Saturation.vs.Intensity Distributions of Quality Color Images

Saturation.vs.Intensity Distributions of Quality Color Images

SATURATION VS. INTENSITY DISTRIBUTIONS OF QUALITY COLOR IMAGES
Alfredo Restrepo (Palacios)
Laboratorio de Senales, Dpt. Ing. Eléctrica y Eectrónica, Universidad de los Andes
A.A. 4976, Bogota, Colombia
[email protected]
ABSTRACT
No-reference image quality assessment is an image characterization task of sorts. We explore the chromatic characterization of color images and relate it to image quality.
Poor image quality is usually related to a loss of contrast;
contrast is measured along the color dimensions of luminance, saturation and hue (which is a circular variable). The
distribution of saturation as a function of luminance, both
at the local and at the global level, is an informative type
of measurement. Likewise, location-distribution plots give
interesting image characterization tools for each of the dimensions of hue, saturation and luminance.
1. INTRODUCTION
Other than fidelity (as in full-reference quality assessment),
two main aspects of image quality are readability and aesthetics. Readability refers to the easiness with which a human observer interprets an image while aesthetics is an even
more subjective, although important aspect. Image characteristics that determine readability are the luminance, hue
and saturation contrasts. Image cahracteristics that modify
the aesthetics of the image are hue balance, hue shifts, variety along the dimensions of hue, saturation and luminance,
and also the distribution of dispersion as a function of location for each of the these components of color.
For natural images, the illumination of the scene is a determinant of the aesthetics of the resulting image as well,
and it is conceivable to estimate the quality of the illumination in the scene with the image data (e.g. with local and
global white balance measurements). High dynamic-range
images result from scenes with strong shadows or with several, different sources of light. Colorfulness is higher under
direct light conditions than under diffuse illumination (e.g.
overcast skies.) Indeed, hue is a more invariant color component than saturation; nevertheless, changes in the spectral contents of the illuminant (e.g. from daylight to incandescent tungsten light, which is less blue and therefore yellower,) change the metameric equivalences of the colors of
objects in a scene, photo or painting. Likewise, the resulting color of human skin is an important determinant of the
quality of a color image.
Full-reference, image-quality measurement, a fidelity issue, is usually not a choice in the case of images of antique
documents, where a well-preserved original is not likely to
exist any more [3]. In fact, we focus on qality measures
that result from the image itself. In this context, the idea of
image quality assessment is related to that of image characterization.
Color, the Eye and the Camera. For natural images,
fidelity is a difficult issue if the ”original” is ”the scene as
a human oberver saw it.” The human eye has three main
modes of vision, regarding the level of the intensity of the
illumination of the scene being watched. For very low illumination intensities, only the rods respond and we have scotopic vision (below 0.034 cd/m2 , with at maximal absortion
at 507 nm and pretty much insensitive to large wavelengths,
near 700 nm (spectral oranges)), which is achromatic and
rather peripheric, making the issue of fidelity a tricky one
in the case of scotopic vision. For higher levels of illumination, also the cones respond and we have mesotopic vision, with a strong perceived component of bluish colors.
At still more intense illuminations, (above 3.4 cd/m2 ,) the
rods saturate and do not respond any more, only the cones
do (cone pigments having peak absortions at 445 nm (S),
535 nm (M) and 575 nm (L); an overall maximun sensitivity
at 555 nm (a spectral yellow)) results and we have photopic
vision, trichromatic and foveated. By using sensors with
different sensitivities and different exposure times, cameras
may overcome the limitations of the eye at low-level illumination. For the visualization of the image we have color
prints (glossy or matte) and luminous screens. As Hunt hass
remarked ”Many color pictures depict brightly-lit outdoor
scenes and are viewed at lower levels of illumination” [5].
Poor image quality is usually related to a loss of luminance, of contrast and of saturation. Many pigments fade
away in time and the optics of cameras and projectors may
defocus image regions. As Hunt remarks, there is the ”...
unavoidable tendency of all processes to produce losses in
colourfulness.
Along the dimensions hue, saturation and luminance,
the image can be characterized at the local (intermediate
betwee pixel and global) level in terms of the corresponding
distributions of dispersion versus location; for this, we use
midrange-range plots [7]. The distrubution of saturation as
a function of luminance is considered at a local level, using
four color spaces (three well-known spaces, plus a new one)
of the type hue-saturation-luminance. Also, the distribution
of saturation as a function of luminance is considered at the
pixel level, using the range and midrange of the triple (R, G,
B), for four types of chromaticity: red-yellow (ry=oranges),
yellow-green (yg=cetrines), green-blue (gb=cyans) and bluered (br=purples). Likewise, we compute (crude) circular
hue histograms on the basis of these four chromaticity bins,
that characterize the image as having either a limited chromaticity distribution or a balanced one, at the global level.
We concentrate on quality estimators that involve chromatic aspects; luminance aspects have been considered for
example in [7], in the context of virtual antique document
restoration.
3. SPACES OF THE TYPE
HUE-SATURATION-LUMINANCE
In the RGB cube, call the origin (0, 0, 0) pure black, the
point (1, 1, 1) pure white, the line segment between them
the achromatic segment Φ and the plane through the origin orthogonal to Φ, the chromatic plane Π. Call the faces
of the cube with points for which min(R, G, B) = 0, the
dark corner of the cube, and those for which max(R, G,
B) = 1, the light corner. Call the polygon formed by the
edges of the cube of points (R, G, B) with min(R, G, B)=0
and max(R, G, B)=1, the chromatic hexagon, see Figure
2; finally, call each of the triangles that have Φ as one its
sides and a point on the chromatic hexagon as one of its
vertices, a (constant-) hue triangle or a chromatic triangle;
see Figure 2. Geometrically, the luminance component is a
measure of the distance of the RGB color point from pure
black, the saturation is a measure of the distance from the
point to Φ and the hue is a measure of the angle that the
projection of the point on Π makes with the projection of
pure red. Color points on Φ (called achromatic colors) have
an undefined hue and the colors on each chromatic triangle have the same hue. As in the local case, we denote
2. ON CONTRAST IN
HUE-SATURATION-LUMINANCE SPACES
The contrast contents of an image is an indicator of image
quality, mainly in the readability aspect. We are sensitive
to contrast in the three dimensions of hue, saturation and
luminance, and the phenomenom of simultaneous contrast
induction can be observed for each of the three cases. In
the hue variable, a colored region induces its complementary color (the one that under additive color combination
produces an achromatic gray) on the immediate surrounds.
Likewise, we have Mach bands for the component of saturation; see Figure 1.
Fig. 1. Mach bands of saturation. Half left parts of squares
have hsv hsi and hsl coordinates at 0.3, 0.8, 0.7, and (right)
runge’s r, θ, φ = 0.2, 0.3(2π), 0.7; half right parts have 0.3,
0.3, 0.7 and runge’s 0.4, 0.3(2π), 0.7.
We measure image contrast at the local level, with a
moving window, by computing the range (i.e. max−min is
denoted ρ) for the cases of luminance and saturation. (The
midrange (max + min)/2 is denoted µ).)
Fig. 2. A labeling {0, 1, 2, 3, 4, 5} of the regions of the cube,
depending on the possible orderings of the triple R, G, B amd the
corresponding partition of the RGB cube.
the range max(R, G, B) − min(R, G, B) as ρ, which is
an unnormalized measure of saturation [4]. The midrange
max(R,G,B)+min(R,G,B)
is the luminance component of the
2
HSV color space; see Figure 3. For the color space HSI, the
projection of the color point C = [R, G, B] on the line Φ is
given by [I, I, I], where I = R+G+B
. Writting the projec3
√
3a
tion of C on Π as [a, b, −(a+b)], we have α = 2√a2 +b
2 +ab
and H = arcos(α), if G ≥ B, and H = −arcos(α)
if G ≤ B. The saturation comonent S is given by S :=
1 − min(R,G,B)
= µ2 −min
. For a given hue H, the possible
I
6I
values of the pair (S, I) are bouded above by a segment of
I0
hyperbola {(S, I) : I = I0 +(1−I
, S ∈ [0, 1]}, where
0 )S
0
I0 = 1+med
, where med0 = median(R0 , G0 , B 0 ) and
3
0
0
0
(R , G , B ) is the point on the chromatic hexagon that is the
vertex of the chromatic triangle that contains the point. HSI
Fig. 3. At left, schematic min, median, max, range and cuasirange. At right, the caped cylinder of image HSI space.
image space is thus not a ”complete cylinder”; see Figure 3
and [6]. For the space HSV, we denote its components as h,
ρ
min
= max
.
s, max. The saturation is given by s = 1 − max
The luminance component is given by the max. As in the
case of the HSL system, the hue component h is of the form
±ρ1
n
1
h = ±ρ
6ρ + 3 , n ∈ {0, 1, 2} so that 6h = ρ + 2n and in
fact, we can make the correspondence 2n + sign(±ρ1 ) and
the codes {−1, 0, 1, 2, 3, 4} for the permutations, as mentioned above; see Figure 2. In [6], it is proposed a spherical
space θ, κ, λ, named after Otto Runge; the space is obtained
by shifting the cube in ambient space so that the central
point (intermediate gray) ends up at the origin, and contracting the cube to a ball of radius 1/2. The color attributes
that are made explicit by using spherical coordinates on the
resulting Runge ball are those of hue θ, grayness γ (and
colorfulness κ = 1 − γ) and lightness λ; they are defined
on the basis of spherical coordinates (r, θ, φ) on the resulting sphere, as γ = 1 − 2r ∈ [0, 1] which measures distance
from intermediate gray (colorfulness measures that from the
surface boundary of the ball,) hue θ ∈ [0, 2π), λ = π−φ
π
∈ [0, 1] is a measure of the distance from pure black. In
the image space, where the achromatic axis points vertically
upwards.
4. CHARACTERIZATION
LUMINANCE-SATURATION
The distribution of the saturation component along the luminance dimension is an important way of characterizing a
color image. In addition to one such local characterization,
we consider a pointwise one as well.
4.1. Pixelwise Saturation vs Luminance Distribution
For each pixel out of 3 pixels by column and by row, for
the images in Figure 5 we compute the range and midrange
of the triple (R, G, B), which are measures of pixel color
saturation and pixel luminance, respectively, and plot the
range as a function of the midrange.
TABLE 1. Pointwise Sat.vs.Lum, by region and by
chromaticity type
(Gabriela)
C
D
c
L
(Gabriela)
total
0
0.5365
0.1845
0.2790
oranges
0
0.4530
0.1564
0.3906
0
0.8941
0
0.1059
cetrines
cyans
0
0.9554
0.0213
0.0233
purples
0
0.4415
0.3459
0.2126
(Grotta)
total
0
0.4067
0.4991
0.0939
0
0.1365
0.7410
0.1221
oranges
purples
0
0.8967
0.1192
0.0111
(Ababoles)
total
0.0474 0.6827
0.1903
0.0796
0.2259
0.0826
oranges 0.1088 0.5827
cetrines 0.0180 0.7348
0.1748
0.0723
0
0.6074
0.0828
0.3098
cyans
purples
0
0.2295
0.0656
0.7049
(Venezia2)
total
0.1272 0.5550
0.2067
0.1110
oranges 0.1283 0.5515
0.2084
0.1118
cetrines
0
0.8571
0.0476
0.0952
cyans
0
1
0
0
purples
0
1
0
0
(Mercado1)
total
0.0208 0.6269
0.1610
0.1913
oranges 0.0438 0.6308
0.2099
0.1154
cetrines
0
0.7321
0.1570
0.1109
cyans
0
0.4906
0.0458
0.4636
purples
0
0.3442
0.0658
0.5885
(Mercado2)
total
0.0119 0.8211
0.0721
0.0950
oranges 0.0340 0.7449
0.1069
0.1142
cetrines
0
0.9311
0.0434
0.0255
cyans
0
0.5167
0.0597
0.4236
purples
0
0.8161
0.0865
0.0964
(Venezia1)
total
0
0.4008
0.0865
0.5126
oranges
0
0.3842
0.0741
0.5416
cetrines
0
0.6532
0.0270
0.3198
cyans
0
0.3859
0.1136
0.5005
purples
0
0.3487
0.0120
0.6393
(Window)
total
0.0017 0.8679
0.0186
0.1117
oranges 0.0022 0.9565
0.0213
0.0201
cetrines
0
0.8534
0.0207
0.1259
cyans
0
0.7698
0.0226
0.2075
purples
0
0.4575
0.0036
0.5389
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We plot the results globally and also discriminating according to chromaticity, observe the µ-ρ triangles for oranges
2π
(added over 0 ≤ θ ≤ 2π
6 ), cetrines (added over 6 ≤ θ ≤
2π
2π
4π
3 ), cyans (added over 3 ≤ θ ≤ 3 ), purples(added over
4π
3 ≤ θ ≤ π). See Figure 5, where a set of 8 test images is
presented,7 where the global distributions are plotted and 7
where the distributions are discriminated by chromaticity.
Each chromatic triangle of the RGB cube maps in a bijective fashion to the µ − ρ triangle. Points on the chromatic hexagon get mapped to (µ, ρ) = (0.5, 1). The achromatic line is mapped to the base of the triangle. Points
on the faces of the dark (resp. light) corner get mapped
to the left (resp. right) edge of the triangle. The µ − ρ
triangle is subdivided as shown in Fig 4, into four subtriangles, called Highly Chromatic (labeled C), Moderately
Chromatic (labeled c), Light (labeled L) and Dark (Labeled
D). The points on each subtriangle are added up and the results are shown in Table 1. The labels of the regions are
ordered according to their resulting relative weights and a
code (a ”Word Descriptor”) results; see the last column of
Table 1.
Fig. 5. Set of images considered: Mercado1, Venezia1, Mercado2, Ababoles, Grotta, Gabriela (photo by Nary Kim), Venezia2
and Window
5. HUE BALANCE
Fig. 4. With reference to the RGB cube, the µ − ρ triangle can be
read as indicated
4.2. Local Saturation.vs.Luminance Distributions
Above the pixel level and below the global level, we have
the local level. For each of the 4 color spaces HSL, HSI,
HSV and RUNGE, and considering partially overlapping
windows of size 5 × 5, we compute scatter plots of local
saturation versus local luminance; see Figure 8. For sun-lit
images, it is typical to have an overall decrement of saturation with luminance. The plots for the HSI space should
be read with care since the the pair (luminance, saturation)
lives in a subset of the square [0, 1]2 , depending on the hue
value. Likewise, the grayness component of RUNGE space
is, broadly speaking, the opposite of saturation.
Even though there are very pleasing images that are nearly
monochromatic, we consider that variety in hue contents is
a useful indicator of color image quality. Thus, from the circular histogram of hue with 4 bins, we compute an index of
uniformity. For a uniform histogram, each bin has a value
of 0.25; on this basis, we define measures of nonuniformity
ν (which has a maximum of 1.5) and uniformity of the histogram. See Tables 2 and 3. The nonuniformity is given by
ν = |ry − 0.25| + |yg − 0.25| + |gb − 0.25| + |br − 0.25|
while the uniformity is given by 1.5−ν
1.5
TABLE 2. Chromaticity Percentages
chr. sector →
ry
yg
gb
mercado1
0.4733 0.3230 0.1298
mercado2
0.3449
0.4370 0.0717
venezia1
0.3998 0.0487 0.4824
venezia2
0.9918 0.0013 0.0000
grotta
0.3622
0
0
ababoles
0.3261 0.6619 0.0095
gabriela
0.5269 0.0179 0.0902
window
0.8018 0.0485 0.0178
br
0.0626
0.1360
0.0518
0.0000
0.2154
0.0018
0.3205
0.0371
Fig. 6. Pixelwise distribution of saturation (measured as the
range of (R,G,B)) as a function of luminance (measured as the
midrange of (R,G,B)) for the images Mercado1, Venezia1, Mercado2, Ababoles, Grotta, Gabriela, Venezia2 and Window.
Fig. 7. Pixelwise luminance-saturation distributions, discrimiTABLE 3. Uniformity
histogram uniformity
mercado1
0.5973
mercado2
0.6172
venezia1
0.4789
venezia2
0.0064
0.3538
grotta
ababoles
0.3489
gabriela
0.5072
window
0.2011
ν
0.6040
0.5742
0.7817
1.4903
0.9643
0.9766
0.7393
1.1984
6. LOCATION-DISPERSION DISTRIBUTION OF
HUE
Here we consider the local variation (circular dispersion) of
hue as a function of lcal hue. The local hue is measured
with the circular mean while the local dispersion is measured with a circular range by measuring first the circle gap
and then the circular range is given by 2π − gap; for more
details, see [1]. See Figure 9.
nated by chromaticity, as: oranges (ry, at left), cetrines (yg), cyans
(gb), purples (br, at right); images Mercado1 (top), Venezia1, Mercado2, Ababoles, Grotta, Gabriela, Venezia2 and Window (bottom).
7. FINAL REMARKS
The color reproduction of natural scenes is a complex theme
and, in practice, the aesthetics of the image usually takes
precedence over the fidelity. Different types of vision, depending on the intensity of the illumination make the issue
more difficult. Conceivably, scotopic scenes can be reproduced with black and white projections in darkened rooms.
Image quality as the result of image characterization, is
a rich subject. Different requirements determine the quality of an image, depending on the subject of the image and
on the field of application. From the data presented, calling
the region of oranges, warm; that of cetrines, sour, that of
cyans, cool and that of purples, sweet, we characterize image Mercado 1 as warm and chromatically balanced, Mercado 2 as quite balanced, chromatically. Venezia1 is warm
and cool, moderately saturated and rather balanced, chro-
Fig. 8. Local Distributions of Saturation versus Luminance: HSL
(left), HSI, HSV and, Grayness versus Lightness of RUNGE space
(right).Images: Mercado1 (top), Venezia1, Mercado2, Ababoles,
Grotta, Gabriela and Venezia2 (bottom)
matically. Venezia2 is warm, very monochromatic and has
a low hue contrast. Grotta is warm, has an atypical distribution of saturation versus luminance, is unsaturated, it is
very monochromatic and has a low hue contrast. Ababoles
is sour, very monochromatic and has a low hue contrast.
Gabriela is warm and sweet, moderately saturated and rather
chromatically balanced. Window is warm, very dark, unsaturated but has a large hue contrast.
Due to lack of space we do not explore the µ − ρ distribution of the saturation component; that is the subject of a
forthcoming paper. That of luminance has been explored in
[7].
8. REFERENCES
[1] Alfredo Restrepo, Carlos Rodriguez and Camilo Vejarano, “Circular processing of the hue variable,” VISAPP 2007, Barcelona, V.1, pp. 69-76, 2007.
[2] Alfredo Restrepo, Stefano Marsi and Giovanni Ramponi, “HSV-Domain enhancement of high contrast images,” VISAPP09, Lisbon, Portugal, 2009.
[3] Filippo Stanco, Alfredo Restrepo and Giovanni Ramponi, “Virtual Restoration of Antique Books and Photographs,” CRC, 20010.
Fig. 9. Location-dispersion plots corresponding to the hue component; window = 5×5. Images: Mercado1 (top-left), Venezia1,
Mercado2, Ababoles, Grotta, Gabriela, Venezia2 and Window
(bottom-right). The horizontal hue axis should be interpreted as
circular. (The plot exists on a cylinder.)
[4] A. Hanbury and J. Serra, “A 3D-polar coordinate colour
representation suitable for image analysis,” Technical
report PRIP-TR-77, TU, Wien, 2002.
[5] R.W.G. Hunt, “The Reproduction of Color,” Wiley (fifth
ed), 2004.
[6] Alfredo Restrepo and Luisa Junco, “On color modification in hue-saturation-luminance spaces (submitted),”
VISAPP 2010, Angers, France, 20010.
[7] Alfredo Restrepo and Giovanni Ramponi, “Word
descriptors of image quality based on local dispersion.vs.location distributions,” EUSIPCO 08, Lausanne, Switzerland, 2008.