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A Bayesian multi-scale model of perceptual organization. James Elder & Francisco Estrada Centre for Vision Research York University Toronto, Canada. Goal. Outline. Probabilistic foundations Limitations A promising direction. Markov Chain Model.
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A Bayesian multi-scale model of perceptual organization James Elder & Francisco Estrada Centre for Vision Research York University Toronto, Canada
Outline • Probabilistic foundations • Limitations • A promising direction
Markov Chain Model • Model contours as Markov chains: assume long-range statistics completely determined by local statistics.
li1 lj1 r li2 lj2 ij t t i j Gestalt Cues: Contours
Gestalt Cues: Natural Image Statistics Elder & Goldberg, 2002
Problem: Natural images are rich in detail – leads to large searchspace
A Possible Solution: Prior Knowledge • Theory 1. Perceptual organization is a general, bottom-up process that precedes scene recognition (e.g. Kanizsa 79) • Theory 2. Perceptual organization is influenced by higher-level objectives, prior knowledge and specific context (e.g. Rock 83, Cavanagh 91).
But this does not solve the general problem • Some Observations • Limitations of Model: • Naïve 1st-order Markov model almost certainly incomplete – fails to capture important global structure (e.g., Ren et al., 2007) • Raising the order of the model is unlikely to fix the problem. • Computational complexity: • Approximate search algorithms may miss global optimum • Myopic algorithms • Difficult to capture global structure
Idea: Coarse-to-Fine Grouping • BYOP (Build Your Own Prior) : • Compute closed contour hypotheses at low resolution. • Project these into higher resolution as statistical priors
Coarse-to-Fine Visual Computation: Not a New Idea • Stereopsis (Marr & Poggio, 1979) • Edge Localization (Bergholm, 1987) • Object Detection (Geman, 2006) • Perceptual Organization (???????)
Coarse-to-Fine Grouping: Observations • Reduced complexity at low resolutions increases chances of hitting global optimum. • Model is still Markov (computationally efficient), but now over scale as well as space • Global structure is captured first (at low complexity) and then controls complexity of grouping at finer scales.
Mean error across all images 1 0.8 0.6 Error 0.4 0.2 0 MS SS RC EJ Experimental Results
Mean relative errors 0.45 0.4 0.35 0.3 0.25 Relative Error 0.2 0.15 0.1 0.05 0 SS vs. MS RC vs. MS EJ vs. MS Experimental Results
Human Perception: Limitations Elder & Morgenstern, 2003
Human efficiency declines with contour length 7000 Ideal Participant 1 Pooled 0.6 0.6 Participant 1 Participant 2 6000 Participant 2 0.5 0.5 5000 0.4 0.4 4000 Efficiency Efficiency Number of elements at threshold 0.3 0.3 3000 0.2 0.2 2000 0.1 0.1 1000 0 0 0 0 5 10 0 5 10 0 5 10 Path length Path length Path length Elder & Morgenstern, 2003
Human Perception: The Global Precedence Effect Navon, 1977; Han et al., 1999
Coarse-to-Fine Perceptual Grouping • Computational Directions • A more interesting feed-forward computation • Monte Carlo sampling to accelerate feedback • Formulation as closed-loop (recurrent) process • Extension to complete scenes • Experimental Directions • Psychophysical methods to identify dynamics?