Scale-based description and recognition of planar curves

A method of finding points of inflection on a planar curve at varying levels of detail and combining them to obtain a representation of the curve invariant under rotation, uniform scaling and translation and an algorithm to match two such representations are developed. This technique is applied to register a Landsat aerial image of an area (corrected for skew) to a map containing the shorelines of the same area. The shorelines are extracted from the Landsat image by forming a histogram of the gray-level distribution of pixels in the image and finding the land and water peaks in that histogram. The value at the trough between the two peaks is then used to threshold the image. Contours of dark regions in the resulting binary image are taken to be the shorelines. The Uniform Cost algorithm is used to find the least cost matches of the "scale-space images" of shorelines extracted from the Landsat image and those in the map giving priority to matches at higher levels of scale. A subset of those matches which are consistent are chosen to estimate the parameters of an affine transformation from the image to the map using a least squares method.Science, Faculty ofComputer Science, Department ofGraduat

A theory of multi-scale, curvature and torsion based shape representation for planar and space curves

This thesis presents a theory of multi-scale, curvature and torsion based shape representation for planar and space curves. The theory presented has been developed to satisfy various criteria considered useful for evaluating shape representation methods in computer vision. The criteria are: invariance, uniqueness, stability, efficiency, ease of implementation and computation of shape properties. The regular representation for planar curves is referred to as the curvature scale space image and the regular representation for space curves is referred to as the torsion scale space image. Two variants of the regular representations, referred to as the renormalized and resampled curvature and torsion scale space images, have also been proposed. A number of experiments have been carried out on the representations which show that they are very stable under severe noise conditions and very useful for tasks which call for recognition of a noisy curve of arbitrary shape at an arbitrary scale or orientation. Planar or space curves are described at varying levels of detail by convolving their parametric representations with Gaussian functions of varying standard deviations. The curvature or torsion of each such curve is then computed using mathematical equations which express curvature and torsion in terms of the convolutions of derivatives of Gaussian functions and parametric representations of the input curves. Curvature or torsion zero-crossing points of those curves are then located and combined to form one of the representations mentioned above. The process of describing a curve at increasing levels of abstraction is referred to as the evolution or arc length evolution of that curve. This thesis contains a number of theorems about evolution and arc length evolution of planar and space curves along with their proofs. Some of these theorems demonstrate that evolution and arc length evolution do not change the physical interpretation of curves as object boundaries and others are in fact statements on the global properties of planar and space curves during evolution and arc length evolution and their representations. Other theoretical results shed light on the local behavior of planar and space curves just before and just after the formation of a cusp point during evolution and arc length evolution. Together these results provide a sound theoretical foundation for the representation methods proposed in this thesis.Science, Faculty ofComputer Science, Department ofGraduat

MOTEXATION: Multi-Object Tracking with the Expectation-Maximization Algorithm

The paper proposes a new edge-based multi-object tracking framework, MO-TEXATION, which deals with tracking multiple objects with occlusions using the Expectation-Maximization (EM) algorithm and a novel edge-based appearance model. In the edge-based appearance model, an object is modelled by a mixture of a non-parametric contour model and a non-parametric edge model using kernel density estimation. Visual tracking is formulated as a Bayesian incomplete data problem, where measurements in an image are associated with a generative model which is a mixture of mixture models including object models and a clutter model and unobservable associations of measurements to densities in the generative model are regarded as missing data. A likelihood for tracking multiple objects jointly with an exclusion principle is presented, in which it is assumed that one measurement can only be generated from one density and one density can generate multiple measurements. Based on the formulation, a new probabilistic framework of multi-object tracking with the EM algorithm (MOTEXATION) is presented. Experimental results in challenging sequences demonstrate the robust performance of the proposed method.

Cyclification of human motion for animation synthesis

In this paper, a cyclification approach is presented for gait motions. It modifies short clips (ideally a gait cycle, but similar movements have been also presented) so that it can seamlessly and repeatedly concatenated to construct longer sequences. This work is motivated by the aim for synthesis of long animation sequences from short clips, which has received little attention in previous research (at that time)