continuous medial representations for geometric object...
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Continuous Medial Representations for Geometric Object Modeling
Wei LiuMar 18, 2010
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Methods to define skeleton of object
● maximal inscribed ball
● Hierarchal Voronoi
● Shock of boundary evolution
● core tracking.
● mrep
● cmrep
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Mrep: Inverse skeletonization
● Traditional: the intersection of the normal.
● Now: a medial point with two boundary point.
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Mrep: sampling
● Medial point are sampled on the axis.
● A sparse representation.
● Sampled medial points are fixed relative to the axis.
http://midag.cs.unc.edu/defmreps/jl3_movie2.gif
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Continuous mrep: cmrep
● Can move the medial points along the axis.
● Generate a synthetic given set of bspline control points.
● Maximize overlapping between this shape and template by adjusting control point.
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●When ||del r|| = 0, meaning r does not change, U = N.
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Bspline interpolation
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constraints
● Closed● Connected● nonsingular
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Parameter estimation
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Parameter estimation
● Obj F = prior + Energy ● Prior: prefer low curvature.
Energy: mean square distance between interpolated boundary and target shape, summed over all sampled points.
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Narrated Quicktime movie about model construction in 3D (.mov with audio, 3 min, 11mb)
Narrated Quicktime movie about fitting models to images in 3D (.mov with audio, 90 sec, 18mb)
Movie of a spinning 3D model of the hippocampus (.avi loop, 200kb)
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