Implicit Evolution of Open Ended Curves

We introduce a theoretical framework for implicit evolution of an open ended curve in a two-dimensional image plane. This approach is particularly suitable for identifying thin filamentous structures present in 2D images. The open ended curve is represented as the of the level set of a function (called the*) defined on the curve. The iterative evolution of the curvature map is guided by a diffusion equation and constrained by the imaging force, such as the image intensity gradient. The centerline of the evolved curvature map provides the position of the curve in subsequent iterations. We have tested this new model on both synthetic and real images that contain structures including rivers/roads/arteries. Nine experiments show that our model is successful in identifying complex topological filaments with a low 9% RMSE pixel error, and that the technique withstands effects of shape irregularities such as kinks, bending, circularity and inconsistent edges.