Network extraction with higherorder active contours

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Network extraction with higher-order active
contours
Ian Jermyn Marie Rochery Josiane Zerubia
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Motivation

• Goal duplication of quality and improvement of
  speed and cost of expert performance.
• Experts possess
• Well-defined semantics.
• Vast general and specific prior knowledge.
• Retrieval and mining , extraction of semantics.
• Necessary we cannot retrieve images of elephants
  if we cannot automatically answer the question
  Is there an elephant in this image?.
• Clearly sufficient.

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Modelling prior knowledge

• Extraction of semantics is hard and requires
  sophisticated prior knowledge.
• To an extent has been avoided in RS due to
  short-range dependencies sufficient for some
  semantics.
• Two modelling paradigms
• Learning using generic models and much data.
• Very wasteful.
• Careful domain-based model design.
• Less data is necessary.
• Better for strong prior constraints.
• But not always obvious how to design the models
  necessary (physics/phenomenology).

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Example of semantics and prior knowledge

• Atomic statements region R of the image has
  parameters P).
• Land cover type height building parameters
  etc.
• Prior model of parameters and region.
• Pr(P, R) Pr(R j P).Pr(P) Pr(P j R).Pr(R).
• Thus models of regions are required.

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Models of regions

• Length, area (MRFs, active contours,)
• Local interactions.
• Describe circles.
• Standard shape models
• Gaussian variation about a template.
• Describe template.
• Goal describe a family of shapes, e.g.
  networks (roads, rivers, vascular,).

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Active contours

• Define an energy E on regions/boundaries.
• Minima of energy are configurations sought.
• Gradient descent used.
• Classical energies are linear (single integral).
• Interactions with short, fixed range.
• Only Euclidean invariant terms are length and
  area.

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Higher-order active contours

• Arbitrarily long-range interactions (pairs,
  triples,).
• Euclidean invariant terms

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Example

• Gradient descent using instance of new energy.
• Pure prior term no data.
• A circle evolves towards a branched network with
  parallel-sided arms.
• Cf. standard models.

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Choice of interaction

• Favours pairs of points with tangent vectors
  parallel.
• Pairs of points with tangent vectors
  anti-parallel repel.

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Geometric evolution

• We can control the width of the arms.

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Geometric evolution

• We can control the number of arms formed from a
  circle, and the density of the network.

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Data terms

• Linear term that favours large gradients normal
  to contour.
• Quadratic term that favours pairs of points with
  tangents and image gradients parallel or
  anti-parallel.

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Experimental results
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Experimental results
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Experimental results
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Experimental results
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Experimental results
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Conclusion

• Open-ended new class of region models.
• Can also be applied to image models.
• Success so far in network extraction
• Generic, automatic initialization.
• Physically meaningful parameters.
• Future
• Quadratic gap closure force.
• What can be modelled?
• Probabilistic framework to learn
  parameters/models.

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• Thank you
• http//www.inria.fr/ariana
• http//www.moumir.org