Shamir

This page contains a brief explanation of the fuzzy sets proposed in the study of Shamir et. al.

Proposal of fuzzy sets

Ten categories are defined: red, dark orange, light orange, yellow, light green, dark green, aqua, blue, dark purple and light purple. By default, each of the classes is represented by the following colour:

Colour label	Index	RGB value	HEX value
Red	0	[255, 33, 36]	#FF2124
Dark orange	1	[255, 140, 0]	#FF8C00
Light orange	2	[255, 165, 0]	#FFA000
Yellow	3	[255, 255, 0]	#FFA000
Light green	4	[144, 238, 144]	#90EE90
Dark green	5	[0, 100, 0]	#006400
Aqua	6	[0, 255, 255]	#00FFFF
Blue	7	[0, 0, 255]	#0000FF
Dark purple	8	[128, 0, 128]	#800080
Light purple	9	[255, 0, 255]	#FF00FF

The colour associated with each label can be changed when calling the function that performs the segmentation. By default, they are the colours shown in the table above.

The indices of the colours must be positive integers. Negative integers are reserved for the internal calculation of the methods.

Partition of the chromatic space

The H channel, whose values must be in range $[0, 360]$, is partitioned using triangular membership functions. For the sake of clarity, the parameters $a$, $b$, $m$ which uniquely determine the expression of the membership function are given. For more information, see section Fuzzy Logic-based methods.

Colour label	$a$	$b$	$m$
Red	330	30	0 or 360
Dark orange	0	45	30
Light orange	30	60	45
Yellow	45	90	60
Light green	60	120	75
Dark green	90	180	120
Aqua	120	240	180
Blue	180	300	240
Dark purple	240	330	300
Light purple	300	360	330

In the definition of the red colour, it can be seen that it is not verified that $a<m<b$. This is because the chromatic component H of the HSV colour space is circular, and the red colour is the one located on the boundary.

References

Shamir, L.. (2006) Human Perception-based Color Segmentation Using Fuzzy Logic. Proceedings: International Conference on Image Processing, Computer Vision, & Pattern Recognition.