On the estimation of optical flow: relations between different approaches and some new results
Artificial Intelligence
Computation of component image velocity from local phase information
International Journal of Computer Vision
Hypercomplex spectral transformations
Hypercomplex spectral transformations
Image-flow computation: an estimation-theoretic framework and a unified perspective
CVGIP: Image Understanding
Performance of optical flow techniques
International Journal of Computer Vision
The Frequency Structure of One-Dimensional Occluding Image Signals
IEEE Transactions on Pattern Analysis and Machine Intelligence
Video Processing and Communications
Video Processing and Communications
Generalized image matching by the method of differences
Generalized image matching by the method of differences
Narrow directional steerable filters in motion estimation
Computer Vision and Image Understanding
Hypercomplex correlation techniques for vector images
IEEE Transactions on Signal Processing
A harmonic retrieval framework for discontinuous motion estimation
IEEE Transactions on Image Processing
Estimation of Multiple Accelerated Motions Using Chirp-Fourier Transform and Clustering
IEEE Transactions on Image Processing
Hypercomplex Fourier Transforms of Color Images
IEEE Transactions on Image Processing
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Although the motion estimation problem has been extensively studied, most of the proposed estimation approaches deal mainly with monochrome videos. The most usual way to apply them also in color image sequences is to process each color channel separately. A different, more sophisticated approach is to process the color channels in a "holistic" manner using quaternions, as proposed by Ell and Sangwine. In this paper, we extend standard spatiotemporal Fourier-based approaches to handle color image sequences, using the hypercomplex Fourier transform. We show that translational motions are manifested as energy concentration along planes in the hypercomplex 3-D Fourier domain and we describe a methodology to estimate the motions, based on this property. Furthermore, we compare the three-channels-separately approach with our approach and we show that the computational effort can be reduced by a factor of 1/3, using the hypercomplex Fourier transform. Also, we propose a simple, accompanying method to extract the moving objects in the hypercomplex Fourier domain. Our experimental results on synthetic and natural images verify our arguments throughout the paper.