Shared Segmentation of Natural Scenes. Dependent Pitman-Yor Processes
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1 Shared Segmentation of Natural Scenes using Dependent Pitman-Yor Processes Erik Sudderth & Michael Jordan University of California, Berkeley
2 Parsing Visual Scenes sky skyscraper sky dome buildings trees temple bell
3 Are Images Bags of Features? Inspired by the successes of topic models for text data, some have proposed learning from local image features
4 Are Images Bags of Features? Inspired by the successes of topic models for text data, some have proposed learning from local image features Compute color & texture descriptors for each superpixel First Approach: Fei-Fei & Perona 2005, Sivic et. al Ignore spatial structure entirely (bag of visual words ) Second Approach: Russell et. al. 2006, Todorovic & Ahuja 2007 Cluster features via one or more bottom-up segmentations
5 Segmentation: Mean Shift EDISON: Comaniciu & Meer, 2002 Cluster by modes of appearance features Often sensitive to bandwidth parameter
6 Segmentation: Normalized Cuts Shi & Malik 2000; Fowlkes, Martin, & Malik 2003 Implicit bias towards equal-sized regions Is this a good model for real scenes?
7 Segmentation: New Approach Spatially Dependent Pitman-Yor Processes Automatically infers the number of segments Handles regions of widely varying size and appearance Statistical framework for discovering shared categories
8 Outline Natural Scene Statistics Counts, partitions, and power laws Hierarchical Pitman-Yor processes Spatial Priors for Image Partitions What s wrong with Potts models? Spatial dependence via Gaussian processes Unsupervised Image Analysis Image segmentation Visual category discovery
9 Priors on Counts & Partitions Segmentation as Partitioning How many regions does this image contain? What are the sizes of these regions? Unsupervised Object Category Discovery How many object categories have I observed? How frequently does each category appear?
10 Pitman-Yor Processes The Pitman-Yor process defines a distribution on infinite discrete measures, or partitions 0 1 Dirichlet process:
11 Why Pitman-Yor? Generalizing the Dirichlet Process Distribution on partitions leads to a generalized Chinese restaurant process Special cases arise as excursion lengths for Markov chains, Brownian motions, Power Law Distributions DP Number of unique clusters in N observations Size of sorted cluster weight k PY Jim Pitman Natural Language Statistics Goldwater, Griffiths, & Johnson, 2005 Teh, 2006 Marc Yor
12 Natural Scene Statistics Does Pitman-Yor prior match human segmentation? How do statistics vary across scene categories? Coast Forest Mountain Opencountry Highway Insidecity Street Tallbuilding Oliva & Torralba, 2001
13 Manual Image Segmentation Labels for more than 29,000 segments in 2,688 images of natural scenes
14 Object Sizes and Counts Small Objects Large Objects insidecity region areas insidecity region counts
15 Object Name Frequencies trees sky waterfall person rainbow wheelbarrow lichen forest scenes insidecity scenes
16 Hierarchical Pitman-Yor Model Set of segments or layers Pitman-Yor prior: segment sizes Pitman-Yor prior: label frequencies No supervision aside from Pitman-Yor hyperparameters Set of global, shared visual categories Set of features in image j (superpixel color & texture) Hierarchical DP: Teh et. al Set of images Hierarchical PY N-gram: Teh 2006
17 Bag of Features Segmentation LabelMe Segments:
18 Outline Natural Scene Statistics Counts, partitions, and power laws Hierarchical Pitman-Yor processes Spatial Priors for Image Partitions What s wrong with Potts models? Spatial dependence via Gaussian processes Unsupervised Image Analysis Image segmentation Visual category discovery
19 Discrete Markov Random Fields Ising and Potts Models Previous Applications Interactive foreground segmentation Supervised training for known categories GrabCut: Rother, Kolmogorov, & Blake 2004 but very little success at segmentation of unconstrained natural scenes. Verbeek & Triggs, 2007
20 10-State Potts Samples States sorted by size: largest in blue, smallest in red
21 1996 IEEE DSP Workshop natural images giant cluster number of edges on which states take same value edge strength very noisy Even within the phase transition region, samples lack the size distribution and spatial coherence of real image segments
22 Geman & Geman, Iterations 128 x128 grid 8 nearest neighbor edges K = 5 states Potts potentials: 10,000 Iterations
23 Spatially Dependent Pitman-Yor Cut random surfaces (samples from a GP) with thresholds (as in Level Set Methods) Assign each pixel to the first surface which exceeds threshold (as in Layered Models) Duan, Guindani, & Gelfand, Generalized Spatial DP, 2007
24 Spatially Dependent Pitman-Yor Non-Markov Gaussian Processes: PY prior: Segment size Normal CDF Feature Assignments
25 Preservation of PY Marginals Why Ordered Layer Assignments? Stick Size Prior Random Thresholds
26 Samples from Spatial Prior Comparison: Potts Markov Random Field
27 Learning & Inference GP Covariance probability that features at locations are in the same segment Bag of features: Image distance Intervening countours UC Berkeley Pb boundary detector Mean Field Variational Inference Factorized Gaussian posteriors on thresholds & eigenvector expansion of dense covariance Jointly optimize surface & threshold via conjugate gradient Initialize by annealing to reduce local optima
28 Outline Natural Scene Statistics Counts, partitions, and power laws Hierarchical Pitman-Yor processes Spatial Priors for Image Partitions What s wrong with Potts models? Spatial dependence via Gaussian processes Unsupervised Image Analysis Image segmentation Visual category discovery
29 Tallbuilding Segments: PY-Edge LabelMe Segments:
30 Mountain Segments: PY-Edge LabelMe Segments:
31 Mountain Baseline: NCuts LabelMe Segments:
32 Visual Categories: Coast
33 Visual Categories: Tallbuilding
34 Challenge: Structured Objects LabelMe Segments:
35 Conclusions Dependent Pitman-Yor Processes allow efficient variational parsing of scenes into unknown numbers of segments empirically justified power law priors learning of shared appearance models from related images & scenes Future Directions parallelized, scalable learning from extremely large image databases nonparametric models of dependency in other application domains
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