Symmetric objects in multiple affine views

Thesis

This thesis is concerned with the utilization of object symmety as a cue for segmentation and object recognition. In particular it investigates the problem of detecting 3D bilaterally symmetric objects from affine views.

The first part of the thesis investigates the problem of detecting 3D bilateral symmetry within a scene from known point correspondences across two or more affine views. We begin by extending the notion of skewed symmetry to three dimensions, and give a definition in terms of degenerate structure that applies equally to an affine 3D structure or to point correspondences across two or more affine views. We then consider the effects of measurement errors on symmetry detection, and derive an optimal statistical test of degenerate structure, and thereby of 3D-skewed symmetry. We then move on to the problem of searching for 3D skewed symmetric sets within a larger scene. We discuss two approaches to the problem, both of which we have implemented, and we demonstrate fully automatic detection of 3D skewed symmetry on images of uncluttered scenes. We conclude the first part by investing means of verifying the presence of bilateral rather than skewed symmetry in the Euclidean space, by enforcing mutual consistency between multiple skewed symmetric sets, and by drawing on partial knowledge about the camera calibration.

The second part of the thesis is concerned with the problem of obtaining feature correspondences across multiple affine views, as required for the detection of symmetry. In particular we investigate the geometric matching constraints that exist between affine views. We start by specilizing the four projective multifocal tensors to the affine case, and use these to carry the bulk of all known projective multi-view matching relations to affine views, unearthing some new relations in the process. Having done that, we address the problem of estimating the affine tensors. We provide a minimal set of constraints on the affine trifocal tensor, and search for ways of estimating the affine tensors from point and line correspondences.

Authors: Thórhallsson, T

• Publication date: 2000
• DOI: 10.5287/ora-go9ddbbe7
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: computer vision; multiple view relations; 3D bilateral symmetry detection; affine geometry; multiple view geometry
• Subjects: Information engineering; Robotics; Image understanding