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Analysis of Contour Motions Ce Liu William T. Freeman Edward H. Adelson

Two-step inference Contour grouping: set switch variables to optimize Pr( S ; B , O ) (hard) Global motion given grouping (easy, least squares) Importance sampling to estimate the marginal of the switch variables Bidirectional proposal density Use marginals to obtain a best grouping.

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Analysis of Contour Motions Ce Liu William T. Freeman Edward H. Adelson

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  1. Two-step inference • Contour grouping: set switch variables to optimize Pr(S; B,O)(hard) • Global motion given grouping (easy, least squares) • Importance sampling to estimate the marginal of the switch variables • Bidirectional proposal density • Use marginals to obtain a best grouping A T-junction edgelet, shown in frame 1. The same edgelet, shown in frame 2. The relevant orientation energy, frame 2 Visualization of the Gaussian pdf. Affinity Reversibility No self-intersection Analysis of Contour Motions Ce Liu William T. Freeman Edward H. Adelson Neural Information Processing Systems Conference 2006 I N P S 1. Introduction 3. Forming edgelets & boundary fragments • Conditioned on the grouping, the graphical model for motion is a Gaussian MRF • Spatial boundary fragment extraction • Steerable filters to obtain edge energy for each orientation band • Track boundary fragments in frame 1 (using Canny-like threshold) • Boundary fragments: lines or curves with small curvature • Edgelet temporal tracking with uncertainties • Frame 1: edgelet (x, y, q) • Frame 2: orientation energy of q • A Gaussian pdf is fit with the weight of orientation energy • 1D uncertainty of motion (even for T-junctions) Existing algorithms cannot correctly analyze the motion of textureless objects under occlusion 5. Inference One frame of motion sequence Output of our contour motion algorithm Output of the state-of-the-art optical flow algorithm [1] 6. Results All results generated using the same parameter settings. The running time varies from ten seconds to a few minutes in MATLAB, as a function of the number of boundary fragments. 4. Forming contours: graphical model for grouping & motion • Problem regions caused by the occlusions of textureless objects • Corners: spurious T- or L-junctions • Lines: boundary ownership • Flat regions: illusory boundaries • Grouping machinery: switch variables (attached to every end of the fragments) • Exclusive: one end connects to at most one other end • Reversible: if end (i,ti) connects to (j,tj), then (j,tj) connects to (i,ti), i.e.S(i,ti) =(j,tj), S(j,tj)=(i,ti), or S(S(i,ti))=(i,ti) Our approach: simultaneous grouping and motion analysis • Multi-level contour representation • Formulate graphical model that favors good contour and motion criteria • Inference using importance sampling Reciprocity constraint Example fragments Grouping ambiguity Legal contours More legal contours • Affinity metric terms: • Motion similarity • Curve smoothness • Contrast consistency • The graphical model for grouping: 2.Three levels of contour representation Edgelet Boundary fragment Contour [1] T. Brox et al. High accuracy optical flow estimation based on a theory for warping. ECCV 2004

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