Hypercomplex Fourier Transforms of Color Images

By Todd A. Ell, Stephen J. Sangwine. IEEE Transactions on Image Processing, 2001

542 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Media Technology

View Paper: https://www.semanticscholar.org/paper/a3dba5a148dd68be3c33a171da9b2aebb0b585b9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Jianyu Ou
2. Ryuichi Ashino
3. Mawardi Bahri
4. Hendrik De Bie
5. João Pedro Morais
6. F. Sommen
7. Nele De Schepper
8. Kit Ian Kou

In Computer Vision and Pattern Recognition

1. Ryuichi Ashino
2. Mawardi Bahri
3. João Pedro Morais
4. Jianyu Ou
5. Liming Zhang
6. Rémi Vaillancourt
7. Kit Ian Kou
8. Xin Xu

In Media Technology

1. Liming Zhang
2. Rémi Vaillancourt
3. João Pedro Morais
4. Kit Ian Kou
5. Xin Xu
6. Ryuichi Ashino
7. Chenlei Guo
8. Qi Ma

Citations in the corpus

• On Uncertainty Principle for Quaternionic Linear Canonical Transform (2013, methodology): “In [25] the authors used the QFT to proceed color image analysis.”
• Visual Saliency Based on Scale-Space Analysis in the Frequency Domain (2013, methodology): “Inspired by [30], [40], [41], we use the so-called hypercomplex matrix to combine multiple feature maps.”
• Convolution Theorems for Quaternion Fourier Transform: Properties and Applications (2013, methodology): “Applications of QFT In [19], the authors proposed to use quaternions in order to define a Fourier transform applicable to color images.”
• Spatio-temporal Saliency detection using phase spectrum of quaternion fourier transform (2008, methodology): “Moreover, this discovery of PFT provides an easy way to extend our work to Quaternion Fourier Transform (QFT) [11].”
• The Class of Clifford-Fourier Transforms (2011, background): “[8, 14, 15, 16, 18]) but also from a purely mathematical point of view (see e.”
• Uncertainty principles associated with quaternionic linear canonical transforms (2016, methodology): “In [25], the authors use the QFT to proceed color image analysis.”
• The unified theory of n-dimensional complex and hypercomplex analytic signals (2011, background): “The definitions are presented in signaland frequency domains.”
• A Novel Multiresolution Spatiotemporal Saliency Detection Model and Its Applications in Image and Video Compression (2010, methodology): “Since there was no definition of a Fourier transform which was applicable to color images in a holistic manner, Ell and Sangwine proposed Quater-nion Fourier Transform of color images and developed the properties of the transform [33].”