Fast and stable Lagrangian approach for digital image segmentation is presented in this work. The Lagrangian approach is based on a discretization of an intrinsic partial differential equation for an evolving curve position vector. Since only the curve discretization by grid points is used it can be very fast. It enables that topological changes which may occur during the curve evolution from the initial guess to a final segmentation result are also resolved in a very fast way. The curve evolution model which we use for the Lagrangian segmentation includes an expanding force in the normal direction, an advective term driving the curve from both sides to an edge and a curvature regularization. The numerical procedures are based on stable semi-implicit scheme in curvature part and on inflow implicit/ outflow explicit method in advective part which corresponds to tangential redistribution of grid points. The tangential velocity which is used to stabilize the Lagrangian computations keeps the evolving curve discretized uniformly and this fact allows the fast O(n) solution of the topological changes. We present all our model and we show its behavior in medical and also satellite image data segmentation.

This presentation is part of Contributed Presentation “CP9 - Contributed session 9”

Authors:

Jozef Urbán (Slovak University of Technology)

Karol Mikula (Slovak University of Technology)

Keywords:

image segmentation, partial differential equation models