טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentKenigsberg Avraham
SubjectA Multigraid Approach for Fast Geodesic Activ Contour
DepartmentDepartment of Computer Science
Supervisors Professor Ron Kimmel
Professor Irad Yavneh


Abstract

A recent geometric approach for image segmentation is the geodesic active contour, which is motivated by previous snakes and geometric models. Segmentation in this model is performed by a dynamic curve, which minimizes several internal and external forces. These forces smooth the curve and attract it to the boundaries of objects. The conventional way of finding the geodesic active contour is by using the level-set method. In this approach, the evolving contour is represented as a level-set of a surface. This gives a stable solution, which naturally handles segmentation of several objects in one image. One drawback of the level-set method is the extended numerical support, which makes its solution computationally expensive. We propose an efficient method for solving this problem by introducing an implicit formulation of the geodesic active contour model. This enables us to compute the solution in a small number of numerical steps. However, every such numerical step requires solving a nonlinear system of equations. To solve these systems efficiently, we use an adaptive multigrid algorithm, which enables us to attain highly accurate and efficient solutions by employing a hierarchy of grids, with high resolutions only in the vicinity of the expected object boundaries.