and a long sequence of thousands frames is automatically divided into subsequences, yielding successful 3D reconstructions. The proposed critical configuration detection and sequence-dividing algorithms provide an essential processing block for an automatical 3D reconstruction on long sequences. The third contribution is that we have proposed a coarse-to-fine multiple-view depth labeling algorithm to compute depth maps from multiple-view videos, where the accuracy of resulting depth maps is gradually refined in multiple optimization passes. In the proposed algorithm, multiple-view depth reconstruction is formulated as an image-based labeling problem using the framework of Maximum A Posterior (MAP) on Markov Random Fields (MRF). The MAP-MRF framework allows the combination of various objective and heuristic depth cues to define the local penalty and the interaction energies, which provides a straightforward and computationally tractable formulation. Furthermore, the global optimal MAP solution to depth labeli ing can be found by minimizing the local energies, using existing MRF optimization algorithms. The proposed algorithm contains the following three key contributions. (1) A graph construction algorithm to proposed to construct triangular meshes on over-segmentation maps, in order to exploit the color and the texture information for depth labeling. (2) Multiple depth cues are combined to define the local energies. Furthermore, the local energies are adapted to the local image content, in order to consider the varying nature of the image content for an accurate depth labeling. (3) Both the density of the graph nodes and the intervals of the depth labels are gradually refined in multiple labeling passes. By doing so, both the computational efficiency and the robustness of the depth labeling process are improved. The experimental results on real multiple-view videos show that the depth maps of for selected reference view are accurately reconstructed. Depth discontinuities are very well preserved

Hierarchical structure-and-motion recovery from uncalibrated images

This paper addresses the structure-and-motion problem, that requires to find camera motion and 3D struc- ture from point matches. A new pipeline, dubbed Samantha, is presented, that departs from the prevailing sequential paradigm and embraces instead a hierarchical approach. This method has several advantages, like a provably lower computational complexity, which is necessary to achieve true scalability, and better error containment, leading to more stability and less drift. Moreover, a practical autocalibration procedure allows to process images without ancillary information. Experiments with real data assess the accuracy and the computational efficiency of the method.Comment: Accepted for publication in CVI

Critical configurations for two projective views, a new approach

The problem of structure from motion is concerned with recovering 3-dimensional structure of an object from a set of 2-dimensional images. Generally, all information can be uniquely recovered if enough images and image points are provided, but there are certain cases where unique recovery is impossible; these are called critical configurations. In this paper we use an algebraic approach to study the critical configurations for two projective cameras. We show that all critical configurations lie on quadric surfaces, and classify exactly which quadrics constitute a critical configuration. The paper also describes the relation between the different reconstructions when unique reconstruction is impossible.Comment: 24 pages, 6 figures, added references, Section 5 expanded, minor changes throughout, in particular Sections 1 and 2, submitted to Journal of Symbolic Computation

Observability/Identifiability of Rigid Motion under Perspective Projection

The "visual motion" problem consists of estimating the motion of an object viewed under projection. In this paper we address the feasibility of such a problem. We will show that the model which defines the visual motion problem for feature points in the euclidean 3D space lacks of both linear and local (weak) observability. The locally observable manifold is covered with three levels of lie differentiations. Indeed, by imposing metric constraints on the state-space, it is possible to reduce the set of indistinguishable states. We will then analyze a model for visual motion estimation in terms of identification of an Exterior Differential System, with the parameters living on a topological manifold, called the "essential manifold", which includes explicitly in its definition the forementioned metric constraints. We will show that rigid motion is globally observable/identifiable under perspective projection with zero level of lie differentiation under some general position conditions. Such conditions hold when the viewer does not move on a quadric surface containing all the visible points

Critical configurations for three projective views

The problem of structure from motion is concerned with recovering the 3-dimensional structure of an object from a set of 2-dimensional images taken by unknown cameras. Generally, all information can be uniquely recovered if enough images and point correspondences are provided, yet there are certain cases where unique recovery is impossible; these are called \emph{critical configurations}. We use an algebraic approach to study the critical configurations for three projective cameras. We show that all critical configurations lie on the intersection of quadric surfaces, and classify exactly which intersections constitute a critical configuration.Comment: 32 pages, 8 figures. This is a companion paper to arXiv:2112.05074. The paper has seen a major revision after the initial referee report, submitted to Mathematica Scandinavic