This paper addresses a fundamental problem in computer vision, curve matching. Curve matching and comparison play a
key role in various applications. High-level vision problems usually require comparing curves, and the quality of tackling
these problems relies much on the underlying curve matching techniques. Our goal is to define a distance on the space of
plane (space) curves. The space of curves is taken as a manifold (topological space), and we consider Riemannian metrics
on the manifold. The distance induced by a Riemannian metric is a metric, which, if not trivial, can be used as a similarity
metric. This work also deals with the problem of partial curve matching given their starting points are known. Dynamic
programming is used to implement partial matching, giving an efficient computational method. Experiments are conducted
to test the distance invariant to translation and scaling.
This paper proposes a line segment based image registration method. Edges are detected and partitioned into line segments.
Line-fitting is applied onto every line segment to rule out those segments of high fitting error. For each segment in a
reference image, putative matching segments in a test image are picked with the constraints obtained by analyzing affine
transformations. Putative segment correspondences result in the correspondences of intersections of segments, which
are used as matching points. An affine matrix is derived from those point correspondences and evaluated by the similarity
metric. The segment correspondences ending up with higher similarity metrics are used to compute the final transformation.
Experimental results show that the proposed method is robust especially when salient points can not be detected accurately.
This paper proposes a junction detection method that detects junctions as those points where edges join or intersect. The
edges that form a junction are searched in a square neighbourhood, and the subtended angles among them are calculated
by using edge orientations. Local edge orientation at a pixel is estimated by utilizing those edge points close to the pixel.
Based on the subtended angles, the pixel is determined to be a junction candidate or not. Each actual junction is accurately
localized by suppressing the candidates of non-minimum orientation difference. The proposed method analyzes real cases
of extracted edges, and estimates the change of orientations of edge segments in digital fields. The experimental results
show that the proposed algorithm can robustly detect junctions in digital images.
This paper describes a new, robustified Hidden Markov Model for target tracking using a subspace representation.
The Hidden Markov Model (HMM) provides a powerful framework for the probabilistic modelling of observations
and states. Visual tracking problems are often cast as an inference problem within the HMM framework.
Probabilistic Principal Component Analysis (PPCA), a classic subspace representation method, is a popular
tool for appearance modelling because it provides a compact representation for high-dimensional data. Previous
subspace based tracking algorithms assume the image observations were generated from a Gaussian distribution
parameterized by principal components. One drawback of using Gaussian density model is that atypical
observations cannot be modelled well. Hence, they are very sensitive to outliers. To address this problem, we
propose to augment the HMM by adding a set of latent variables {wi}ti=1 to adjust the shape of the observation
distribution. By carefully choosing the distribution of {wi}ti=1, we obtain a more robust observation distribution
with heavier tails than a Gaussian. Numerical experiments demonstrate the effectiveness of this new framework
in cases where the target objects are corrupted by noise or occlusion.
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