Estimation of Motions in Color Image Sequences Using Hypercomplex Fourier Transforms

• Published in: IEEE transactions on image processing Vol. 18; no. 1; pp. 168 - 187
• Main Authors: Alexiadis, D.S., Sergiadis, G.D.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.01.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Artificial Intelligence; Channels; Color; Color video processing; Colorimetry - methods; Exact sciences and technology; Fourier Analysis; Fourier transforms; Frequency domain analysis; hypercomplex Fourier transform; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Image processing; Image sequences; Information, signal and communications theory; Miscellaneous; Motion; Motion analysis; Motion estimation; Pattern Recognition, Automated - methods; Quaternions; Reproducibility of Results; Sensitivity and Specificity; Signal processing; Spatiotemporal phenomena; Studies; Subtraction Technique; Telecommunications and information theory; Three dimensional; Transaction processing; Translational motion; Video Recording - methods; Videos; Object extraction; Fourier transformation; quaternions; Moving target; Motion estimation; Image processing; Quaternion; hypercomplex Fourier transform; Translation motion; Computational complexity; Color image; Video signal processing; Color video processing; Image sequence; Signal processing; Feature extraction
• ISSN: 1057-7149; 1941-0042
• DOI: 10.1109/TIP.2008.2007603

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 ldquoholisticrdquo 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 3D 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.