Separating Rigid Motion for Continuous Shape Evolution

• Main Authors: Niels Chr. Overgaard, Jan Erik Solem
• Format: Article
• Language: English
• Published: Computer Vision Center Press 2007-02-01
• Series: ELCVIA Electronic Letters on Computer Vision and Image Analysis
• Subjects: Computer Vision; Variational Problems; Gradient Descent; L2-gradient; Level Set Methods; Normal Velocity
• Online Access: https://elcvia.cvc.uab.es/article/view/144

A method is proposed for the construction of descent directions for the minimization of energy functionals defined for plane curves. The method is potentially useful in a number of image analysis problems, such as image registration and shape warping, where the standard gradient descent curve evolutions are not always feasible. The descent direction is constructed by taking a weighted average of the three components of the gradient corresponding to translation, rotation, and deformation. Our approach differs from previous work in the field by the use of implicit representation of curves and the notion of normal velocity of a curve evolution. Thus our theory is morphological and well suited for implementation in the level set framework.