Date of Award


Degree Type


Degree Name

Doctor of Philosophy


In the field of computational vision, 'motion understanding' roughly describes a system's ability to extract information about the 3D position, trajectory, or structure of visible objects by analysing the way their 2D images change over time. Although this inverse problem is ill-posed at outset, it is possible to utilize the principle of spatio-temporal coherence the hypothesis that objects surfaces and motion are locally continuous--to form localized estimates of the changing state of regions of the image. Two main results are achieved in the thesis:;A technique is presented for estimating the infinitesimal translation group component acting at a local spatial neighbourhood of a visual signal. A stochastic estimation technique is developed, and tested using Monte Carlo methods. Its development addresses the problems that arise due to the fact that the estimates of translation must be derived from local neighbourhoods. In other words, their measures must have controllable support over finite spatial domains. According to the same constraints on measurement which give rise to the Heisenberg uncertainty principle, this spatial localization imposes a finite uncertainty on the observations of translation. The developed framework provides a measure of this uncertainty.;Using this method for estimating the action of the translation group, the framework is extended to span the six degrees-of-freedom of the 3D Euclidean motion group. In the 2D image, this group action is modelled locally by the six-parameter tangent space of the 2D affine group. Since not all of the elements of this group commute, a controlled decomposition of their individual actions is needed in order to estimate the changing states resulting from 3D motions. The decomposition is specified by the Lie algebra of the 2D affine group, and implicates a need for tracking and data-directed estimation for computational motion perception.



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