CSCI-256 Data Structures & Algorithm Analysis Lecture Note: Some slides by Kevin Wayne. Copyright © 2005 Pearson-Addison Wesley. All rights reserved. 26

Image segmentation –Central problem in image processing –Divide image into coherent regions –Very difficult problem in broad image domains Semantic gap Ex: Three people standing in front of complex background scene. Identify each person (and each object in the background) as a coherent object

Foreground / background segmentation Separate foreground from background

Foreground / background segmentation Label each pixel in picture as belonging to foreground or background V = set of pixels, E = pairs of neighboring pixels a i  0 is likelihood pixel i in foreground b i  0 is likelihood pixel i in background p ij  0 is separation penalty for labeling one of i and j as foreground, and the other as background

Foreground / background segmentation Goals –Accuracy: if a i > b i in isolation, prefer to label i in foreground –Smoothness: if many neighbors of i are labeled foreground, we should be inclined to label i as foreground –Find partition (A, B) that maximizes: foreground background

Formulate as min cut problem –Maximization –No source or sink –Undirected graph Turn into minimization problem –Maximizing –is equivalent to minimizing

Pixel graph to flow graph s t

G' = (V', E') Add source to correspond to foreground; add sink to correspond to background Use two anti-parallel edges instead of undirected edge p ij st ij ajaj G' bibi

Formulate as min cut problem Consider min cut (A, B) in G' –A = foreground –Precisely the quantity we want to minimize if i and j on different sides, p ij counted exactly once G' st ij A p ij bibi ajaj

Baseball elimination Can the Dinosaurs win the league? Remaining games: –AB, AC, AD, AD, AD, BC, BC, BC, BD, CD WL Ants42 Bees42 Cockroaches33 Dinosaurs15 A team wins the league if it has strictly more wins than any other team at the end of the season A team ties for first place if no team has more wins, and there is some other team with the same number of wins

Baseball elimination Can the Fruit Flies win the league? Remaining games: –AC, AD, AD, AD, AF, BC, BC, BC, BC, BC, BD, BE, BE, BE, BE, BF, CE, CE, CE, CF, CF, DE, DF, EF, EF WL Ants1712 Bees167 Cockroaches167 Dinosaurs1413 Earthworms1410 Fruit Flies1215

Assume Fruit Flies win remaining games Fruit Flies are tied for first place if no team wins more than 19 games Allowable wins –Ants (2) –Bees (3) –Cockroaches (3) –Dinosaurs (5) –Earthworms (5) 18 games to play –AC, AD, AD, AD, BC, BC, BC, BC, BC, BD, BE, BE, BE, BE, CE, CE, CE, DE WL Ants1713 Bees168 Cockroaches169 Dinosaurs14 Earthworms1412 Fruit Flies1915

Remaining games AC, AD, AD, AD, BC, BC, BC, BC, BC, BD, BE, BE, BE, BE, CE, CE, CE, DE s ACADBCBDBE CE ABCD E T DE