Rank classification of linear line structure in determining trifocal tensor.

Zhao, Ming.Thesis (M.Phil.)--Chinese University of Hong Kong, 2008.Includes bibliographical references (p. 111-117) and index.Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Motivation --- p.1Chapter 1.2 --- Objective of the study --- p.2Chapter 1.3 --- Challenges and our approach --- p.4Chapter 1.4 --- Original contributions --- p.6Chapter 1.5 --- Organization of this dissertation --- p.6Chapter 2 --- Related Work --- p.9Chapter 2.1 --- Critical configuration for motion estimation and projective reconstruction --- p.9Chapter 2.1.1 --- Point feature --- p.9Chapter 2.1.2 --- Line feature --- p.12Chapter 2.2 --- Camera motion estimation --- p.14Chapter 2.2.1 --- Line tracking --- p.15Chapter 2.2.2 --- Determining camera motion --- p.19Chapter 3 --- Preliminaries on Three-View Geometry and Trifocal Tensor --- p.23Chapter 3.1 --- Projective spaces P3 and transformations --- p.23Chapter 3.2 --- The trifocal tensor --- p.24Chapter 3.3 --- Computation of the trifocal tensor-Normalized linear algorithm --- p.31Chapter 4 --- Linear Line Structures --- p.33Chapter 4.1 --- Models of line space --- p.33Chapter 4.2 --- Line structures --- p.35Chapter 4.2.1 --- Linear line space --- p.37Chapter 4.2.2 --- Ruled surface --- p.37Chapter 4.2.3 --- Line congruence --- p.38Chapter 4.2.4 --- Line complex --- p.38Chapter 5 --- Critical Configurations of Three Views Revealed by Line Correspondences --- p.41Chapter 5.1 --- Two-view degeneracy --- p.41Chapter 5.2 --- Three-view degeneracy --- p.42Chapter 5.2.1 --- Introduction --- p.42Chapter 5.2.2 --- Linear line space --- p.44Chapter 5.2.3 --- Linear ruled surface --- p.54Chapter 5.2.4 --- Linear line congruence --- p.55Chapter 5.2.5 --- Linear line complex --- p.57Chapter 5.3 --- Retrieving tensor in critical configurations --- p.60Chapter 5.4 --- Rank classification of non-linear line structures --- p.61Chapter 6 --- Camera Motion Estimation Framework --- p.63Chapter 6.1 --- Line extraction --- p.64Chapter 6.2 --- Line tracking --- p.65Chapter 6.2.1 --- Preliminary geometric tracking --- p.65Chapter 6.2.2 --- Experimental results --- p.69Chapter 6.3 --- Camera motion estimation framework using EKF --- p.71Chapter 7 --- Experimental Results --- p.75Chapter 7.1 --- Simulated data experiments --- p.75Chapter 7.2 --- Real data experiments --- p.76Chapter 7.2.1 --- Linear line space --- p.80Chapter 7.2.2 --- Linear ruled surface --- p.84Chapter 7.2.3 --- Linear line congruence --- p.84Chapter 7.2.4 --- Linear line complex --- p.91Chapter 7.3 --- Empirical observation: ruled plane for line transfer --- p.93Chapter 7.4 --- Simulation for non-linear line structures --- p.94Chapter 8 --- Conclusions and Future Work --- p.97Chapter 8.1 --- Summary --- p.97Chapter 8.2 --- Future work --- p.99Chapter A --- Notations --- p.101Chapter B --- Tensor --- p.103Chapter C --- Matrix Decomposition and Estimation Techniques --- p.104Chapter D --- MATLAB Files --- p.107Chapter D.1 --- Estimation matrix --- p.107Chapter D.2 --- Line transfer --- p.109Chapter D.3 --- Simulation --- p.10

Ambiguous configurations for 3-view projective reconstruction

The critical configurations for projective reconstruction from three views are discussed. A set of cameras and points is said to be critical if the projected image points are insufficient to determine the placement of the points and cameras uniquely, up to projective transformation. For two views, the classification of critical configurations is well known-the configuration is critical if and only if the points and camera centres all lie on a ruled quadric. For three views the critical configurations have not been identified previously. In this paper it is shown that for any placement of three given cameras there always exists a critical set consisting of a fourth-degree curve – any number of points on the curve form a critical set for the three cameras. Dual to this result, for a set of seven points there exists a fourth-degree curve such that a configuration of any number of cameras placed on this curve is critical for the set of points. Other critical configurations exist in cases where the points all lie in a plane, or one of the cameras lies on a twisted cubic.

A fast webcam photogrammetric system to support optical imaging of brain activity

Optical topography (OT) is an emerging neuroimaging technique utilising the tight coupling between neural activity and regional cerebral blood flow to monitor relative regional changes of haemoglobin concentration. OT systems are compact, low cost, easily portable, and relatively tolerant of body movements enabling clinical diagnosis, psychological experiments and even monitoring brain activities during daily living. There is a requirement for such systems to present their output functional data in a brain model based coordinate space in order to map to the signal source with brain anatomy. However OT data are obtained from a network of OT sensing devices (optodes) placed in contact with the head surface and cannot capture structural information of the underlying brain which might otherwise be used for registration. An appropriate registration method, widely used in Electroencephalography (EEG), is the 10-20 system which utilises bony landmarks as common points to co-register locations on the scalp with a brain model to a repeatability of a few millimetres in clinical applications to an MRI set of reference points. Inheriting the low cost and portability of OT, this thesis develops and validates a novel registration approach utilising off-the-shelf webcam technology in combination with photogrammetric bundle adjustment techniques in order to reliably coordinate targets on optodes and bony landmarks within the 10:20 reference frame to an accuracy of better than 1mm. Initial research includes an assessment of the 3D coordination accuracy, precision and stability of a series of low cost webcams in order to prove their suitability for clinical applications. Results demonstrate the capability of a system based on these cameras to reliably coordinate 3D target locations to the order of 0.5mm and better. Difficulties in automated clinical target image extraction due to poor image quality are circumvented through the development of new target image detection methods. Incremental improvements in image quality from successive webcam generations, up to and including the latest HD systems, are shown to increase coordination accuracy by one order of magnitude. The result is a novel webcam photogrammetric system that is able to rapidly and consistently coordinate targets on optodes and bony landmarks to better than 1mm in OT studies and is able to take advantage of the rapid advances being made in consumer webcam technology. The system is proven in pre-clinical studies to evaluate its coordination accuracy and in simulated clinical OT studies with a head-sized phantom conducted in collaboration with Department of Medical Physics and Bioengineering. Clinical OT studies with human subjects, demonstrate the capability of the system to continuously coordinate targets on optodes and scalp and detect differential movement between optodes and scalp which would invalidate a static registration procedure