Automatic Perceptual Color Quantization of Dermoscopic Images

Vittoria Bruni

,Giuliana Ramella

and Domenico Vitulano

Department of SBAI, University of Rome La Sapienza, Rome, Italy

Institute for the Applications of Calculus, CNR, Rome, Italy

Keywords:

Color Quantization, Perception Laws, Visual Quality, Dermoscopy.

Abstract:

The paper presents a novel method for color quantization (CQ) of dermoscopic images. The proposed method

consists of an iterative procedure that selects image regions in a hierarchical way, according to the visual

importance of their colors. Each region provides a color for the palette which is used for quantization. The

method is automatic, image dependent and computationally not demanding. Preliminary results show that the

mean square error of quantized dermoscopic images is competitive with existing CQ approaches.

1 INTRODUCTION

Color Quantization (CQ) is the process that selects

and assigns a limited set of colors for representing

a color image with maximum ﬁdelity (Burger and

Burge, 2009). The need of performing a CQ pro-

cess frequently arises in image display (Heckbert,

1982; Weeks, 1998) and image compression (Wal-

lace, 1991; Plataniotis and Venetsanopoulos, 2000).

Moreover, CQ is considered as a prerequisite for

many image processing tasks (i.e. color segmenta-

tion, color-texture analysis, content based retrieval)

and it also has a wide range of applicative ﬁeld. In

particular, CQ plays an important role in dermoscopy

since the colors of melanin, the most important chro-

mophore in melanocytic neoplasms not visible by the

naked eye, essentially depend on its localization in

the skin (Braun et al., 2005; Korotkov and Garcia,

2012; Celebi et al., 2013). Even though CQ task is

easy, rapid and efﬁcient for a human observer (Rosch,

1978; Kuriki, 2004), CQ implementation is a very

difﬁcult task (NP-complete) (Braquelaire and Brun,

1997).

In the literature CQ has been widely studied and

several methods have been proposed. The critical

common aspect to all methods is the efﬁcient simu-

lation of the visual perception process that minimizes

the error relative to the image quality. CQ exist-

ing methods can be classiﬁed in numerous ways on

the basis of criteria taking into account different fea-

tures of the CQ method at hand (Brun and Trmeau,

2002; Celebi, 2011). According to the adopted

image processing technique, CQ based on cluster-

ing (Celebi et al., 2014), evolutionary approach (Hr-

uschka et al., 2009), histogram analysis (Ramella and

di Baja, 2013), neural network (Palomo and Dom-

nguez, 2014), perceptual laws (Beghdadi et al., 2013),

and so on, can be distinguished. Here we focus our

attention on perception-based CQ methods since we

are interested to investigate how the visual laws can

be used to guide efﬁciently the CQ processing of der-

moscopic images. Since there are several ways to

include visual perception into a CQ scheme, there

exists a large number of papers on this topic. At

least two main sub-classes of methods can be distin-

guished for the this special category: the ones based

on DCT/DWT transform, that are oriented to im-

prove JPEG standard from a perceptual point of view

(Battiato et al., 2001); and the ones based on visual

distortion, where a visual threshold-based processing

for the quantization error of quality measures is em-

ployed (Schaefer and Nolle, 2014).

In this paper, we propose to incorporate human

perception into a CQ scheme by using visibility laws

(Bruni et al., 2006) based on the measure of the con-

trast sensitivity, the luminance adaptation and the con-

trast masking according to the color variable percep-

tive context determined by the original color distribu-

tion. To this purpose we determine iteratively a hierar-

chical color regions partition according to their color

importance at perceptive level and we compute the

dominant color of the partition until a ﬁxed number

of colors is obtained. In the successive step a suitable

color mapping is performed. Our perceptual-based

method is automatic since perceptive thresholds are

automatically tuned according to the analyzed image;

323

Bruni V., Ramella G. and Vitulano D..

Automatic Perceptual Color Quantization of Dermoscopic Images.

DOI: 10.5220/0005304903230330

In Proceedings of the 10th International Conference on Computer Vision Theory and Applications (VISAPP-2015), pages 323-330

ISBN: 978-989-758-089-5

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

it can be considered as context adaptable, since the

resulting CQ is image-dependent. With regard to the

speciﬁc domain of the images (dermoscopy), the re-

sults of this preliminary study, evaluated in terms of

MSE and MAE and compared with those obtained by

other authors (Celebi et al., 2013), are encouraging.

The computational load required by the algorithm is

very moderate and comparable to the most perform-

ing color quantization methods.

The outline of the paper is the following. Section

2 gives a detailed description of the general perceptual

model. Section 3 provides a thorough description of

the main steps of the whole quantization procedure.

Experimental results and discussions are in Section 4

while concluding remarks are drawn in Section 5.

2 PERCEPTUAL MODEL

Even though the image can be composed of differ-

ent colors, human eye is able to classify and detect

its dominant colors after observing the image just for

few milliseconds. It means that the visual mecha-

nisms of the early vision (preattentive phase) are not

completely independent on those colors that mainly

characterize the observed scene (image). In the case

of dermoscopic images, the object of interest is well

deﬁned since the contextof the images is limited (usu-

ally image backgroundis the skin) and then anomalies

of the skin attract human attention at the ﬁrst glance

— some examples are shown in Fig. 1. Based on

these considerations, the problem of CQ in dermo-

scopic images can be viewed in the more general con-

text of the detection of local image anomalies. In

fact, as several neurological studies show, if on the

one hand human eye is used to recognize those re-

gions in the image with which it is very familiar; on

the other hand, it is instinctively attracted by the most

unnatural parts of the image, probably due to safety

instincts (i.e. to check if there are dangers/unnatural

components in the scene) (Monte et al., 2005; Fra-

zor and Geisler, 2006; Moorthy and Bovik, 2009).

That is why in this paper we aim at modelling the der-

moscopic image as an image with a given distortion,

namely skin mole (melanoma), and we want to detect

and characterize it by means of a hierachical detection

of those image regions that attract human attention at

the ﬁrst glance. To this aim we consider the defect

detection method in (Bruni et al., 2006; Bruni et al.,

2013) and we adapt it to the case of dermoscopic im-

ages. The main features of this model are:

• to project the analysed image into a new space that

is able to better reproduce image components in a

way that is consistent with their visual perception

at the ﬁrst glance: for example, the objects that at-

tract ﬁrst human attention are the brighter parts in

the projected image. The projection space has to

depend on the kind of image and the characteristic

of the distortion;

• to deﬁne the level of resolution that reproducesthe

perceived image information: human eye is not

sensitive to ﬁne textures in the preattentive phase;

that is why, usually textured regions are perceived

as uniform regions having constant color. The

level of resolution is used for the characterization

of a low pass ﬁlter to apply to the projected image;

• to deﬁne a detection operator whose goal is to de-

tect those regions in the projected and ﬁltered im-

age that correspond to the ones that attract more

eye attention at the ﬁrst glance. Since, the pro-

jection space is selected as the one where image

anomalies become the brighter part of the image,

a thresholding operator is used for detection and

the threshold is automatically selected by measur-

ing the local and global visual image contrast.

This general model has some nice features. It is com-

pletely automatic and does not require user’s inter-

vention in parameters setting; it is simple since it is

based on simple operations like linear ﬁltering, con-

trast evaluation and thresholding operations; it is not

computationally demanding and it is easy to imple-

ment making it useful for real time applications.

Figure 1: Eight dermoscopic images. From left to right,

top to bottom: Acl285, Nbl034, Nbl063, Nml012, Ael484,

Fel096, Nml024 and Newl012 (Argenziano et al., 2002).

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3 PERCEPTUAL COLOR

QUANTIZATION

The selection of the projection operator to apply to

the original image, as explained in the previous sec-

tion, has to take into account the class of images and

the type of application we are dealing with. This step

tries to simulate the human visual system that reacts in

the presence of different colored objects in the scene.

In the speciﬁc case of dermoscopic images we have

to consider both color perception and the presence of

skin anomalies. On the other hand, in this paper we

do not want to use too complicated models in order

to limit the computational effort of the whole proce-

dure. That is why the luminance component of the

YIQ color space (Gonzalez and Woods, 2002) has

been considered. The YIQ system takes advantage

of human color-response characteristics. In particu-

lar, it is based on the sensitiveness to changes in the

orange-blue (I) range than in the purple-green range

(Q) - therefore less bandwidth is required for Q than

for I. In addition, Y (that represents the luminance

component and preserves the 90% of the whole im-

age information (Winkler, 2005)) is the one used for

black and white television and it is a weighted average

of red, green and blue components. The weights re-

ﬂect the fact that human eye is more sensitive to green

than red, but is more sensitive to red than blue; that is

why the weights in the average are about .3, .6 and

.1 respectively for red, green and blue color compo-

nents.

Finally, since melanoma are in general of dark col-

ors with respect to the skin, and since we are inter-

ested in better distinguishing those colors that charac-

terize it for clinical purposes, the negative of Y com-

ponent has been considered. In this way, skin anoma-

lies become the brighter parts of this component. An

example is shown in Fig. 2.

Figure 2: Acl285 test image. From left to right, top to bot-

tom: Image luminance component Y; negative of the lu-

minance

Y; ﬁltered version of

Y at the optimal resolution

¯r (1

level of a db2 wavelet decomposition has been auto-

matically selected).

As mentioned above, in the preattentivephase, hu-

man eye acts as a low pass ﬁlter since it is not inter-

ested in the detection of image details in this phase.

As a result non-homogeneous colored image regions

are usually perceived at the ﬁrst glance as uniform ar-

eas. For the selection of this ”visual resolution” (and

then the order of the low pass ﬁlter to be applied to

the image), the same arguments and methods given in

(Bruni et al., 2006; Bruni et al., 2013) have been used.

The ”visual resolution” must be a good trade off be-

tween the enhancement of the degraded region and

the preservation of their geometrical shape and color

features. Perception rules are employed also for the

selection of this resolution ¯r, that is automatically se-

lected by computing the contrast between two succes-

sive low-pass ﬁltered versions of the detection space.

A moving average ﬁlter φ

of order r can be then used

to smooth the negative of the Y component, namely

Y. The rationale is that the best level of resolution ¯r

is that which measures the minimum perceivable con-

trast, i.e. 0.02 (Winkler, 2005), between two succes-

sive blurred images, i.e.

¯r = argmin

r∈N

{C(r) ≤ 0.02}. (1)

where

C(r) =

Ω

Y ∗ φ

(x, y) −

Y ∗ φ

r−1

(x, y)|

|Ω| (

Y ∗ φ

(x, y))

dxdy, (2)

is the deﬁnition of visual contrast given by Peli (Win-

kler, 2005), Ω is the image domain and |Ω| is its size.

It is worth observing that φ

is a low pass ﬁlter; hence

the numerator of the integrand function in eq. (2) is a

sort of derivative of

Y, while

Y ∗ φ

is its local mean.

Fig. 3 depicts a typical behaviour of the con-

trast curve C(r) versus the level of resolution r: it

is a decreasing function and the optimal point ¯r co-

incides with the maximum inﬂection of the curve.

The value of

r can be associated to a precise scale

level J in a pyramidal decomposition (for instance a

dyadic wavelet decomposition) by means of the equa-

tion J = ⌈log





⌉ , where H is the length of the ﬁlter

associated to the adopted wavelet (Mallat, 1998), see

(Bruni et al., 2006) for details. In our experiments the

low pass ﬁlter associated to the Daubechies wavelet

with 2 vanishing moments (Mallat, 1998) has been

adopted since it has minimum support and reasonable

regularity that are well adapted to the analysed im-

ages. Let

be the low pass ﬁltered version of

Y. As

it can be observed in Fig. 2, skin anomalies are the

brighter objects in

3.1 Selection of Dominant Colors

The objective of this section is to iteratively separate

foreground (skin anomalies) and background. The

AutomaticPerceptualColorQuantizationofDermoscopicImages

325

2 4 6 8 10 12 14 16 18 20 22

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

C(r)

Figure 3: Contrast C(r), as in eq. (2), versus the resolution

r. The arrow indicates the optimal resolution ¯r.

goal is to iteratively detect image regions according to

their visual importance (from the most to the less im-

portant in the pre-attentive vision process). The num-

ber of iterations is represented by the number of col-

ors K to be used for image quantization; K is consid-

ered as an input known value. In particular, regions of

interest in

are selected using a threshold value that

has to correspond to the point of maximum visibil-

ity of the foreground with respect to its background.

To this aim, a suitable distortion based on the image

visual contrast is deﬁned.

Let M be the mean value of

, that measures its

global background; let us deﬁne a reference image

as follows

(x, y) =



(x, y) if

(x, y) ≥ M

M otherwise;

(3)

and let T (

, T) be the clipping operator, i.e.

T (

, T)(x,y) =



(x, y) if

(x, y) ≤ T

T otherwise.

(4)

The goal is to select a suitable value for T (namely

that is able to separate

foreground (the brightest

regions) from the rest of the image. In particular,

will be the one that maximizes a visual distortion D

that depends on both local and global image contrast,

as explained in the following.

Deﬁnition 1. Let Ω

= {(x, y) ∈ Ω :

(x, y) > T}

be the set of pixels whose

value over-exceeds the

threshold value T. Let D

and D

be deﬁned as

(x, y) =

(x, y) − T (

, T)(x, y)

(x, y) =

(x, y)|M

− M|

with M

the average value of T (

, T) in Ω − Ω

then the visual distortion for the set Ω

is deﬁned as

D(Ω

) =

|Ω

∑

(x,y)∈Ω

(x, y)D

(x, y). (5)

The distortion D describes the interaction between

image background and foreground. D

(x, y) measures

the contrast variation of a changing object with re-

spect to a ﬁxed background: the contrast is measured

through the Weber’s law, the changing object is a re-

gion of

before and after clipping, while the ﬁxed

background is given by M. Hence, D

evaluates how

an object changes its perception if it is substituted for

the threshold value T. It is worth outlining that: i)

(x, y) = 0 ∀ (x, y) ∈ Ω− Ω

; ii) the value of D

Ω

is an increasing function for decreasing threshold

values (increasing |Ω

|). In particular, D

(Ω

) grows

quickly for higher thresholds since clipping involves

less uniform regions with small area; on the contrary,

the growing law changes as the threshold value de-

creases, since the clipping selects many points whose

values are closer to the background.

measures the contrast variation of the same ob-

ject of

over different backgrounds — M

is the

background of the image after the clipping operation

and it decreases toward M as T decreases. D

is the

product of two different components: the former,

is a growing function as M

decreases. The latter,

−M|

, is a decreasing function converging to zero

for smaller threshold values. Hence, D

revealsa con-

vex shape. In fact, the term

−M|

gives a minor

contribution in the ﬁrst part, since the clipping opera-

tor involves few pixels and then M

does not change

signiﬁcantly. On the contrary, in the second part M

approaches M faster, as more points close to the back-

ground are selected, and then D

approaches zero.

The visual distortion D combines D

and D

us-

ing a multiplicative model, that is the conventional

way of combining contrast based measures. Since

increases while D

decreases, the optimal sep-

aration point is the equilibrium point of the prod-

uct of the two measures. Then, the optimal detec-

tion threshold

T is the one that realizes the maximum

value of D (see Fig. 4) and provides the frontier be-

tween image foreground and background. From that

point on, pixels of the background are selected by the

clipping operator, confusing the most visual attractive

part of image with the remaining part. The most vi-

sually important region Ω

is then deﬁned as

Ω

= {(x, y) ∈ Ω :

(x, y) ≥

T}.

The mean value of the colors (in the RGB color

space) of points belonging to Ω

is considered as the

dominant color of the region and it is set to the ﬁrst

value c

of the color palette to be used in the quanti-

zation step. By excluding from the image the selected

region Ω

, the procedure can be reapplied to the re-

maining part of the image (Ω − Ω

) in order to select

a number of representative regions from which to ex-

tract the dominant colors to add to the desired color

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0 2 4 6 8 10 12 14

x 10

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

|Ω

D(Ω

)

Figure 4: Distortion curve D(Ω

) versus the size of Ω

palette. As a result, the detection algorithm is iter-

ated K times, with K the number of desired colors

in the palette. In order to adapt the algorithm to the

number of desired colors, the value M in eq. (3) is

differently deﬁned and computed at each iteration. In

fact, the detection algorithm can be less sensitive to

some details as K decreases; while it is the opposite

as K increases. That is why, the value M, that repre-

sents the image background, is deﬁned as a correction

of the average value of the image to be analysed. The

correction term is deﬁned as 1− k

−Mo|

, where k is

the k−th region we are going to select while M

and

Mo respectively are the average value and the most

frequent value of

3.2 Algorithm

1. Convert the original RGB image to the luminance

componentY.

2. Find the best level of resolution

r via eq. (1) and

compute the blurred negative of Y, i.e.

3. Compute the mean value M

and the mode Mo

and repeat the following steps K times (for

k = 1, 2, . . . , K)

• Compute the mean value of

; set M =



1− k

−Mo|



and evaluate eq. (3).

• For each integer T ∈ [M, 255], in decreasing

order, evaluate D(Ω

• Extract the optimal

T as the maximum point of

the curve (|Ω

|, D(Ω

)).

• Extract the binary mask: Ω

(x, y) =



1 if

(x, y) ≥

0 otherwise.

• Compute the average color c

of image pixels

such that Ω

(x, y) = 1 and put it in the palette.

• Set Ω = Ω − Ω

and

(Ω)

4. Assign to each pixel in the original image

the closest color in the selected color palette

, c

, . . . , c

, } and let I

the quantized image.

Figure 5: Test Image Nml012. From left to right, top to

bottom: regions Ω

, Ω

selected by the proposed

algorithm and the quantized image (K = 4).

4 EXPERIMENTAL RESULTS

The proposed method has been tested on several im-

ages extracted from different dermoscopy databases.

The results presented in this section concern eight test

images contained in the database included in (Argen-

ziano et al., 2002) in order to provide fair comparative

studies with existing methods.

Accounting for the medical interest for the charac-

terization of melanoma according to its different col-

ors, the results we are going to present in this sec-

tion concern the selection of very few colors from

the original image to be used in the deﬁnition of the

new color palette, i.e., K = 4, 6, 8, that is ﬁxed by

the user. The quantization results will be measured

in terms of Mean Square Error (MSE) between the

original and the quantized image, and also in terms of

Mean Absolute Error (MAE). The evaluation of the

results will be made by means of comparisons with

some well knownmethodsfor CQ, especially the ones

that have been used in the processing of dermoscopic

images. To this aim we have considered the work in

(Celebi et al., 2013) (WSM), since it is very recent

and provides very impressive results on dermoscopic

images. In addition, it provides several comparative

studies with existing CQ algorithms. WSM consists

of an optimization of the classical K-means clustering

procedure from both computational and faithfulness

of the results points of view. In particular, it reﬁnes

the inizialization step of the K-means algorithm and

optimizes its implementation. In addition, we com-

pare the proposed method with the Median-Cut (MC)

AutomaticPerceptualColorQuantizationofDermoscopicImages

327

Table 1: MSE and MAE (in the brackets) results on some test dermoscopic images achieved by the methods in (Heckbert,

1982; Wu, 1991; Cheng and Yang, 2001; Celebi, 2009; Celebi et al., 2013) and the proposed one for a different number K of

colors in the palette.

Method K Acl285 Nbl034 Nbl063 Nml012 Ael484 Fel096 Nml024 Newl012

4 759.1 1177.3 1610.4 1400.2 625.9 945.4 1761.6 770.5

(35.7) (47.5) (54.9) (46.3) (31.6) (41.3) (56.2) (36.8)

MC 6 639.1 939.8 892.2 520.0 524.6 787.5 1016.2 655.8

(33.2) (41.9) (41.8) (31.2) (29.7) (38.2) (43.0) (34.8)

8 526.1 761.7 791.0 418.4 379.5 762.8 960.7 528.9

(30.2) (37.5) (39.2) (27.8) (26.0) (37.6) (41.6) (31.9)

4 823.9.4 1325.0 1283.6 1331.8 684.2 1027.1 1735.5 852.7

(37.9) (50.6) (50.3) (46.6) (34.8) (43.2) (56.3) (39.9)

CY 6 433.9.9 777.6 708.1 479.9 410.9 572.3 956.7 567.5

(26.3) (37.9) (36.5) (29.6) (27.8) (31.1) (42.2) (31.0)

8 329.5.0 533.1 486.5 371.0 234.9 424.5 561.0 381.0

(22.8) (30.9) (29.7) (25.5) (19.6) (27.8) (32.8) (26.4)

4 786.7 1249.0 1086.0 922.6 598.6 1182.1 1444.3 776.1

(36.2) (48.1) (44.0) (38.1) (30.3) (44.0) (52.6) (37.2)

WU 6 477.6 779.9 751.0 458.0 295.3 540.4 825.2 477.7

(27.3) (37.1) (36.3) (27.4) (20.5) (30.4) (38.8) (28.5)

8 283.7 628.2 509.9 306.8 228.6 380.1 592.9 354.0

(22.0) (33.1) (28.6) (22.7) (17.9) (24.5) (32.4) (24.1)

4 718.8 1242.5 1085.8 1133.4 1070.9 1329.8 1443.2 1000.4

(33.5) (49.5) (44.9) (45.6) (30.6) (40.1) (53.0) (35.8)

ADU 6 406.7 648.3 674.9 466.7 685.3 491.9 789.0 409.2

(24.6) (33.6) (34.7) (28.2) (24.3) (29.4) (38.5) (26.3)

8 297.1 476.3 457.3 292.1 240.4 334.2 587.5 310.2

(21.3) 29.0) (27.3) (22.0) (16.4) (23.1) (32.9) (22.2)

4 714.6 1147.0 1062.2 789.1 522.8 884.4 1316.6 726.6

(33.0) (46.5) (43.7) (37.1) (29.1) (40.3) (50.5) (35.6)

WSM 6 359.8 637.0 726.2 412.8 256.5 436.8 763.7 393.8

(24.5) (33.6) (35.8) (26.3) (19.7) (27.1) (37.2) (26.4)

8 234.5 458.9 405.4 274.3 173.5 313.1 550.7 281.8

(19.9) (28.4) (26.8) (21.5) (15.9) (22.5) (31.6) (22.4)

4 658.4 1126.1 986.7 546.9 415.1 786.9 1613.8 711.2

(33.7) (48.9) (44.1) (31.4) (26.2) (36.2) (53.0) (35.2)

PCQ 6 319.9 640.2 623.0 349.9 253.9 420.7 765.3 508.2

(23.5) (34.2) (32.2) (24.1) (17.3) (26.4) (37.6) (26.8)

8 199.0 516.7 577.5 292.8 226.4 302.2 565.5 431.3

(18.1) (29.4) (29.5) (21.6) (15.2) (21.0) (32.3) (23.4)

(Heckbert, 1982) and its modiﬁcations in (Cheng and

Yang, 2001) CY and (Wu, 1991) WU. Similarly to

the proposed method, all of them are based on a re-

cursive optimization of color histogram but they use

different criteria and measures (respectivelyvariances

and directional distances from the mean) that do not

explicitely depend on visual perception rules. The re-

sults have also been compared with the Adaptive Dis-

tributing Units (ADU)(Celebi, 2009) that is a learn-

ing clustering algorithm. Even though some of these

methods are not recent, they perform quite well on

dermoscopic images.

Table 1 gives MSE and MAE results provided by

the selected methods and the proposed one, indicated

with PCQ (Perceptual Color Quantization), on the

same test images and for different number of desired

colors K; the best results are in bold. As it can be ob-

served, the proposed method is able to outperfom its

competitors in most cases. In particular, it is able to

greatly improve WSM results when the desired num-

ber K of colors in the palette is small, while it shows

comparable results when K increases. This is very in-

teresting as the challenge of any information coding

framework is to get better performance at very low

bit rates. It is worth noting that the proposed method

does not use any reﬁnement of both the ﬁnal and the

partial results in the deﬁnition of the color palette. As

it can be observed in Figs. 5 and 6, the quantized

image reﬂects the color content and also the nature of

the image content, giving a consistent segmentation of

skin anomalies and skin itself. Figure 5 also depicts

all the intermediate steps of the detection procedure

and shows the regions from which the dominant color

is extracted.

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Figure 6: For each selected test image: original image and

its quantized version for different number of desired colors

(from top to bottom: K = 4, 6, 8).

It is worth stressing that the proposed method is

completely automatic, since it is able to adapt to the

analysed image thanks to the consistent use of per-

ception rules in the whole procedure (from the pro-

jection space to the selection of the best threshold

for separating image background and foreground). It

is also competitive from the computational point of

view. In fact, as it is evident from the Algorithm,

the method uses simple linear operations or compar-

isons. In particular, the complexity of the method de-

pends on the number of colors K in the ﬁnal palette as

well as on the number of gray levels N

′

in the pro-

jected and ﬁltered luminance component (i.e. less

than 256). Hence, the complexity of each iteration

of the method (step 3 of the Algorithm) is O(N

′

), and

then the complexity for the selection of the colors in

the ﬁnal palette is O(KN

′

). The additional cost re-

quired by the computation of

is proportional to the

image size and does not depend on the desired num-

ber of colors K, making the method competitive even

with respect the computational point of view.

5 CONCLUSIONS

The paper has presented a new method for CQ of der-

moscopic images that is based on the use of some vi-

sual perception laws at the early stage. The goal of

the method is to detect in a hierarchical way those

regions in the image that attract human attention at

the ﬁrst glance, and to derive from each of them a

dominant color to use in the successive quantization

step. To this aim the color image is transformed in

a gray-level image at a given resolution where the

brighter parts represent the regions that attract hu-

man attention at the ﬁrst glance; then, a proper vi-

sual distortion measure is used for iteratively select-

ing adaptive thresholds that separate regions having

different visual importance. Presented results are en-

couraging since the method is completely automatic,

image dependent and requires low computing time,

resulting competitive with existing approaches. Fu-

ture research will be oriented to the extension of the

method to a wider class of images. This extension

would require the choice of a projection space that

is more consistent with the way colors are perceived

by human eye, and a ﬁner extraction of the dominant

color in each selected region.

ACKNOWLEDGEMENTS

The Authors would like to thank Prof. Celebi for hav-

ing encouraged their research in color quantization of

dermoscopic images.

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