Probabilistic Continuous Edge Detection using Local Symmetry

We describe a new model for the detection of edges in a given image. The model takes the invariance of local features of the image w.r.t translational symmetry operations into account. This is done by expressing the symmetries as a local Lie group and their associated Lie algebras in the regularizer of our model. Central to our work is the formulation of an energy density for the regularizer which itself is invariant under the action of a Lie algebra. Formulated as a Gaussian Markov Random Field, the parameters of the model are estimated by the EM principle.