non-rigid registration between color channels based on joint-histogram entropy in subspace

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

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

Introduction

• Color Image sampling methods:– Color decoupling

– Spatial sampling

– Endoscopic images and time-sampling

Introduction

• Color Image sampling methods:– Color decoupling

Introduction

• Color Image sampling methods:– Spatial sampling

Introduction

• Endoscopic images

Introduction

• Endoscopic images

Introduction

• Color Image sampling methods:– Time-sequential

• Objective:– Implement a registration algorithm to remove the color artifacts

Joint histogram of time-sequential sampled images

• Natural image x channel shifted image

Joint entropy of a projected histogram

• Dominant plane

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

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

Non rigid motion model

• Non-rigid model

• Problems with SSD

• Minimization by Entropy

Non rigid motion model

• Minimization by Entropy

vset of vectors

vxAxvxW )();(

Area affected by control point

• Also known as correlation-like methods

• General registration problem definition (Fischer & Modersitzki 2003):

][];,[][ uSuTRDuu argmin

Similarity function

Regularization term

Warping parameters

Non rigid registration

Non rigid registration

• Problems with SSD

Red channel

Green channel

Blue channel

Registration with SSD

Poor correlation with the other

channels

Non rigid registration

• Mutual Information:– Generaly yield the correct registration– However, 2 registrations are required

Non rigid registration

• Entropy:– Generaly yield the correct registration– Only one registration is required

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.

Non rigid registration

• Minimization by Entropy

Experimental results

• Results with real images– 14x11– Up to convergence

• Simulated results– 7x5 grid– 20 iterations

Experimental results

• Results with real images

No registration

Experimental results

• Results with real images

SSD

Experimental results

• Results with real images

MI

Experimental results

• Results with real images

Proposed method

Experimental results

• Simulated results

Experimental results

• Simulated results

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