1. Image Segmentation Ioana Policeanu

2. Brief Intro • In Computer Vision, segmentation refers to the process of partitioning a digital image into multiple segments (set of pixels) • Goal: • Simplifies/changes an image into something more meaningful and easier to analyze • Locates objects and boundaries

3. Edge detection Classical Methods An image of blood vessel Thresholding

4. An Advanced Method: Active Contour Model

5. Applications • Medical imaging (locating tumors, measuring tissue volumes, treatment planning, computer-guided surgery) • Face and fingerprint recognition • Traffic control systems • Agricultural imaging (detecting crop disease) • Location objects in various images

6. Deformable Contours • Given: initial contour (model) near desired object • Goal: evolve the contour to fit exact object boundary

7. Curve Propagation • How is the current contour adjusted to find the new contour at each iteration? • Define a cost function (“energy” function) that says how good a possible configuration is • Seek next configuration that minimizes that cost function

8. External Energy • Measures how well the curve matches the image data • “Attracts” the curve toward different image features (edges, lines) • Think of it as gravitational pull towards areas of high contrast Magnitude of gradient -Magnitude of gradient

9. Formulas • Image I(x,y) • Gradient images and • External energy at a point v(s) on the curve is • External energy for the whole curve:

10. Internal Energy • We want to favor smooth shapes, contours with low curvature, contours similar to a known shape • For a continuous curve, a common internal energy term is the “bending energy” • The more the curve bends  the larger this energy value is

11. Formulas • Internal energy at some point v(s) on the curve: • Internal energy for the whole curve: The weights α and β dictate how much influence each component has Elasticity,Tension Stiffness,Curvature

12. Level Set Method • Osher and Sethian, 1988 • Popular method for curve propagation by evolving the curve towards the lowest potential (value) of the cost function • The idea is to represent the evolving contour using a signed function, where its zero level corresponds to the actual contour

13. Level Set Representation

14. N Level Set Representation • Curve evolution (F = speed function; N=normal vector to curve C) • Level set formulation zero level

15. Two-phase Case using a Statistical Model (Gauss) Energy function Level set function

16. Two-phase case Estimating the Parameters of the Gaussian densities

17. Implementation • The level set is evolved with a gradient descent using • The Gaussian parameters are updates at each iteration where

18. Two-phase Case

19. Code and Demo

20. http://www.youtube.com/watch?v=TZcUG4i-Hmc