Amante-Fonseca

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

Proposal of fuzzy sets

Nine categories are defined: red, brown, orange, yellow, green, cyan, blue, purple and pink. By default, each of the classes is represented by the following colour:

Colour label	Index	RGB value	HEX value
Red	0	[255, 33, 36]	#FF2125
Brown	1	[170, 121, 66]	#AA7942
Orange	2	[255, 146, 0]	#FF9200
Yellow	3	[255, 251, 0]	#FFFB00
Green	4	[0, 255, 0]	#00FF00
Cyan	5	[0, 253, 255]	#00FFFF
Blue	6	[0, 0, 255]	#0000FF
Purple	7	[147, 33, 146]	#932191
Pink	9	[255, 64, 255]	#FF40FF

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	335	20	350	10
Brown	10	35	20	30
Orange	30	50	34	42
Yellow	44	100	50	70
Green	70	160	100	140
Cyan	140	220	160	200
Blue	200	290	220	260
Purple	260	320	290	310
Pink	310	350	315	335

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.

Classification of achromatic colours

The study of Amante et al. proposes the classification of achromatic colours. This is because, depending on the values of the V and S channels, the colour can be more or less saturated. In this case, the achromatic colours are black, grey and white. For this classification, the S and V channels must be in range $[0, 1]$. If $p=(h,s,v)$is an HSV-encoded pixel, the criterion is as follows:

• If $v \leq V_1$, pixel is classified as black. Black colour is represented by index -1.

• If $v>V_2$ and $s\leq S_1$, pixel is classified as white. White colour is represented by index -2.

• If $V_1 < v \leq V_2$ and $s\leq S_1$, pixel is classified as gray. Gray colour is represented by index -3.

The thresholds that appear have been experimentally fixed by Amante et al., and they are $V_1=0.19$, $V_2=0.81$ and $S_1=0.14$.

References

Amante, José; Fonseca, Manuel J.. (2012). Fuzzy Color Space Segmentation to Identify the Same Dominant Colors as Users. Proceedings: DMS 2012 - 18th International Conference on Distributed Multimedia Systems. 48-53.