Constraining Active Contour Evolution via Lie Groups of Transformation

Lie Transformation Groups and Geometry

We present geometrical aspects of Lie groups and reductive homogeneous spaces, and some resent results on homogeneous geodesics and homogeneous Einstein metrics. The article is based on the four lectures given in Varna, June 2007.

FACE: fast active-contour curvature-based evolution

This paper presents an active contour model for fast object segmentation called FACE. A novel energy term that takes into account the computational complexity of the active contour is introduced together with related constraints and minimization procedure. The described process is based on the regularization and optimization of the active contour control points position. The trade-off between c...

Hippocampus Segmentation via active contour model

Since hippocampal volume measurement is often used in studying Alzheimer’s disease to assess disease progression, automatic hippocampus segmentation is an important task in clinical applications. However, it is a challenging task due to its small size, complex shape, fuzzy boundaries, partial volume effects, and anatomical variability. In this paper we propose a new segmentation method to segme...

Irreducible Representations of Infinite-dimensional Transformation Groups and Lie Algebras

INEXTENSIBLE FLOWS OF CURVES IN LIE GROUPS

In this paper, we study inextensible ows in three dimensional Lie groups with a bi-invariant metric. The necessary and sucient conditions for inextensible curve ow are expressed as a partial dierential equation involving the curvatures. Also, we give some results for special cases of Lie groups.