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Image Segmentation. Ioana Policeanu. 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
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Image Segmentation Ioana Policeanu
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
Edge detection Classical Methods An image of blood vessel Thresholding
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
Deformable Contours • Given: initial contour (model) near desired object • Goal: evolve the contour to fit exact object boundary
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
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
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:
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
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
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
N Level Set Representation • Curve evolution (F = speed function; N=normal vector to curve C) • Level set formulation zero level
Two-phase Case using a Statistical Model (Gauss) Energy function Level set function
Two-phase case Estimating the Parameters of the Gaussian densities
Implementation • The level set is evolved with a gradient descent using • The Gaussian parameters are updates at each iteration where
