Gradient Flows and Geometric Active Contour Models Gradient Flows and Geometric Active Contour Models

In this note, we analyze the geometric active contour models proposed in 10, 31] from a curve evolution point of view and propose some modiications based on gradient ows relative to certain new metrics. This leads to a novel snake paradigm in which the feature of interest may be considered to lie at the bottom of a potential well. Thus the snake is attracted very naturally and eeciently to the desired feature. Moreover, we consider some 3-D active surface models based on these ideas. Abstract In this note, we analyze the geometric active contour models proposed in 10, 31] from a curve evolution point of view and propose some modiications based on gradient ows relative to certain new metrics. This leads to a novel snake paradigm in which the feature of interest may be considered to lie at the bottom of a potential well. Thus the snake is attracted very naturally and eeciently to the desired feature. Moreover, we consider some 3-D active surface models based on these ideas. 1 Summary 1. Original contribution: The contribution of this work is an active contour and surface model based on novel gradient ows, diierential geometry, and curve and surface evolutions. 2. Importance of the contribution: The scheme we derive for the computation of de-formable contours as well as our numerical routines make this type of approach ideal for segmentation, edge and curve detection, visual tracking, and shape modelling. Moreover , we believe we elucidate some underlying mathematical principles for geometric active contour models based on our gradient ow paradigm. the geometric evolution models of Caselles et al. 10] and Malladi et al. 31]. There is an extensive literature on deformable contours references to which may be found in the book by Blake and Yuille 8]. However, in our case we derive our model from basic diierential geometric principles (gradient ows relative to a Riemannian metric which depends on the given image) which leads to a new gradient term appearing in these previous models and which makes the evolution more eecient and natural. 4. How other researchers can make use of this work: Researchers working in active vision will have an eecient natural procedure for employing active contours to various kinds of imagery. Our scheme seems to work very well on noisy images with which other methods seem to have problems.