MULTISCALE MULTISCALE SEGMENTATION SEGMENTATION Florence B Florence B ENEZIT , Jianbo SHI, 2004 ENEZIT , Jianbo SHI, 2004
MULTISCALEMULTISCALESEGMENTATIONSEGMENTATION
Florence BFlorence BENEZIT , Jianbo SHI, 2004ENEZIT , Jianbo SHI, 2004
IntroductionIntroduction
Graph Based Object SegmentationGraph Based Object Segmentation
Wij
Wiji
j
V: graph nodesE: edges connection nodes
Image = { pixels }Pixel similarity
Segmentation = Graph partition
Pixel Affinity graphPixel Affinity graph
Normalized Cut As Generalized Eigenvalue problemNormalized Cut As Generalized Eigenvalue problem
y2i iA
y2ii
A
Program PNCX:
Relaxed to program PNCZ:
How big connection radius?How big connection radius?
BAD AND GOODBAD AND GOODEIGENVECTORSEIGENVECTORS
ACCURACY VERSUSACCURACY VERSUSCOMPUTATION TIMECOMPUTATION TIME
MULTISCALEMULTISCALEAFFINITY MATRIXAFFINITY MATRIX
AND LAYERAND LAYERCONSTRAINTSCONSTRAINTS
Long range connectionsLong range connections
Statistics of W on natural imagesStatistics of W on natural images
MultiscaleMultiscale graph decomposition graph decomposition
Multi-Multi-scalescale graph decomposition graph decomposition
Original graph weight:O(N^2)
Multi-scale graph weights:O(N)
MULTISCALE MATRIXMULTISCALE MATRIX
AVERAGE MATRIXAVERAGE MATRIX
0001/9
1/9
1/9
0000001/9
1/9
1/9
0000001/9
1/9
1/9
0
AVERAGE MATRIXAVERAGE MATRIX
Con-current partitioning of Multi-Con-current partitioning of Multi-scalescale graph graph
MULTISCALE REPRESENTATIONMULTISCALE REPRESENTATIONAND CONSTRAINTSAND CONSTRAINTS
PROBLEMPROBLEM
MAXIMIZING ENERGYMAXIMIZING ENERGY
Cross scale constraintsCross scale constraints
RELAXED PROBLEMRELAXED PROBLEM
Can be done in O(N) operations.
Computational speed upComputational speed up
RESULTSRESULTS
EXAMPLESEXAMPLES
EXAMPLESEXAMPLES
EXAMPLESEXAMPLES