A Case Study of Higher Order Tikhonov Regularization Terms Influence on the Convergence of Active Contours

An explicit snake is a smooth closed curve which deforms towards the desired features in an image. There are two types of force controlling the motion of the snake: internal and external forces. The former usually constrains the snake’s curvature and tension, through first and second Tikhonov smoothness force terms, while the latter generates attraction forces. To investigate the possible role of higher Tikhonov constraint parameters, third and fourth force regularizing terms are added in this study. The related theoretical equations are derived and the respective influence of the four internal force terms are examined and followed on test images. While still at the preliminary stage, the present study shows that the added internal force terms may improve the smoothness and convergence of the snake.