R-snakes Lyubomir Zagorchev, Ardeshir Goshtasby, Martin Satter Speaker: HongxingShi Image and Vision Computing 25 (2007) 945–959

Author Ardeshir Goshtasby · Postion Professor of Department of Computer Science and Engineering, Wright State University · Education B.E. Electronics Engineering, University of Tokyo M.S. Computer Science, University of Kentucky Ph.D. Computer Science, Michigan State University · Journal Special Issues Edited Pattern Recognition on Image Registration Computer Vision and Image Understanding Information Fusion on Image Fusion

Introduction and background What is snake? · An energy minimizing countours · Continuously deform to minimize its energy · Slither while deforming, like snake

Energy Contours Internal force · Constrain the smoothness of contours External force · Push the contours toward image features

Situations of curves’ definition Discrete Defined by a sequence of points Continuous Defined by a parametric curve, such as B-Splines, NURBS,RaG curves, and so on…

Energy definition Total energy Internal energy External energy

Compute From the calculas of variations, obtain: After discrezing….

Result The equations can be written where A is a pentadiagonal matrix.

B-snakes Definition Energy function

B-snakes Minimize the total energy Obtain

Rational Gaussian curves Definition Control points Blending functions

Rational Gaussian curves Where is the weight, and are standard deviation are nodes The blending function can be varied.

RaG curves are (a)0.05 (b)0.1 (c)0.15

Closed RaG curves Replaced the Gaussian function with are (a) (b) 0.06 (c) 0.085

RaG snakes As the situation of discrete snakes: Let

RaG snakes Discrete, and obtain The extern energy

Synthetical images

Parameters in synthetic image

CT images

Parameters in CT images

Parameters analyse Standard deviation and the number of nodes n –bigger, smoother shapes –larger n,smoother shapes Experientially, we let

Standard deviations: (c)-(h)0.015, 0.025, 0.035, 0.045, 0.055, 0.065

Coarse-to-fine segmention How to select the n, number of nodes? –First, with a small n and a large, find a coarse boundary –Then, increase n until the finest resolution image is segmented

Conclusions Advantages over B-snakes –The stiffness can be varied to recover shapes containing smooth as well as detailed parts –The stiffness can be continuously varied to track a boundary from coarse to fine Disadvantage –Complexity

References [1] L Zagorchev, A Goshtasby, M Satter, R-snakes, Image and Vision Computing, 2007 [2] M. Kass, A. Witkin and D. Terzopoulos, Snakes: Active contour models, International journal of computer vision , 1988 [3] A. Goshtasby, Geometric modelling using rational Gaussian curves and surfaces, Computer Aided Design 27 (5) (1995) 363–375

Q&A