An uncertainty principle for quaternion Fourier transform
Computers & Mathematics with Applications
Computer Vision and Image Understanding
Color Image Segmentation in a Quaternion Framework
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Quaternion-Based Color Image Smoothing Using a Spatially Varying Kernel
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
A system for retargeting of streaming video
ACM SIGGRAPH Asia 2009 papers
Estimation of motions in color image sequences using hypercomplex fourier transforms
IEEE Transactions on Image Processing
Journal of Visual Communication and Image Representation
Local quaternion Fourier transform and color image texture analysis
Signal Processing
Biological plausibility of spectral domain approach for spatiotemporal visual saliency
ICONIP'08 Proceedings of the 15th international conference on Advances in neuro-information processing - Volume Part I
Adaptive lattices on the unit sphere: application to remote sensing
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
IEEE Transactions on Image Processing
Quaternion Fourier-Mellin moments for color images
Pattern Recognition
A Quaternion Framework for Color Image Smoothing and Segmentation
International Journal of Computer Vision
Bottom-up saliency detection model based on amplitude spectrum
MMM'11 Proceedings of the 17th international conference on Advances in multimedia modeling - Volume Part I
The trinion Fourier transform of color images
Signal Processing
Hypercomplex Mathematical Morphology
Journal of Mathematical Imaging and Vision
Nonparametric bottom-up saliency detection using hypercomplex spectral contrast
MM '11 Proceedings of the 19th ACM international conference on Multimedia
Fast hypercomplex polar fourier analysis for image processing
PSIVT'11 Proceedings of the 5th Pacific Rim conference on Advances in Image and Video Technology - Volume Part II
Robust color image watermarking using LS-SVM correction
ISNN'12 Proceedings of the 9th international conference on Advances in Neural Networks - Volume Part II
Quaternion-Based spectral saliency detection for eye fixation prediction
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part II
A robust blind color image watermarking in quaternion Fourier transform domain
Journal of Systems and Software
Visual saliency and distortion weighting based video quality assessment
PCM'12 Proceedings of the 13th Pacific-Rim conference on Advances in Multimedia Information Processing
Prediction of wide-sense stationary quaternion random signals
Signal Processing
Attention selection using global topological properties based on pulse coupled neural network
Computer Vision and Image Understanding
Color Fourier-Mellin descriptors for image recognition
Pattern Recognition Letters
Convolution Products for Hypercomplex Fourier Transforms
Journal of Mathematical Imaging and Vision
New feature extraction approach for bank note classification using Quaternion Wavelets
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
Full 4-D quaternion discrete Fourier transform based watermarking for color images
Digital Signal Processing
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Fourier transforms are a fundamental tool in signal and image processing, yet, until recently, there was no definition of a Fourier transform applicable to color images in a holistic manner. In this paper, hypercomplex numbers, specifically quaternions, are used to define a Fourier transform applicable to color images. The properties of the transform are developed, and it is shown that the transform may be computed using two standard complex fast Fourier transforms. The resulting spectrum is explained in terms of familiar phase and modulus concepts, and a new concept of hypercomplex axis. A method for visualizing the spectrum using color graphics is also presented. Finally, a convolution operational formula in the spectral domain is discussed