This code reimplements Section 3 of T.-S. Chan and A. Kumar, "Reliable ear identification using 2-D quadrature filters," Pattern Recognition Lett., vol. 33, no. 14, pp. 1870-1881, 2012.
Here, quaternionic matrices are decomposed as A+Bj where A and B are complex matrices [1], and spherical quadrature filters use a complexified version of the Riesz transform [2]-[4].
The following functions are available:
| Function | Description |
|---|---|
hd |
Hamming distance |
iqft |
Inverse quaternion Fourier transform |
phasequant |
Phase quantization |
plotqqf |
Plot quaternionic quadrature filters |
plotsqf |
Plot spherical quadrature filters |
qft |
Quaternion Fourier transform |
qqf |
Quaternionic quadrature filter |
sqf |
Spherical quadrature filter |
Here is an example of quaternionic log-Gabor filtering:
f = imread('circuit.tif');
g = imread('circbw.tif');
[fq1,fq2] = qqf(f,'loggabor',1/18,0.55/18);
[gq1,gq2] = qqf(g,'loggabor',1/18,0.55/18);
[f1,f2] = phasequant(fq1,fq2);
[g1,g2] = phasequant(gq1,gq2);
hd(f1,f2,g1,g2)A longer example with multiscale quaternionic Cauchy filtering:
f = imread('circuit.tif');
g = imread('circbw.tif');
[fq1,fq2] = qqf(f,'cauchy',1/18,2.8737*18);
[fq3,fq4] = qqf(f,'cauchy',1/54,2.8737*54);
[gq1,gq2] = qqf(g,'cauchy',1/18,2.8737*18);
[gq3,gq4] = qqf(g,'cauchy',1/54,2.8737*54);
% Concatenate both scales.
[f1,f2] = phasequant(cat(3,fq1,fq3),cat(3,fq2,fq4));
[g1,g2] = phasequant(cat(3,gq1,gq3),cat(3,gq2,gq4));
hd(f1,f2,g1,g2)To reproduce Figs. 1-6 in the paper, run plotqqf and plotsqf. For
segmentation, database rotations and template shifting, please refer to
[5], [6] for further details.
Tak-Shing Chan
22 July 2017
[1] S.-C. Pei, J.-J. Ding, and J.-H. Chang, "Efficient implementation of quaternion Fourier transform, convolution, and correlation by 2-D complex FFT," IEEE Trans. Signal Process., vol. 49, no. 11, pp. 2783-2797, 2001.
[2] M. Unser, D. Sage, and D. Van De Ville, "Multiresolution monogenic signal analysis using the Riesz-Laplace wavelet transform," IEEE Trans. Image Process., vol. 18, no. 11, pp. 2402-2418, 2009.
[3] K. G. Larkin, D. J. Bone, and M. A. Oldfield, "Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform," J. Opt. Soc. Amer. A, vol. 18, no. 8, pp. 1862-1870, 2001.
[4] P. Kovesi. (2009). MATLAB and Octave functions for computer vision and image processing. Phase symmetry of an image using monogenic filters. Available: http://www.peterkovesi.com/matlabfns/PhaseCongruency/phasesymmono.m
[5] L. Masek and P. Kovesi. (2003). MATLAB source code for a biometric identification system based on iris patterns. Available: http://www.peterkovesi.com/studentprojects/libor/sourcecode.html
[6] A. Kumar and C. Wu, "Automated human identification using ear imaging," Pattern Recognition, vol. 45, no. 3, pp. 956-968, 2012.