Chamorro-Martínez

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

Proposal of fuzzy sets

Twelve categories are defined: red, orange, yellow, yellow-green, green, green-cyan, cyan, cyan-blue, blue, blue-magenta, magenta and magenta-red. 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
Orange	1	[255, 148, 9]	#FF9409
Yellow	2	[255, 255, 13]	#FFFF0D
Yellow-Green	3	[186, 255, 15]	#BAFF0F
Green	4	[6, 155, 9]	#069B09
Green-Cyan	5	[12, 255, 116]	#0CFF74
Cyan	6	[11, 254, 255]	#0BFEFF
Cyan-Blue	7	[8, 192, 255]	#08C0FF
Blue	8	[0, 0, 255]	#0000FF
Blue-Magenta	9	[92, 8, 253]	#5C08FD
Magenta	10	[238, 3, 249]	#EE03F9
Magenta-Red	11	[254, 6, 180]	#FE06B4

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 trapezoidal membership functions. For the sake of clarity, the parameters $a$, $b$, $m$, $n$ which uniquely determine the expression of the membership function are given. For more information, see section Fuzzy Logic-based methods.

Colour label	$a$	$b$	$m$	$n$
Red	350	20	340	10
Orange	10	50	20	40
Yellow	40	80	50	70
Yellow-Green	70	110	80	100
Green	100	140	110	130
Green-Cyan	130	170	140	160
Cyan	160	200	170	190
Cyan-Blue	190	230	200	220
Blue	220	260	230	250
Blue-Magenta	250	290	260	280
Magenta	280	320	290	310
Magenta-Red	310	350	320	340

In the definition of the red colour, it can be seen that it is not verified that $a<m<n<b$. 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

Chamorro-Martínez, J.; Medina, J.M.; Barranco, C.D.; Galán-Perales, E.; Soto-Hidalgo, J.M.. (2007) Retrieving images in fuzzy object-relational databases using dominant color descriptors. Fuzzy Sets and Systems, Volume 158, Issue 3. Pages 312-324.