We present a new approach to segmentation of 3-D shapes that initializes and then optimizes a 3-D surface model given only the data and a very small number of 3-D seed points and corresponding surface normals. This is a valuable capability for medical, robotic and cartographic applications where such seed points can be naturally supplied. In effect, the surface model is clamped onto the object boundary in manner reminiscent of a Velcro being closed. We develop the method's mathematic framework and show preliminary results using volumetric medical data.>

We propose a snake-based approach that lets a user specify only the distant end points of the curve he wishes to delineate without having to supply an almost complete polygonal approximation. We achieve much better convergence properties than those of traditional snakes by using the image information around these end points to provide boundary conditions and by introducing an optimization schedule that allows the snake to take image information into account first only near its extremities and then, progressively, towards its center. These snakes could be used to alleviate the often repetitive task practitioners have to face when segmenting images by abolishing the need to sketch a feature of interest in its entirety, that is, to perform a painstaking, almost complete, manual segmentation.>

In the present paper we address the problem of establishing contours in static monocular scenes. We propose to use features from unified edge and key-point detection to drive an active contour model. We present a framework for image segmentation consisting of: 1) detection of 1D and 2D intensity discontinuity, i.e. general edges and key-points; 2) reformulation of the active contour model to an expanding version, called a "growing snake"; 3) automatic initialization; 4) image and internal geometry driven expansion; and 5) controlled termination. The objective is to explore the potential of a fully automatic segmentation scheme. The performance and present limitations of growing snakes are demonstrated on images representative for diverse classes of scenes.

In this paper, we present a new snake-based method to delineate contours where the user has to specify only the two distant end points without having to supply an almost complete polygonal approximation. We achieve much better convergence properties than those of traditional snakes by propagating the image information along the curve from both end points towards its center. We use our new method to outline curved object boundaries and for interactive road delineation.

Many scientific applications require computation of the derivatives of a function f : l?" -Etm as well as the function values off itself.AH computer algebra systems can dtierentiate functions represented by formulae.But not all functions can be described by formulae.And formulae are not always the most effective means for representing functions and derivatives.In this paper we describe the algorithms used by the Maple [2] routine GRADIEHT that accepts as input a Maple procedure for the computation off and outputs a new Maple procedure that computes the gradient of f.The design of the GRADIElfT routine is such that it is also trivial to generate Maple procedures for the computation Jacobians and Hessians.