Form From Flow Presented by Megan Wachs

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Form From FlowPresented by Megan Wachs

• Region-Based Segmentation on Evolving Surfaces
  with Application to 3D Reconstruction of Shape
  and Piecewise Constant Radiance
• Hailin Jin, Anthony J. Yezzi, Stefano Soatto

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What is the problem?

• Given a set of images of an object
• We should be able to do 3D reconstruction.
• We should be able to estimate the radiance of the
  object

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What are the assumptions?

• The object is Lambertian
• The scene is a collection of smooth surfaces and
  a background.
• The foreground radiance is piecewise constant
• The discontinuities in radiance can be modeled as
  smooth closed curves

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What are the assumptions?
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What is the Goal?

• Determine the surface S
• Determine the curve C that separates regions of
  different radiance
• Determine the radiance values p1 and p2 of the
  different regions.

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Previous Approaches

• Two main approaches
• Stereo Correspondence
• Image Carving

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Previous ApproachesStereo Correspondence

• From multiple images/cameras, find corresponding
  points and triangulate.

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Previous ApproachesStereo Correspondence

• Problems
• Need to be able to find points, which is hard on
  objects with low texture and few features.
• Need to be able to correspond points
• Cameras have to be close to avoid problems with
  occlusion, which causes greater error.

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Previous ApproachesImage Carving

• Take silhouettes of an object from multiple views
• Carve away the part that isnt object
• Results in largest object that is in agreement
  with all scenes

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The New Approach

• Match images to the underlying model, not just to
  themselves
• This has been done before!
• The new part
• Allow objects to have discontinuities in radiance
• Model the discontinuities as well as the shape

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The New Approach

• Start with a set of images
• Give a starting estimate to S, C, and p1 and p2.
• Compute the cost function for the surface and the
  curves
• Iterate by updating the unknowns along their
  gradients until the solution converges to a local
  minimum

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An Example Run

• Start with a set of images of a Lambertian object
  captured with a calibrated camera

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An Example Run

• Give Starting estimate to S, C, p1, p2

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An Example Run

• Compute the cost function for the surface and the
  curves
• E(S,C,p1,p2,h) Edata??Esurf?Ecurv
• Edata comes from error in pixel coloration based
  on the model
• Esurf comes from the surface area
• Ecurv comes from the length of the curve

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An Example Run

• Determine the gradient descent flow, and update
  the unknowns in that direction.

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An Example Run

• Results

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My Plan Before Break

• Gather data
• Calibrate camera
• Calibrated image set
• Represent the surface S and curve C
• Represent the cost and gradient descent flow
  equations

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My Plan After Break

• Implement iterative algorithm
• Apply the method to a simple surface with 2
  radiance regions and one discontinuity.