Higher-Order Feature-Preserving Geometric Regularization

Higher-Order Feature-Preserving Geometric Regularization

We introduce two fourth-order regularization methods that remove geometric noise without destroying significant geometric features. These methods leverage ideas from image denoising and simplification of high contrast images in which piecewise affine functions are preserved up to infinitesimally small transition zones. We combine the regularization techniques with active contour models and appl...

Geometric and Higher Order Logicin

Semi-supervised Learning by Higher Order Regularization

In semi-supervised learning, at the limit of infinite unlabeled points while fixing labeled ones, the solutions of several graph Laplacian regularization based algorithms were shown by Nadler et al. (2009) to degenerate to constant functions with “spikes” at labeled points in R for d ≥ 2. These optimization problems all use the graph Laplacian regularizer as a common penalty term. In this paper...

A Fourth-order Positivity Preserving Geometric Flow

In this note we investigate a fourth-order geometric flow on closed, compact Riemannian manifolds of dimension greater than four. In the presence of a positive conformal invariant it can be shown that this flow must be positivity preserving.

Image matching with higher-order geometric features.

We propose a geometric matching technique in which line segments and elliptical arcs are used as edge features. The use of these higher-order features renders feature representation efficient. We derive distance measures to evaluate the similarity between the features of the model and those of the image. The model transformation parameters are found by searching a 3-D transformation space using...