Normalised Color Distances
Andr
´
e R. S. Marc¸al
1,2 a
1
Departamento de Matem
´
atica, Faculdade de Ci
ˆ
encias da Universidade do Porto,
Rua do Campo Alegre s/n, 4169-007, Porto, Portugal
2
INESC TEC, Porto, Portugal
Keywords:
Color Distance, Color Perception, Color Normalisation, Dunn Index.
Abstract:
This paper presents normalised color distances based on widely used metrics in the RGB and L*a*b* color
models, and an adjusted City Block distance for the HSV model. Three experiments were carried out, focusing
on color perception, the identification of the actual range of the various normalised color distances, and their
ability of compare and match images which have a predominant color perceived by a human observer. For
this task, a spatially tolerant color distance is proposed. The image comparison experiment uses subsets of
6 images, out of 15 square tile images, with a total of 270 test cases considered. A modified Dunn index
is proposed for the evaluation. L*a*b* based distances were found to be better adjusted to the human color
perception. Color distances based on L*a*b* model were also more effective for image comparison, with
spatially tolerant color distances having slightly better performance than using a direct image pixel pairing.
1 INTRODUCTION
Color plays a key role in the visual interpretation and
understanding of images. The human perception of
color is however highly subjective. Our visual sys-
tem has a tendency to keep its perceptions invariant
to illumination changes (Vanrell et al., 2011). Fur-
thermore, the perception of color differences is dis-
torted by categorical boundaries (to which we asso-
ciate color names) (Hu et al., 2014). Image process-
ing and computer vision systems also make use of the
information provided by a color image, rather than
using only a gray-scale (single band) version of the
image. There are several mathematical/computational
models (or spaces) for the representation of color, but
the relation between these models and the human per-
ception of color is not straightforward. Neverthe-
less, some of these colour spaces are optimized to
correspond as best as possible to the human percep-
tion (Brychtova and Coltekin, 2015).
The process of measuring color differences must
be designed to balance between the computed and the
perceived difference (Vertan et al., 2003). A color dis-
tance provides a numeric representation of the simi-
larity (or difference) between two colors. This dis-
tance can be used in relative terms or, in some con-
texts, as an absolute measurement where a normalised
a
https://orcid.org/0000-0002-8501-0974
version is preferable. Despite the many color mod-
els and metrics available, there is not an establish
color distance that exactly matches the human per-
ception of color similarity / difference, as they rely
on a simplified model of the world that allows these
models to isolate the capabilities of the human vi-
sual system from the complexities introduced by real-
world viewing (Sharma et al., 2005). Presently, the
CIEDE2000 color-difference formula (∆E
00
) is re-
garded as the best, coinciding with subjective visual
perception (Brychtova and Coltekin, 2015). How-
ever, as a number of discontinuities occur in the
CIEDE2000 implementations (Sharma et al., 2005),
the triangular inequality is not always satisfied and
thus ∆E
00
is in fact not a metric. Simpler color dif-
ferences, such as the Euclidean distance, can thus be
popular choices for color analysis and visualization
tools (Szafir, 2018).
The objective of this paper is to present and eval-
uate normalised color distances. After this introduc-
tion, it has four additional sections: in section 2 the
color models and distances used are presented; sec-
tion 3 describes two small experiments focusing on
color perception and the actual range and distribution
of each color distance; section 4 presents an exper-
iment to evaluate the ability of the color distances to
compare images; and section 5 draws the conclusions.
134
Marçal, A.
Normalised Color Distances.
DOI: 10.5220/0011965700003497
In Proceedings of the 3rd International Conference on Image Processing and Vision Engineering (IMPROVE 2023), pages 134-141
ISBN: 978-989-758-642-2; ISSN: 2795-4943
Copyright
c
 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

2 COLOR MODELS AND COLOR
DISTANCES
A number of color models and metrics are presented
next, without aiming in any way to be a comprehen-
sive review of the topic. More details about color
models and the conversion between models can be
found in several digital image processing papers and
textbooks, such as (Gonzalez and Woods, 2008).
2.1 Color Models
For digital image processing, additive models are gen-
erally preferred when working on standard displays
(emitting light), whereas subtractive models are more
suitable when the focus is printed media. Most color
models have 3 independent variables, in line with
the 3 degrees of freedom of the human visual sys-
tem (Gonzalez and Woods, 2008).
The most widely used color model in digi-
tal image processing is probably the RGB color
model (Bratkova et al., 2009), where the 3 variables
R (Red), G (Green) and B (Blue) are the 3 primary
colors of this additive model. For digital images, the
intensity of each of these variables is quantised in a
number of discrete values. For example, a RGB 24-
bit color image has 8-bit for each color component,
allowing for a total of 2
24
number of different color to
be represented (≈ 16.7 millions).
One disadvantage of the RGB color model is that
all 3 components are responsible for both color and
intensity (brightness). There are however some mod-
els where the color component is decoupled from the
intensity, such as the HSV model, where H (Hue) and
S (Saturation) are related only to color, and V (Value)
only to intensity (Gonzalez and Woods, 2008). An-
other example is the CIELAB color space, also re-
ferred to as L*a*b* (or Lαβ) model (Reinhard and
Pouli, 2011). The variable L∗ is related to lightness,
whereas the color is represented by a∗ and b∗, which
are related to four unique colors of human vision: red,
green, blue and yellow.
2.2 Color Distances
There are several possibilities for establishing dis-
tances in the various color models, including the
Minkowsky distance or L-norm. The most basic ver-
sions are L1 (City Block or Manhattan distance) and
L2 (Euclidean distance).
Often distances are used for comparisons in a con-
text where only relative values are needed. For exam-
ple, to select the the best match to a color, out of a set
of reference colors. However, in some cases it might
be relevant to have not only the best match (the color
reference with the lowest distance), but also a numeric
value that can provide a reliable measurement of the
similarity between two colors. For this purpose, it is
preferable to use normalized color distances, where
the co-domain of the distance function is [0, 1]. The
most dissimilar colors possible will have a distance of
1, and the color distance will tend to 0 as the colors
become more and more similar.
In the RGB model, a normalised distance is de-
fined as d
RGB
: [0, 1]
3
→[0, 1]. The Euclidean distance
(d
E
RGB
) is computed by (1) and the City Block distance
(d
CB
RGB
) by (2), where R
i
, G
i
, B
i
are the color intensities
for element i (i=1,2).
d
E
RGB
=
1
√
3
q
(R
1
−R
2
)
2
+ (G
1
−G
2
)
2
+ (B
1
−B
2
)
2
(1)
d
CB
RGB
=
1
3

|R
1
−R
2
|+ |G
1
−G
2
|+ |B
1
−B
2
|

(2)
A normalised distance in the HSV model is de-
fined as d
HSV
: [0, 1]
3
→ [0, 1]. The domain is [0, 1]
for all three model components, similarly to RGB.
However, as Hue is an angular measurement, the dif-
ference in Hue |H
1
− H
2
| cannot be calculated di-
rectly (Montenegro et al., 2008), as that does not
properly account for the artificial discontinuity in Hue
imposed by the linear domain [0, 1]. For example, two
colors with H
1
= 0.01 and H
2
= 0.99 (and equal S and
V ) are almost indistinguishable reds, yet |H
1
−H
2
| =
0.98. In fact, the Hue difference (∆
Hue
) in this case
should be only 0.02 if the circular nature of the vari-
able is considered, and thus ∆
Hue
is computed by (3).
An adjusted City Block distance (d
ACB
HSV
) is proposed
for the HSV model (4). The factor of 2 for ∆
Hue
in (4)
assures that the contribution from each parcel is the
same, as the range of ∆
Hue
is [0, 0.5] instead of [0, 1].
∆
Hue
= min
n
|H
1
−H
2
|, 1 −|H
1
−H
2
|
o
(3)
d
ACB
HSV
=
1
3

2 ×∆
Hue
+ |S
1
−S
2
|+ |V
1
−V
2
|

(4)
In the L*a*b* model, the domain of the variables
a* and b* is [−1, 1], thus a normalised distance is de-
fined as d
Lab
: [0, 1] ×[−1, 1] ×[−1, 1] → [0, 1]. The
Euclidean distance in the L*a*b* model (d
E
LAB
) is
computed by (5) and the City Block distance (d
CB
LAB
)
by (6). These equations are very similar to those for
the RGB model (1, 2), except for the normalisation
coefficients that are different. One alternative often
Normalised Color Distances
135

Figure 1: Color test sequence (uniformly spaced in RGB) representation in the 3D Cartesian space for the RGB model (left),
HSV conic (centre) and L*a*b* model (right).
used in the L*a*b* color model is the Hybrid dis-
tance (Abasi et al., 2020). The normalised Hybrid
distance in L*a*b* (d
H
LAB
) is defined by (7). It is com-
puted as an Euclidean distance in the a*b* plane com-
bined with a City Block distance in what regards this
plane and L*.
d
E
Lab
=
1
3
q
(L
∗
1
−L
∗
2
)
2
+ (a
∗
1
−a
∗
2
)
2
+ (b
∗
1
−b
∗
2
)
2
(5)
d
CB
Lab
=
1
5

|L
∗
1
−L
∗
2
|+ |a
∗
1
−a
∗
2
|+ |b
∗
1
−b
∗
2
|

(6)
d
H
Lab
=
|L
∗
1
−L
∗
2
|+
p
(a
∗
1
−a
∗
2
)
2
+ (b
∗
1
−b
∗
2
)
2
1 + 2
√
2
(7)
It is worth mentioning that the actual range of the
color distances is a subset of the co-domain. Another
aspect that should be considered is that the domain
amplitude of the variables responsible for the color
information in the L*a*b* model is twice the ampli-
tude of the domain of L
∗
. So the relative contribution
of a∗ and b∗ to the color distance is potentially larger
than L
∗
, thus making L*a*b* based distances more in-
fluenced by the color component than those distances
based on the RGB and HSV models.
A normalised version of the CIEDE2000 color-
difference (∆E
00
) is used for comparison purposes,
as CIEDE2000 is considered closely aligned with the
human color perception. A normalisation factor of
125 was used (for 24-bit color images), which for
all tests carried out produced values within the [0, 1]
range.
3 INITIAL EVALUATION
The normalised color distances proposed for RGB,
HSV and L*a*b* color models were evaluated with
the aim of identifying some of their potential advan-
tages and limitations. Three experiments were de-
signed and implemented using Matlab (MathWorks,
2021). The first experiment focus on the relation be-
tween distance and color perception, and the second
one on identifying the actual range and distribution
of each color distance. The third experiment, pre-
sented in a separate section, was designed to evaluate
the ability of the color distances to compare images.
3.1 Color Perception
A sequence of uniformly spaced RGB colors was cre-
ated. The first color is black (0,0,0), with increments
of 0.1 used for only one of the R,G,B components at
a time. The distance between any two consecutive
colors in the sequence is thus constant for both Eu-
clidean and City Block metrics. For the standard def-
initions, the distance is 0.1. However, due to the nor-
malisation factors in (1) and (2), the values for nor-
malised distances are different: d
E
RGB
= 0.0577 and
d
CB
RGB
= 0.0333. The sequence of colors is presented
in the 3D Cartesian space for the RGB model in fig-
ure 1 (left). This test sequence has a total of 71 col-
ors along 7 edges of the RGB cube, including all pri-
mary (red, green, blue) and secondary colors (cyan,
magenta, yellow), as well as black and white.
In figure 1 the color sequence is also presented in
the HSV model (centre) and L*a*b* model (right).
IMPROVE 2023 - 3rd International Conference on Image Processing and Vision Engineering
136

Figure 2: Color test sequence (bottom) and plot of the normalised distances for color pairs.
The HSV representation used for figure 1 is conic, al-
though other geometries could be used, such as cylin-
drical or pyramidal (Gonzalez and Woods, 2008). It
is worth noting that the Hue (H) and Saturation (S)
components correspond to polar coordinates in the HS
plane, thus the visual perception of distances from the
figure is slightly misleading.
The color sequence presentation in the 3D Carte-
sian space for the L*a*b* model (figure 1, right) is
particularly interesting. Unlike for the HSV model,
the distances perceived in the L*a*b* 3D space di-
rectly relate to the L*a*b* Euclidean distance (d
E
LAB
).
It is clearly noticeable that some color pairs are very
close together, such as those in the green region (top
left), whereas some color pairs are much further away.
For example, in the sequence of colors form blue to
green the distance between consecutive colors is con-
siderably larger than color pairs with two types of
green. These differences in distances between con-
secutive color pairs seem to be better matched to our
perception of color similarity than the constant values
provided by the RGB based distances.
Figure 2 shows an alternative graphic presenta-
tion of the color sequence, together with a plot of
the distances between consecutive pairs. In this fig-
ure it is possible to observe each color pair (in the
bottom scale) and the corresponding normalised color
distances. The black dotted and dashed lines are the
distances computed in the RGB model, both having a
constant value throughout.
The adjusted City Block distance for the HSV
model (4) is presented in Figure 2 as an orange solid
line, with large dots. The distance for the first color
pair is very high due to a change of saturation (S) from
0 to 1. The remaining pairs have constant values along
sub-sections of the sequence, with the lowest values in
the centre of the sequence, where only the Hue com-
ponent changes.
The 3 distances based on the L*a*b* model are
presented in Figure 2 with solid lines without dots.
There are some difference between them, but not sig-
nificant. The distances are much lower for some
color pairs than for others, which seems to be well
aligned with the perceived color difference, consid-
ering the human interpretation perspective. The nor-
malised version of CIEDE2000 (∆E
00
) is also pre-
sented in Figure 2. The general behaviour of ∆E
00
is well aligned with the 3 L*a*b* distances, but with
even larger values for highly dissimilar color pairs.
3.2 Color Distances Distribution
The second experiment consists of a brief statisti-
cal evaluation of the 6 normalised distances, using
N RGB color pairs generated randomly. Initially one
million color pairs were created (N = 10
6
), with the
color distances computed used to create the boxplots
presented in Figure 3. The mean, standard deviation
and 0.1 and 99.9 percentiles (Pctl) were computed for
a larger set of random color pairs (N = 10
8
), with the
results presented in Table 1.
One first aspect that can be observed, is that the
median (Figure 3) and mean (Table 1) are lower for
the L*a*b* distances that for those based on the RGB
and HSV models. The interquartile range is also
lower for L*a*b* distances, particularly for d
CB
LAB
and
d
H
LAB
. But perhaps the most relevant issue is the fact
that the range of values actually used is far from cov-
ering the co-domain [0, 1]. This can be observed
by the whiskers in the boxplots, and by the differ-
Normalised Color Distances
137

Figure 3: Boxplots for normalised distances of one million
random color pairs.
ence between the 99.9 and 0.1 percentiles. The RGB
Euclidean distance have the largest range, and the
L*a*b* City Block and Hybrid the lowest.
Table 1: Statistic parameters for normalised distances of
10
8
random color pairs.
Pctl 0.1 Pctl 99.9 Mean St.Dev.
d
E
RGB
0.0369 0.7913 0.3835 0.1445
d
CB
RGB
0.0314 0.7804 0.3346 0.1366
d
ACB
HSV
0.0293 0.7322 0.3275 0.1304
d
CB
Lab
0.0163 0.7035 0.2511 0.1293
d
H
Lab
0.0182 0.6930 0.2650 0.1273
d
E
Lab
0.0184 0.7376 0.2795 0.1373
4 IMAGE COMPARISON
An experiment was designed to evaluate the ability
of the normalised color distances to compare images
and to identify the best image match. A total of 15 im-
ages of square tiles were used, all with 267 ×267 pix-
els and 24-bit RGB color. The images were grouped
by visual interpretation into 5 classes, based on the
predominant color present: yellow (A), red/pink (B),
blue (C), brown (D) and green (E). Figure 4 shows the
15 images with the class assignment (3 for each class)
and label. Despite the diversity of colors in some tiles
(e.g. blue and white is present in tiles A1 and A2,
both labeled as yellow), there is a predominant color
on each tile that is likely the dominant aspect used for
the class labeling made by human interpretation.
4.1 Image Similarity
The evaluation of the similarity between two images
is based on the mean normalised color distance be-
tween all image pixel pairs. However, the direct pair-
ing of pixels form two images might not be the most
suitable approach, as there might be a small geomet-
ric misalignment between the two images. It is thus
worth considering a small tolerance in what regards
the positioning of the pixel pairing. To address this
issue, a spatially tolerant color distance D
(v)
is pro-
posed, considering a neighborhood v of a pixel. It is
defined by (8), where each pixel (x, y) in image I
1
is
compared with all pixel (x
′
, y
′
) in image I
2
that are
within the neighborhood v of (x, y). The color dis-
tance D
(v)
, for a pixel (x , y), is the smallest normalised
color distance of all (x, y) - (x
′
, y
′
) pairs.
D
(v)
12
(x, y) = min
n
d

I
1
(x, y), I
2
(x
′
, y
′
)

o
with (x
′
, y
′
) ∈ v(x, y) (8)
The neighborhoods used here were: direct pairing
(v = 1), where x = x
′
∧y = y
′
; 4-neighbors (v = 4),
where |x −x
′
|+|y −y
′
|= {0, 1}; 8-neighbors (v = 8),
where x − x
′
= {−1, 0, 1}∧y − y
′
= {−1, 0, 1}. A
total of 18 color distances were thus considered: 6
normalised color distances (1-7) × 3 neighborhoods
(v = 1, v = 4 and v = 8).
4.2 Experimental Procedure
Initially a set of 6 tiles is selected from the image set
(Figure 4), with 3 classes used and 2 images from
each class selected. The color distances between all
pairs of images are then computed. For each im-
age, the shortest distance is used to establish the best
match. Ideally, each image would be matched with
the other image in the set belonging to the same class,
but that does not always happen. In fact, the best case
scenario would be to have a very low distance for a
pair of images of the same class, and large distances
when two images belong to different classes.
4.3 Evaluation Criteria
An evaluation parameter inspired by the Dunn simi-
larity index used for data clustering (Dunn, 1973) is
proposed - the Modified Dunn Index. It is based on
internal distances (for observations of the same class)
and external distances (for observations of different
classes). The Modified Dunn Index (MDI) is com-
puted by (9), where C(i) is the class of element i. MDI
is the ratio of the minimum external and maximum in-
ternal distances, which one aims at maximising.
MDI
i
=
min

d(i, j )

max

d(i, k)

with C( j) ̸= C(i) , C(k) = C(i) (9)
IMPROVE 2023 - 3rd International Conference on Image Processing and Vision Engineering
138

Figure 4: Test images (square tiles), grouped in 5 classes: yellow (A), red/pink (B), blue (C), brown (D) and green (E).
For each image in a test set, there are 4 external
distances, and only one internal distance to consider.
If MDI < 1 for an image, it means that it is mis-
matched, as there is an image from another class in
the set with a shorter distance than the other image of
its class.
4.4 Results for a Test Case
To illustrate the procedure, a test case (TC1) is pre-
sented in some detail next. The image tiles of TC1
are from classes yellow (A1, A2), red/pink (B1, B2)
and blue (C1, C2), identified in the top left corner of
Figure 4 by a gray dotted line.
Table 2: Color distances D
1
for the test case image pairs,
with Normalised RGB Euclidean distance (d
E
RGB
).
Tile B1 C1 A2 B2 C2
A1 0.267 0.395 0.240 0.228 0.386
B1 0.383 0.302 0.130 0.394
C1 0.382 0.356 0.207
A2 0.263 0.359
B2 0.354
The Color distances D
1
for each image pair are
presented in Table 2, using the normalised RGB Eu-
clidean distance (and v = 1). For image A1, the inter-
nal distance is D
1
{A1, A2}= 0.240, and the minimum
external distance is D
1
{A1, B2} = 0.228, resulting in
MDI = 0.951 (< 1). Thus, somehow surprisingly, tile
A1 is matched to tile B2 (with d
E
RGB
, v = 1), possibly
due to the fact that these tiles are slightly darker.
The MDI values for all color distances and tiles
in TC1 are presented in Table 3, for a direct pairing
of image pixels (v = 1). For most tiles, the MDI
value is high (well above 1) for all color distances
(e.g. tile B1). As it happens, the only MDI values
below 1 (class mismatch) are for tile A1 using RGB
based distances. The results clearly indicate that the
HSV and L*a*b* based distances are more effective
(higher MDI values), with the L*a*b* distances per-
forming better than d
ACB
HSV
for the harder cases (tiles A1
and A2).
Table 3: MDI values for all color distances and tiles in test
case 1, using D
(1)
(direct pixel pairing).
A1 B1 C1 A2 B2 C2
d
E
RGB
0.95 2.06 1.72 1.10 1.76 1.71
d
CB
RGB
0.92 1.86 1.43 1.08 1.59 1.43
d
ACB
HSV
1.04 3.19 2.29 1.13 3.06 2.23
d
CB
Lab
1.32 3.13 2.23 1.38 2.74 2.05
d
H
Lab
1.18 2.94 1.99 1.31 2.59 1.87
d
E
Lab
1.23 3.29 2.09 1.26 2.92 2.07
The procedure was repeated using the spatially
tolerant color distance D
(v)
with neighborhoods (v) 4
and 8. The results are presented in Table 4 (v = 4) and
Table 5 (v = 8). The results for v = 4 are better than
using a direct pixel pairing (v = 1) for all cases (tiles
and color distances). The results for v = 8 are equal
or better than for v = 4.
Normalised Color Distances
139

Table 4: MDI values for all color distances and tiles in test
case 1, using D
(4)
(neighborhood of 4).
A1 B1 C1 A2 B2 C2
d
E
RGB
1.04 2.30 1.84 1.20 2.00 1.83
d
CB
RGB
1.03 2.12 1.53 1.19 1.85 1.57
d
ACB
HSV
1.18 3.49 2.30 1.19 3.44 2.38
d
CB
Lab
1.50 3.39 2.31 1.54 3.01 2.17
d
H
Lab
1.33 3.19 2.15 1.48 2.86 2.04
d
E
Lab
1.39 3.59 2.27 1.42 3.23 2.27
Table 5: MDI values for all color distances and tiles in test
case 1, using D
(8)
(neighborhood of 8).
A1 B1 C1 A2 B2 C2
d
E
RGB
1.09 2.36 1.85 1.25 2.08 1.88
d
CB
RGB
1.08 2.20 1.59 1.25 1.93 1.63
d
ACB
HSV
1.24 3.47 2.30 1.21 3.54 2.45
d
CB
Lab
1.57 3.44 2.31 1.60 3.09 2.23
d
H
Lab
1.39 3.24 2.23 1.55 2.93 2.11
d
E
Lab
1.46 3.65 2.36 1.49 3.31 2.36
It is worth noting that using a spatially tolerant im-
age comparison, the distance between two images de-
creases as the neighborhood size increases. Thus, for
any given image pair, D
(8)
≤ D
(4)
≤ D
(1)
. However,
for TC1 the MDI values of spatially tolerant color dis-
tances are higher (Tables 3 - 5). In this case, the best
choice for pairing tiles according to their color classes
is to use a neighborhood of 8 (D
(8)
).
4.5 Global Results
A total of 270 test cases were created by grouping the
15 image tiles presented in Figure 4. This results from
10 possible class choices (combinations of 3 out of
5), with 27 tile selections possible for each class set-
ting (combinations of 2 out of 3 for each class). The
same procedure described for test case 1 was applied
to all test cases. A total of 1620 observations were
thus obtained (6 tiles ×270 test cases), for each color
distance and neighborhood.
A summary of the MDI results is presented in Ta-
ble 6, for a direct pairing of image pixels (v = 1). The
table include the minimum, mean and median MDI
values for each color distance, and the total number
of failures (image mismatches, MDI < 1). The worst
case for each distance (minimum MDI value) is bet-
ter for L*a*b* based distances, although still with a
value below 1. The number of failures is high for
RGB based distances (about 20%) and rather low for
L*a*b* based distances. The mean and median MDI
values are also better (higher) for L*a*b* distances,
with RGB based distances performing worst. The per-
formance of ∆E
00
is in line with d
CB
Lab
, d
CB
Lab
and d
CB
Lab
,
with slightly higher mean and median MDI, but also
with a larger number of failures.
Table 6: Summary of MDI results for the complete experi-
ment, with v = 1 (1620 observations).
min. mean median No. fails (%)
d
E
RGB
0.857 1.374 1.284 294 (18.1%)
d
CB
RGB
0.805 1.324 1.248 327 (20.2%)
d
ACB
HSV
0.705 1.542 1.348 174 (10.7%)
d
CB
Lab
0.942 1.602 1.510 36 (2.2%)
d
H
Lab
0.911 1.564 1.481 45 (2.8%)
d
E
Lab
0.920 1.606 1.516 72 (4.4%)
∆E
00
0.922 1.663 1.613 86 (5.3%)
A summary of the MDI results using the spatially
tolerant color distance D
(v)
is presented in Table 7 for
a neighborhood of 4, and in Table 8 for a neighbor-
hood of 8. The results are slightly better for v = 8, but
the differences are small.
Table 7: Summary of MDI results for the complete experi-
ment, with v = 4 (1620 observations).
min. mean median No. fails (%)
d
E
RGB
0.854 1.456 1.384 232 (14.3%)
d
CB
RGB
0.811 1.410 1.335 316 (19.5%)
d
ACB
HSV
0.690 1.631 1.439 183 (11.3%)
d
CB
Lab
0.957 1.716 1.624 36 (2.2%)
d
H
Lab
0.922 1.672 1.592 54 (3.3%)
d
E
Lab
0.942 1.723 1.635 68 (4.2%)
∆E
00
0.917 1.802 1.718 101 (6.2%)
Table 8: Summary of MDI results for the complete experi-
ment, with v = 8 (1620 observations).
min. mean median No. fails (%)
d
E
RGB
0.824 1.494 1.429 230 (14.2%)
d
CB
RGB
0.787 1.449 1.371 294 (18.1%)
d
ACB
HSV
0.685 1.666 1.471 183 (11.3%)
d
CB
Lab
0.967 1.765 1.700 36 (2.2%)
d
H
Lab
0.928 1.720 1.654 45 (2.8%)
d
E
Lab
0.949 1.773 1.676 77 (4.8%)
∆E
00
0.892 1.861 1.763 105 (6.5%)
The mean and median MDI values are better for
the spatially tolerant distances than using a direct
pixel pairing (v = 1), for all color distances. The MDI
of the worst case (minimum value) is little changed
for all distances, with small positive and negative vari-
ations observed. The number of failures is improved
for the RGB based distances, but only marginally
changed for the other color distances. Overall, the
best choice is the spatially tolerant D
(8)
L*a*b* City
Block color distance (d
CB
Lab
).
IMPROVE 2023 - 3rd International Conference on Image Processing and Vision Engineering
140

5 CONCLUSIONS
This paper presents 6 normalised color distances,
based on widely used metrics in the RGB and L*a*b*
color models. An adjusted City Block normalised
color distance is proposed for the HSV model. The
color distances were evaluated with 3 experiments.
The first one, focusing on color perception, clearly
indicated that the L*a*b* based distances are much
better than those based on RGB and HSV for the eval-
uation of color similarity (and difference), being more
closely aligned with the human color perception. The
differences between the L*a*b* distances themselves
were found to be negligible, in what regards the color
perception evaluation performed.
The second experiment showed that although the
normalised distances all have values between 0 and
1 potentially, in reality the range of values used is
much smaller. This is particularly noticeable for the
L*a*b* based distances. This fact is irrelevant if the
distance is used in a relative context, but it can be an
issue when the color distance is used as an absolute
measurement. A possible solution could be to remap
the distance, for example with a linear transforma-
tion mapping the 0.1 and 99.9 percentiles (Table 1) to
[0, 1]. This would result in some saturation (of 0.2%
of the elements), which could be reduced by using
more extreme percentile values (e.g. 0.01 and 99.99).
The third experiment was designed to evaluate the
ability of the color distances to compare and identify
the best image match. The test images selected have
some diversity, but they also have a predominant color
and are thus easily matched in color classes by a hu-
man observer. The goal was to verify the effectiveness
of the normalised color distances to perform the same
task. For this experiment, a spatially tolerant color
distance D
(v)
was proposed, to account for a possi-
ble geometric misalignment between two images be-
ing compared, as well as a modified Dunn index for
the evaluation of the results. The modified Dunn in-
dex was found to be an useful tool, allowing for large
number of image (and color) comparisons to be sum-
marised effectively. The spatially tolerant color dis-
tance D
(v)
was found to be slightly better than a com-
parison of images with a direct pixel by pixel pairing.
The L*a*b* based distances proved to be much better
than those based on the HSV and RGB color models
for the comparison of images, with the L*a*b* City
Block distance (d
CB
Lab
) having the best performance.
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