Certifying the Existence of Epipolar Matrices

Given a set of point correspondences in two images, the existence of a fundamental matrix is a necessary condition for the points to be the images of a 3-dimensional scene imaged with two pinhole cameras. If the camera calibration is known then one requires the existence of an essential matrix. We present an efficient algorithm, using exact linear algebra, for testing the existence of a fundamental matrix. The input is any number of point correspondences. For essential matrices, we characterize the solvability of the Demazure polynomials. In both scenarios, we determine which linear subspaces intersect a fixed set defined by non-linear polynomials. The conditions we derive are polynomials stated purely in terms of image coordinates. They represent a new class of two-view invariants, free of fundamental (resp.~essential)~matrices

Nonrigid reconstruction of 3D breast surfaces with a low-cost RGBD camera for surgical planning and aesthetic evaluation

Accounting for 26% of all new cancer cases worldwide, breast cancer remains the most common form of cancer in women. Although early breast cancer has a favourable long-term prognosis, roughly a third of patients suffer from a suboptimal aesthetic outcome despite breast conserving cancer treatment. Clinical-quality 3D modelling of the breast surface therefore assumes an increasingly important role in advancing treatment planning, prediction and evaluation of breast cosmesis. Yet, existing 3D torso scanners are expensive and either infrastructure-heavy or subject to motion artefacts. In this paper we employ a single consumer-grade RGBD camera with an ICP-based registration approach to jointly align all points from a sequence of depth images non-rigidly. Subtle body deformation due to postural sway and respiration is successfully mitigated leading to a higher geometric accuracy through regularised locally affine transformations. We present results from 6 clinical cases where our method compares well with the gold standard and outperforms a previous approach. We show that our method produces better reconstructions qualitatively by visual assessment and quantitatively by consistently obtaining lower landmark error scores and yielding more accurate breast volume estimates

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