Active Contour with A Tangential Component

TL;DR

This paper introduces GeoSnakes, a novel active contour model that addresses early termination issues by ensuring the full gradients vanish at the solution, using an auxiliary equilibrium flow to solve the Euler-Lagrange equation.

Contribution

The paper proposes GeoSnakes, a new active contour method with an auxiliary equilibrium flow to overcome early termination and pseudo stationary phenomena.

Findings

GeoSnakes effectively overcomes early termination.

The equilibrium flow solves the full Euler-Lagrange equation.

Experimental results validate the geometrical interpretation.

Abstract

Conventional edge-based active contours often require the normal component of an edge indicator function on the optimal contours to approximate zero, while the tangential component can still be significant. In real images, the full gradients of the edge indicator function along the object boundaries are often small. Hence, the curve evolution of edge-based active contours can terminate early before converging to the object boundaries with a careless contour initialization. We propose a novel Geodesic Snakes (GeoSnakes) active contour that requires the full gradients of the edge indicator to vanish at the optimal solution. Besides, the conventional curve evolution approach for minimizing active contour energy cannot fully solve the Euler-Lagrange (EL) equation of our GeoSnakes active contour, causing a Pseudo Stationary Phenomenon (PSP). To address the PSP problem, we propose an auxiliary curve evolution equation, named the equilibrium flow (EF) equation. Based on the EF and the conventional curve evolution, we obtain a solution to the full EL equation of GeoSnakes active contour. Experimental results validate the proposed geometrical interpretation of the early termination problem, and they also show that the proposed method overcomes the problem.