Non-Rigid Registration between Color Channels based on Joint-Histogram Entropy in Subspace
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Non-Rigid Registration between Color Channels
based on Joint-Histogram Entropy in Subspace
Masao Shimizu, Rafael H. C. de Souza, Shin Yoshimura, and Masatoshi Okutomi
Tokyo Institute of Technology
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Outline• Introduction
• Joint histogram of time-sequential sampled images
• Joint entropy of a projected histogram
• Non rigid motion model
• Non rigid registration
• Experimental results
• Conclusions and future work
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Introduction
• Color Image sampling methods:– Color decoupling
– Spatial sampling
– Endoscopic images and time-sampling
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Introduction
• Color Image sampling methods:– Color decoupling
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Introduction
• Color Image sampling methods:– Spatial sampling
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Introduction
• Endoscopic images
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Introduction
• Endoscopic images
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Introduction
• Color Image sampling methods:– Time-sequential
• Objective:– Implement a registration algorithm to remove the color artifacts
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Joint histogram of time-sequential sampled images
• Natural image x channel shifted image
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Joint entropy of a projected histogram
• Dominant plane
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Joint entropy of a projected histogram
• Joint entropy of a two-dimensional color space
Probability of the same coordinate to have a pixel value of a in image A and b in image B.
ξ ϵ projected color space RGB value of a pixel
Projection matrix
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Joint entropy of a projected histogram
• Choosing the subspace:– There are not much
artifacts on the brightness component
– Changes are concentrated in CbCr space
*figure to be improved
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Non rigid motion model
• Non-rigid model
• Problems with SSD
• Minimization by Entropy
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Non rigid motion model
• Minimization by Entropy
vset of vectors
vxAxvxW )();(
Area affected by control point
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• Also known as correlation-like methods
• General registration problem definition (Fischer & Modersitzki 2003):
][];,[][ uSuTRDuu argmin
Similarity function
Regularization term
Warping parameters
Non rigid registration
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Non rigid registration
• Problems with SSD
Red channel
Green channel
Blue channel
Registration with SSD
Poor correlation with the other
channels
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Non rigid registration
• Mutual Information:– Generaly yield the correct registration– However, 2 registrations are required
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Non rigid registration
• Entropy:– Generaly yield the correct registration– Only one registration is required
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Non rigid registration
• Minimization by Entropy
Joint probability over the
projected space
RGB value
Projection Matrix
For natural images, a good projection is The CbCr space.
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Non rigid registration
• Minimization by Entropy
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Experimental results
• Results with real images– 14x11– Up to convergence
• Simulated results– 7x5 grid– 20 iterations
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Experimental results
• Results with real images
No registration
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Experimental results
• Results with real images
SSD
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Experimental results
• Results with real images
MI
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Experimental results
• Results with real images
Proposed method
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Experimental results
• Simulated results
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Experimental results
• Simulated results
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Conclusions and future work
• Conclusion– A method for aligmment of time-sampled
images– Non-rigid model– Channels with different spectra
• Future work– Multiple images– Regularization– Better optimization