1## Copyright (C) 2015 Hartmut Gimpel 2## 3## This program is free software; you can redistribute it and/or 4## modify it under the terms of the GNU General Public License as 5## published by the Free Software Foundation; either version 3 of the 6## License, or (at your option) any later version. 7## 8## This program is distributed in the hope that it will be useful, but 9## WITHOUT ANY WARRANTY; without even the implied warranty of 10## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 11## General Public License for more details. 12## 13## You should have received a copy of the GNU General Public License 14## along with this program; if not, see 15## <http:##www.gnu.org/licenses/>. 16 17## -*- texinfo -*- 18## @deftypefn {Function File} {@var{lab} =} xyz2lab (@var{xyz}) 19## @deftypefnx {Function File} {@var{lab_map} =} xyz2lab (@var{xyz_map}) 20## Transform a colormap or image from CIE XYZ to CIE L*a*b* color space. 21## 22## A color in the CIE XYZ color space consists of three values X, Y and Z. 23## Those values are designed to be colorimetric, meaning that their values 24## do not depend on the display device hardware. 25## 26## A color in the CIE L*a*b* (or CIE Lab) space consists of lightness L* and 27## two color-opponent dimensions a* and b*. The whitepoint is taken as D65. 28## The CIE L*a*b* colorspace is also a colorimetric colorspace. It is designed 29## to incorporate the human perception of color differences. 30## 31## Input values of class single and double are accepted. 32## The shape and the class of the input are conserved. 33## 34## The return values of L* are normally in the inteval [0, 100] 35## and the values of a* and b* in the interval [-127, 127] 36## 37## @seealso{lab2xyz, rgb2lab, rgb2hsv, rgb2ind, rgb2ntsc} 38## @end deftypefn 39 40## Author: Hartmut Gimpel <hg_code@gmx.de> 41## algorithm taken from the following book: 42## Burger, Burge "Digitale Bildverarbeitung", 3rd edition (2015) 43 44function lab = xyz2lab (xyz) 45 46 if (nargin != 1) 47 print_usage (); 48 endif 49 50 [xyz, cls, sz, is_im, is_nd, is_int] ... 51 = colorspace_conversion_input_check ("xyz2lab", "XYZ", xyz, 1); 52 # only accept single and double inputs because valid xyz values can be >1 53 54 ## normalize with the whitepoint D65 55 ## (reference: en.wikipedia.org/wiki/Illuminant_D65) 56 D65 = [0.95047, 1, 1.08883]; 57 xyz_D65 = xyz ./ D65; 58 # Matlab truncates to D65_Matlab = [0.9504, 1.0000, 1.0888]; 59 60 ## transformation xyz -> xyz' 61 epsilon = (6/29)^3; 62 kappa = 1/116 * (29/3)^3; 63 xyz_prime = xyz_D65; 64 mask = xyz_D65 <= epsilon; 65 xyz_prime(mask) = kappa .* xyz_D65(mask) + 16/116; 66 xyz_prime(! mask) = xyz_D65(! mask) .^(1/3); 67 x_prime = xyz_prime(:,1); 68 y_prime = xyz_prime(:,2); 69 z_prime = xyz_prime(:,3); 70 71 ## transformation xyz' -> lab 72 L = 116 .* y_prime - 16; 73 a = 500 .* (x_prime - y_prime); 74 b = 200 .* (y_prime - z_prime); 75 76 lab = [L, a, b]; 77 78 # always return values of type double for Matlab compatibility (exception: type single) 79 lab = colorspace_conversion_revert (lab, cls, sz, is_im, is_nd, is_int, 1); 80 81endfunction 82 83## Test pure colors, gray and some other colors 84## (This set of test values is taken from the book by Burger.) 85%!assert (xyz2lab ([0, 0, 0]), [0 0 0], 5e-2) 86%!assert (xyz2lab ([0.4125, 0.2127, 0.0193]), [53.24, 80.09, 67.20], 5e-2) 87%!assert (xyz2lab ([0.7700, 0.9278, 0.1385]), [97.14, -21.55, 94.48], 5e-2) 88%!assert (xyz2lab ([0.3576, 0.7152, 0.1192]), [87.74, -86.18, 83.18], 5e-2) 89%!assert (xyz2lab ([0.5380, 0.7873, 1.0694]), [91.11, -48.09, -14.13], 5e-2) 90%!assert (xyz2lab ([0.1804, 0.07217, 0.9502]), [32.30, 79.19, -107.86], 5e-2) 91%!assert (xyz2lab ([0.5929, 0.28484, 0.9696]), [60.32, 98.24, -60.83], 5e-2) 92%!assert (xyz2lab ([0.9505, 1.0000, 1.0888]), [100, 0.00, 0.00], 5e-2) 93%!assert (xyz2lab ([0.2034, 0.2140, 0.2330]), [53.39, 0.00, 0.00], 5e-2) 94%!assert (xyz2lab ([0.2155, 0.1111, 0.0101]), [39.77, 64.51, 54.13], 5e-2) 95%!assert (xyz2lab ([0.0883, 0.0455, 0.0041]), [25.42, 47.91, 37.91], 5e-2) 96%!assert (xyz2lab ([0.02094, 0.0108, 0.00098]), [9.66, 29.68, 15.24], 5e-2) 97%!assert (xyz2lab ([0.5276, 0.3812, 0.2482]), [68.11, 48.39, 22.83], 5e-2) 98 99## Test tolarant input checking on floats 100%!assert (xyz2lab ([1.5 1 1]), [100, 82.15, 5.60], 5e-2) 101 102%! xyz_map = rand (64, 3); 103%! assert (lab2xyz (xyz2lab (xyz_map)), xyz_map, 1e-5); 104 105%!test 106%! xyz_img = rand (64, 64, 3); 107%! assert (lab2xyz (xyz2lab (xyz_img)), xyz_img, 1e-5); 108 109## support sparse input (the only useful xyz value with zeros is black) 110%!assert (xyz2lab (sparse ([0 0 0])), [0 0 0], 5e-2) 111 112## conserve class of single input 113%!assert (class (xyz2lab (single([0.5 0.5 0.5]))), 'single') 114 115## Test input validation 116%!error xyz2lab () 117%!error xyz2lab (1,2) 118%!error <invalid data type 'cell'> xyz2lab ({1}) 119%!error <XYZ must be a colormap or XYZ image> xyz2lab (ones (2,2)) 120 121## Test ND input 122%!test 123%! xyz = rand (16, 16, 3, 5); 124%! lab = zeros (size (xyz)); 125%! for i = 1:5 126%! lab(:,:,:,i) = xyz2lab (xyz(:,:,:,i)); 127%! endfor 128%! assert (xyz2lab (xyz), lab) 129