Angle between two RGB vectors
Read a test image. The image is the raw data captured with a Canon EOS 30D digital camera after correcting the black level and scaling the intensities to 16 bits per pixel. No demosaicing, white balancing, color enhancement, noise filtering, or gamma correction has been applied.
RAW = imread('foosballraw.tiff');
Interpolate using the
demosaic function to obtain a color image. The color filter array pattern is RGGB.
A = demosaic(RAW,'rggb');
Display the image. Because the image is in linear RGB color space, apply gamma correction so the image appears correctly on the screen.
A_sRGB = lin2rgb(A); imshow(A_sRGB)
The image contains an X-Rite® ColorChecker® chart. Specify the ground truth illuminant, which was calculated in advance using the neutral patches of the chart.
illuminant_groundtruth = [0.0717 0.1472 0.0975];
To avoid skewing the estimation of the illuminant, exclude the ColorChecker chart by creating a mask.
mask = true(size(A,1), size(A,2)); mask(920:1330,1360:1900) = false;
illuminant_whitepatch = illumwhite(A,'Mask',mask); illuminant_grayworld = illumgray(A,'Mask',mask); illuminant_pca = illumpca(A,'Mask',mask);
Compare each estimation against the ground truth by calculating the angle between each estimated illuminant and the ground truth using the
colorangle function. The smaller the angle, the better the estimation. The magnitude of the estimation does not matter because only the direction of the illuminant is used to white-balance an image with chromatic adaptation.
angle_whitepatch = colorangle(illuminant_whitepatch, illuminant_groundtruth)
angle_whitepatch = 5.0921
angle_grayworld = colorangle(illuminant_grayworld, illuminant_groundtruth)
angle_grayworld = 5.1036
angle_pca = colorangle(illuminant_pca, illuminant_groundtruth)
angle_pca = 5.0134
The value of
angle_pca is smallest, indicating that the PCA illuminant estimation algorithm is closest to the ground truth illumination for this image.
rgb1— First RGB vector
First RGB vector, specified as a 3-element numeric vector.
rgb2— Second RGB vector
Second RGB vector, specified as a 3-element numeric vector.
angle— Angle between RGB vectors
Angle between RGB vectors, returned as a numeric scalar.
Angular error is a useful metric to evaluate the estimation of an illuminant against the ground truth. The smaller the angle between the ground truth illuminant and the estimated illuminant, the better the estimate.