Image Features Based on a New Approach to 2D Rotation Invariant Quadrature Filters
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
The Two-Dimensional Clifford-Fourier Transform
Journal of Mathematical Imaging and Vision
Signal modeling for two-dimensional image structures
Journal of Visual Communication and Image Representation
Quaternion involutions and anti-involutions
Computers & Mathematics with Applications
Analyzing Image Structure by Multidimensional Frequency Modulation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Technical Section: Texture synthesis based on Direction Empirical Mode Decomposition
Computers and Graphics
Artificial Intelligence in Medicine
Improved bi-dimensional EMD and Hilbert spectrum for the analysis of textures
Pattern Recognition
Generalized Hilbert transform and its properties in 2D LCT domain
Signal Processing
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
The quaternion LMS algorithm for adaptive filtering of hypercomplex processes
IEEE Transactions on Signal Processing
Construction of Hilbert transform pairs of wavelet bases and Gabor-like transforms
IEEE Transactions on Signal Processing
The monogenic wavelet transform
IEEE Transactions on Signal Processing
Analytic estimation of subsample spatial shift using the phases of multidimensional analytic signals
IEEE Transactions on Image Processing
An iterative learning scheme for multistate complex-valued and quaternionic hopfield neural networks
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Multiresolution monogenic signal analysis using the Riesz-Laplace wavelet transform
IEEE Transactions on Image Processing
Local quaternion Fourier transform and color image texture analysis
Signal Processing
Journal of Mathematical Imaging and Vision
Multiscale AM-FM demodulation and image reconstruction methods with improved accuracy
IEEE Transactions on Image Processing
Quaternion multiplier inspired by the lifting implementation of plane rotations
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Hypercomplex Mathematical Morphology
Journal of Mathematical Imaging and Vision
The complex bidimensional empirical mode decomposition
Signal Processing
Directional Multiscale Amplitude and Phase Decomposition by the Monogenic Curvelet Transform
SIAM Journal on Imaging Sciences
On analysis of bi-dimensional component decomposition via BEMD
Pattern Recognition
Applications of geometric algebra in robot vision
IWMM'04/GIAE'04 Proceedings of the 6th international conference on Computer Algebra and Geometric Algebra with Applications
The monogenic curvature scale-space
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
An algorithm for fast multiplication of sedenions
Information Processing Letters
Convolution Products for Hypercomplex Fourier Transforms
Journal of Mathematical Imaging and Vision
Hi-index | 35.69 |
The construction of Gabor's (1946) complex signal-which is also known as the analytic signal-provides direct access to a real one-dimensional (1-D) signal's local amplitude and phase. The complex signal is built from a real signal by adding its Hilbert transform-which is a phase-shifted version of the signal-as an imaginary part to the signal. Since its introduction, the complex signal has become an important tool in signal processing, with applications, for example, in narrowband communication. Different approaches to an n-D analytic or complex signal have been proposed in the past. We review these approaches and propose the hypercomplex signal as a novel extension of the complex signal to n-D. This extension leads to a new definition of local phase, which reveals information on the intrinsic dimensionality of the signal. The different approaches are unified by expressing all of them as combinations of the signal and its partial and total Hilbert transforms. Examples that clarify how the approaches differ in their definitions of local phase and amplitude are shown. An example is provided for the two-dimensional (2-D) hypercomplex signal, which shows how the novel phase concept can be used in texture segmentation