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Active Contours (“Snakes”)

Active Contours (“Snakes”). Goal. Start with image and initial closed curve Evolve curve to lie along “important” features Edges Corners Detected features User input. Applications. Region selection in Photoshop Segmentation of medical images Tracking. Snakes: Active Contour Models.

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Active Contours (“Snakes”)

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  1. Active Contours (“Snakes”)

  2. Goal • Start with image and initial closed curve • Evolve curve to lie along “important” features • Edges • Corners • Detected features • User input

  3. Applications • Region selection in Photoshop • Segmentation of medical images • Tracking

  4. Snakes: Active Contour Models • Introduced by Kass, Witkin, and Terzopoulos • Framework: energy minimization • Bending and stretching curve = more energy • Good features = less energy • Curve evolves to minimize energy • Also “Deformable Contours”

  5. Snakes Energy Equation • Parametric representation of curve • Energy functional consists of three terms

  6. Internal Energy • First term is “membrane” term – minimum energy when curve minimizes length(“soap bubble”) • Second term is “thin plate” term – minimum energy when curve is smooth

  7. Internal Energy • Control a and b to vary between extremes • Set b to 0 at a point to allow corner • Set b to 0 everywhere to let curve follow sharp creases – “strings”

  8. Image Energy • Variety of terms give different effects • For example,minimizes energy at intensity Idesired

  9. Edge Attraction • Gradient-based: • Laplacian-based: • In both cases, can smooth with Gaussian

  10. Constraint Forces • Spring • Repulsion

  11. Evolving Curve • Computing forces on v that locally minimize energy gives differential equation for v • Euler-Lagrange formula • Discretize v: samples (xi, yi) • Approximate derivatives with finite differences • Iterative numerical solver

  12. Corpus Callosum [Davatzikos and Prince]

  13. Corpus Callosum [Davatzikos and Prince]

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