Representing Edge Models via Local Principal Component Analysis [chapter]

Patrick S. Huggins, Steven W. Zucker
2002 Lecture Notes in Computer Science  
Edge detection depends not only upon the assumed model of what an edge is, but also on how this model is represented. The problem of how to represent the edge model is typically neglected, despite the fact that the representation is a bottleneck for both computational cost and accuracy. We propose to represent edge models by a partition of the edge manifold corresponding to the edge model, where each local element of the partition is described by its principal components. We describe the
more » ... ction of this representation and demonstrate its benefits for various edge models. Representing Edge Models via Local Principal Component Analysis 385 edge model E with parameter space Θ, we seek the 'best' explanation of I, e.g., findingθ ∈ Θ that maximizes p(E(θ)|I). The parameter estimation problem can be viewed geometrically [27] [3]: the edge model E is a low-dimensional manifold embedded in a high-dimensional space, where the dimensionality is given by the number of pixels in the image neighborhood. Our contribution here is to develop a representation of this manifold that reflects its intrinsic geometry. We construct our representation using the method of local principal component analysis [34] . The advantages of our representation lie in its relationship to the geometry of the edge manifold. This leads to an accurate representation, and it can be applied to a wide variety of models, even nonparametric ones.
doi:10.1007/3-540-47969-4_26 fatcat:ibh6gfydmrhgrdrp2jhbukk7mq