IEEE Computer 28(9)

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• IEEE Computer 28(9)
• IEEE Trans. On PAMI 18(8)
• Pattern Recognition 30(4)
• Image and Vision Computing 17(7)

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• Photobook, MIT
• face, texture and shape database
• WebSeek, Columbia U
• WWW image search engine
• include more than 650,000 images
• ImageRover, Boston U
• WWW image search engine
• use 32 robots to collect one million images
  monthly
• VideoBook, HKUST
• video retrieval system

• QBIC, IBM
• commercial system (trademark)
• MARS, Illinois
• image retrieval with relevance feedback mechanism
• VideoClip, Columbia U
• video parsing and editing
• Princeton University
• high-level video representation
• NeTra, UCSB
• object-based video representation

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Shape Retrieval and Matching by Schwarz Integral
Yang MA Pattern Recognition 1999
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A close-form solution for shape matching and
similarity measurement
A multi-scale matching
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1. Multi-scale representation by Schwarz
integral
Shape contour is presented by a 1D periodic
function
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• We define a complex function defined on
  a
• disc of radius 1.

Where is the shape function
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It can be proved that
is a smoothed function of
Where r is the scale.
is the smoothed function of
where r is the scale.
The Schwarz Integral can be considered as the
multiscale representation of the shape function.
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2. Signal matching and similarity measurement
Matching model Let
be two signals. is a
one-to-one smooth function such that
is the matching function of two signals
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• If were a bijective function, then
• But in fact, is a multi-values
  function

• , may not be in the same
  scale, so matching
• two functions in different scales is not
  reasonable.

• Instead of matching , we propose
  to match
• their Schwarz representations ,
  by

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Algorithm

• (1) Extract tangent function of shape as feature
  function
• (2) Expand the feature function
• into Fourier series

(3) We obtain the Schwarz representation of the
shape
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3. Compute the inverse functions of

And expand them into polynomials.
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• Image Retrieval from model image

• (1) Extract the one-dimensional feature of model
  image,
• expand the feature function in to Fourier
  series and obtain the Schwarz integral
• (2)Compute the matching function by
• (3)Compute similarity measure
• (4)Output the most k similar image as result.

The matching method can be used both to find
the correspondent points and to measure the
similarity between two shapes
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Summary

• Shape representation and Matching
• Global region or local feature based
• Optimization framework
• Research work
• image segmentation
• 3D object and occlusion
• fast algorithms for large data base
• robustness

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