HSV-DOMAIN ENHANCEMENT OF HIGH-CONTRAST IMAGES

Power Laws and Unsharp Masking for Bounded and Circular Signals

Alfredo Restrepo (Palacios), Stefano Marsi and Giovanni Ramponi

DEEI, University of Trieste, Via Valerio 10, Trieste, Italy

Keywords:

Tone mappings, Gamma correction, Unsharp masking, Circular processing, Color enhancement.

Abstract:

We present techniques for the ampliﬁcation of small contrast of bounded signals; one is based on gamma

correction and another is of an unsharp-masking type; the one of the unsharp-masking type is suitably modiﬁed

for its application on circular signals as well. We enhance the saturation and luminance components of high

dynamic range images on the basis of a segmentation of the image into light and dark regions.

1 INTRODUCTION

Image contrast results both from luminance contrast

and from hue contrast. By a High Contrast (HC)

image we mean an image (that typically corresponds

to a high radiance range (Debevek and Malik, 1997)

scene) with a luminance histogram having modes near

0 and 1, that correspond to very light and very dark

regions in the image; such regions usually contain

(perhaps unnoticeable) subregions at small contrast.

The relatively low dynamic range of visualization de-

vices makes it impossible to literally display HDR

images. After rendering the scene radiance to image

luminance, large radiance contrast is likely to be ob-

servable but small contrast, even though present in

the resulting image, and probably observable in the

original scene, may not be noticeable. Thus, HC im-

ages beneﬁt from small contrast ampliﬁcation that im-

proves their quality and readability.

The luminance and saturation components of an

image are normally coded in the interval [0, 1] while

the hue is circulary coded in the interval [0, 2P) (we

denote the angle pi with the letter P). Increasing maps

that ﬁx the points 0 and 1, such as the power law x

are appropriate for the modiﬁcation of the magnitudes

of luminance and saturation. In Section 2, we am-

plify luminance contrast using a variant map related

to gamma correction. One other related tool is used

for amplifying luminance contrast in Section 3 and,

in a circular version, in Section 4, for amplifying hue

contrast. The tools apply a variant map that ﬁxes lo-

cal value and has a high gain in the immediate vicin-

ity of this local value. The map respects the bounded

and (in the case of the hue) the circular natures of the

magnitudes.

A high radiance range scene is typically composed

of objects illuminated by direct and reﬂected or ﬁl-

tered light and, in some cases, radiant objects. We

consider that saturation contrast should not be ampli-

ﬁed and that the luminance component of an HC im-

age can usually be meaningfully segmented into light

and dark regions; we base a correction of luminance

and color saturation of HC images on such a segmen-

tation. For scenes where the eye of the observer is

likely to be more adapted to the dark region than to

the light region (e.g. an observer in a room with a

window at daylight), we increase the saturation of the

dark pixels using a power law and leave the usually-

unsaturated light pixels as such; this gives realism to

the resulting image; otherwise, e.g. in the case of

an outdoors scene containing shadows, we take the

reverse stance increasing the saturation of the light

pixels only (the luminance of shadowed pixels is in-

creased).

The lack of true or uniform color spaces can be

a source of confusion; e.g. RGB functions are dif-

ferent from SLM photoreceptor responses, the psy-

chophysical magnitudes of hue and saturation behave

differently from the h and s variables in hsv color

space. The Bezold-Brucke effect (Pridmore, 1999)

predicts a clustering of (perceived) hues towards yel-

low (of oranges and cetrines) and blue (of violets and

cyans) for large illumination intensities and another

towards red (of oranges and violets) and green (of

cyans and cetrines) for low illumination intensities;

in both cases, the range of perceived hue decreases.

On the other hand, it is likely that strong illumination

clusters colors near the white corner of the RGB cube

and near the black corner for low luminance. Both the

hsv and the hsl color systems use the RGB range (i.e.

Restrepo Palacios A., Marsi S. and Ramponi G.

HSV-DOMAIN ENHANCEMENT OF HIGH-CONTRAST IMAGES - Power Laws and Unsharp Masking for Bounded and Circular Signals.

DOI: 10.5220/0001781600280033

In Proceedings of the Fourth International Conference on Computer Vision Theory and Applications (VISIGRAPP 2009), page

ISBN: 978-989-8111-69-2

the max minus the min) in the numerator of the def-

initions of the saturation variable; in the denomina-

tor, the hsv has min(2midrange, 2(1-midrange)) (the

midrange is the average of max and min of RGB)

while the hsl system uses the max of RGB. Thus, a

decrease of the RGB range is likely to decrease the

saturation in both cases. But the effect for light pixels

in hsv is to decrease the saturation while increasing it

for dark pixels; the hsl system increases the saturation

values both cases.

Even though there is no consensus regarding a

formula for the conversion of radiance into lumi-

nance, there is an agreement that it should be ap-

proximately logarithmic. We map the radiance r onto

the [0, 1]-coded luminance X by means of the inter-

mediate variable Y = k.log(r) (k is a positive con-

stant), compute its min (which typically is negative)

and range (i.e. the max minus the min of Y) and put

X = (Y − min)/range. For example, consider the use

of the formula as applied to image memorial.hdr (k=1

and r was calculated as 0.3R+0.6G+0.1B), as shown

in Figure 1.

Figure 1: (logR+7.2)/13, applied to the radiance of memo-

rial.hdr.

In addition to logarithmic nonlinearities, other types

of nonlinearity have been considered for the rendering

of HDR images; in particular, those suspected to play

a role in the retina of vertebrates (Meylan et al., 2007).

(Naka and Rushton, 1966) proposed the nonlinearity

V = 0.5(1+tanh(x −x

)) (we have added the normal-

izing factor 0.5) to model the S-potential response to

ﬂashes of monochromatic light of (probably bipolar)

retinal cells, where the variable x represents the log(I)

of the intensity I. In terms of I, the nonlinearity be-

comes: V = 0.5(1 + tanh(log(

))) =

which is

closely related to the other nonlinearity they propose:

J+1

, better known in the form y =

x+x

The enhancement of contrast for the visualization

of HC images is a topic of actuality. Meylan and

Susstrunk (Meylan and Susstrunk, 2006) locally en-

hance contrast within a retinex framework by com-

puting a local luminance using a mask resulting from

the convolution of the image and a Gaussian surround

function. (Drago and Chiba, 1997) use a logarithmic

law where the base of the logaithm is made dependant

on a power law of the pixelwise (rather than local) lu-

minance.

2 ON GAMMA CORRECTION

AND CONTRAST

ENHANCEMENT

(Unsigned) luminance contrast can be large or small;

for [0, 1]-coded luminance, by small local contrast

we mean a small luminance difference, e.g. less than

0.1; by large local contrast we mean neighbor pix-

els differing in luminance by a large amount, e.g.

more than 0.3; we are concerned here with small con-

trast. We deﬁne the small contrast ampliﬁcation fac-

tor (SCA) of a tone map as the value of the deriva-

tive of the mapping evaluated at the local luminance

(which is measured using a location statistic such as

the average, the median, the midrange of the lumi-

nances in the window. A [0, 1] → [0, 1] luminance

map has different effects on small contrast at differ-

ent luminances. For the power-law technique also

known as gamma correction the luminance of each

pixel is raised to a positive power; by using an expo-

nent g larger (resp. lower) than one an image becomes

darker (resp. lighter); this effect has been exploited

in the restoration of faded prints (Restrepo and Ram-

poni, 2008); by looking at the derivative of the map-

ping it is seen that small contrast is improved where

it matters, i.e. at small luminances when g < 1 and

at large luminances when g > 1. Thus, it is conceiv-

able to use an adaptive power law approach to im-

prove the contrast of images; consider choosing an

exponent that maximizes the SCA of a power law at

the luminance of each pixel; from

dgdL

= 0 one gets

exponent g(L) = −

log(L)

. Instead of using it directly

as in l

g(l)

(which gives a constant), we compute the

corrected luminance as A

L,C

(l) = l

1+(g(L)−1)C

where l

is the original (pointwise) luminance and L and C are

the local (rather than pointwise) luminance and con-

trast, suitably computed from the data in each win-

dow. Here, we use L = 0.5l + 0.5N where N is the

median of the data, and C = 0.5R+0.5Q where R is

HSV-DOMAIN ENHANCEMENT OF HIGH-CONTRAST IMAGES - Power Laws and Unsharp Masking for Bounded

and Circular Signals

Figure 2: Plot of A

L,C

(L); for C = 0.1, 0.3, 0.5, 0.7 and 1.0

(indicated on the right). In each case, A

L,C

(L) > L if L <

and viceversa;

is a ﬁxed point for each C.

Figure 3: Result of the application of the gamma variant

technique A

L,C

(l) to image in Figure 1.

the range and Q an inner quasirange of the windowed

data (A. Restrepo and de la Vega, 1995). The maps

shown in the ﬁgure darken light pixels (those with lu-

minances above

,) and viceversa; this type of behav-

ior is apropriate since, in HC images, both dark and

light gray levels tend to cluster.

The 1D version of the technique performs as

shown in Figure 4.

Figure 4: Application of the gamma variant technique

to the column number 550 of the McGill-texture image

merry-mexico0140.tif; original signal in green and contrast-

enhanced signal in blue.

3 A TYPE OF UNSHARP

MASKING FOR BOUNDED

SIGNALS

A more direct approach to contrast enhancement

along the lines of the technique of variant gamma cor-

rection described in the previous section is as follows;

unlike more standard techniques for contrast enhance-

ment, it explicitly takes into account that the magni-

tude being processed is bounded. Consider a fam-

ily of increasing maps f

: [0,1] → [0,1] with f(0)=0,

f(1)=1. Then, for each pixel luminance l, depending

on the local luminance L, one of the maps in the fam-

ily of tone maps is applied, and the corrected lumi-

nance f

(l) results. The chosen map f

(l) is such

that it has a large slope for pixel luminances l near

the local luminance L; in this way, small contrast is

ampliﬁed. Each map f

: [0,1] → [0,1] in the fam-

ily is a continuous function and moreover f

(L) = L,

so that it ﬁxes local luminance; also, it has a convex

derivative f

and f

(l) has a maximum at l = L, in-

creasing small contrast for luminances l near the lo-

cal luminance L. The requirement that the functions

be strictly increasing ensures that luminances (even

those far off the local luminance) do not cluster near

0, 1 or any other intermediate level. The methodology

can be catalogued as one of unsharp masking, even if

of a special type, speciﬁcally designed to be applied

to signals that live in the interval [0, 1].

In particular, consider the following family of

functions

(l) = l + h

(

l − L

), l ∈ [0,L] (1)

(l) = l + h

(

l − L

1 − L

), l ∈ [L,1] (2)

where the functions h

1,2

and are given by

(x) =

−c

MAX

(−x)

(1 + x), x ∈ [−1,0] (3)

(x) =

MAX

1 − l

(x)

(1 − x), x ∈ [0,1] (4)

the functions h have inﬁnite slope at x=0 (a re-

lated but independent approach has been used in

(Velde, 1999)); the positive integer n controls the be-

haviour near the point of inﬁnite slope, for our pur-

poses, n=1 is enough; the constant MAX is given by

2n+1

(

2n+1

)

and c ∈ [0, 1] is a constant that can be

used for tuning the desired amount of masking.

The technique is of the unsharp masking type

whenever the computation of the local luminance l

involves an operation of the smoothing type, as it is

usually the case (location estimators are usually con-

sidered as smoothers even though this is discussable).

VISAPP 2009 - International Conference on Computer Vision Theory and Applications

Figure 5: c=0.5, n=5, l=0.6.

Figure 6: The image in Figure 1, after the application of

bounded unsharp masking; c=0.3, n=1.

Figure 7: Application of the unsharp masking technique

to the column number 550 of the McGill-texture image

merry-mexico0140.tif; original signal in green and contrast-

enhanced signal in blue.

The difference between the signal and the smoothed

version is ampliﬁed accordingly. Figure 6 shows an

example of the application of the technique to the im-

age in Figure 1.

4 UNSHARP MASKING FOR

CIRCULAR SIGNALS

The angular hue variable h of the hsv color system

measures 0 degrees for RGB = 100, 120 degrees for

RGB = 010 and 240 degrees for and RGB = 001;

nevertheless, for better uniformity, yellow not being

a binary color (it is possible to talk of unique yel-

low,) the perceptual difference between red and yel-

low and that between yellow and green, are the same

as those between green and blue, and blue and red.

Thus, we transform the hue variable h of the hsv

and hsl systems to a modiﬁed hue H, also circular,

as follows. For angles h between 0 and (2/3)P, put

H=(3/2)h while for angles h between (2/3)P and 2P,

put H=(3/4)h + (1/4)2P. It is also convenient to de-

note each angle x with the complex number e

, where

j2P

represent the basic hues red,

yellow, green and blue, respectively, and where the

binary hues are correspondingly in between, e.g. the

oranges are of the form e

with 0 < w <

For the enhancing of hue contrast, the hue H of

each pixel is mapped to a hue m

(H); the function m

depends on the local hue t, which is computed using

e.g. the circular average or a circular median, (when

they exist, see (Mardia and Jupp, 2000) and (Restrepo

et al., 2007)) of the hues in the window. Here, we

use the circular mean. The map m

(H) has inﬁnite

“slope” at the local hue t; in this way, the variations

of hue near the local hue are ampliﬁed. m

is deﬁned

on the basis of a continuous, increasing function f :

[0,2P] → [0, 2P] with f (0) = 0, f (2P) = 2P, f (P) = P

such that the derivative of f is maximal at P. with

inﬁnite slope at P given by

f (x) = x − cx(P − x)

, x ∈ [0,P] (5)

f (x) = x + c(2P − x)(x − P)

, x ∈ [P,2P] (6)

where the constant c ensures that f’ is positive every-

where.

Figure 8: n=1, c=.3; consider the rectangle [0, 2P]×[0, 2P]

as a torus split along a meridian and a longitude.

HSV-DOMAIN ENHANCEMENT OF HIGH-CONTRAST IMAGES - Power Laws and Unsharp Masking for Bounded

and Circular Signals

Figure 9: Image of a faded tapestry.

Figure 10: Chroma processing of the image in Figure 9;

saturation processing with g = 0.7 and hue processing with

c=0.3, n=1.

Now, for each t, let m

: S

→ S

{

z ∈ C :

= 1

}

is the unit circle) be the function

given by m

(H) = −e

j f (∠

−e

)

where ∠z stands

for the angle of the complex number z. This effec-

tively implements a circular map,whose graph lives

on the torus S

× S

, that has inﬁnite derivative at

t. It ﬁxes local hue: m

(t) = t and has a convex

derivative m

; m

(H) is maximal at H = t, and min-

imal and smaller than one, at the opposed hue. As

in the previous section, the methodology presented is

of the unsharp masking type, circular in this case; the

technique compares well with that in (Restrepo et al.,

2008).

5 POWER-LAW LUMINANCE

AND SATURATION

ENHANCEMENT OF HC

IMAGES

Consider the enhancement of the HC image shown in

Figure 11.

Since it can be argued that the corrections needed

depend on the level of radiance coming from each

part in the 3D scene, rather than making corrections

to the image on the basis of pointwise luminance, we

Figure 11: An image of high contrast, resulting from a high

dynamic radiance scene.

Figure 12: The image is segmented into light and dark re-

gions.

Figure 13: The image in Figure 11, after adaptive saturation

and value enhancement.

segment the image using a standard region-growing

routine (Kroon, 2008) into light and dark regions and

apply a correction that depends on the region. See

Figure 12.

We use power laws on the saturation and value

components of the image. For saturation enhance-

ment, we used the exponents 0.95 (a slight adjust-

ment) and 0.7 for the clear and dark regions, respec-

tively. For the luminance component V, we applied

no correction in the light region and the exponent 0.5

in the dark regions. See the result in Figure 13. There

seems to be no reason to decrease the saturation at any

part of the image.

6 CONCLUSIONS

It is of value to have tools for increasing the con-

trast of signals with bounded range such as luminance

and saturation signals, and of signals with a circular

range such as hue and phase signals. The presented

VISAPP 2009 - International Conference on Computer Vision Theory and Applications

tools leave room for the choice of the location (lumi-

nance) and dispersion (contrast) estimators involved;

likewise, several parameters are tuned here in an ad

hoc fashion. For aesthetic reasons it may be conve-

nient to let an experienced user choose the parame-

ters; nevertheless, for the processing of large image

databases, it is convenient to use heuristics that auto-

matically determine the values of the parameters. We

are preparing a set of guidelines for automatic param-

eter selection but this is not a clear cut subject. In

(Restrepo and Ramponi, 2008) gamma is chosen so

that the correlation coefﬁcient between luminance and

contrast is minimized. Regarding unsharp masking, if

both the V and the H components are sharpened the

image may become too crispy. The readability of an

HC image is usually improved manipulating the lu-

minance of the image; this nevertheless usually also

leads to a loss of depth (in the perceived 3D scene): a

compromise must be made.

Many continuous magnitudes in the physical

world are unbounded and linearly ordered and are

typically modeled on the real line or on the positive

real line. Transducers give bounded electrical read-

ings normally using a saturating nonlinearity. Both

bounded and circular magnitudes play an important

roles in image processing.

It is usually a fruitful strategy to simulate the

known mechanisms present in biological vision sys-

tems for their implementation in cameras and in im-

age processing software; nevertheless, it must not be

forgotten that, when seen, the image will again, in

some sense, be processed by the Human Visual Sys-

tem and there is a risk of overdoing things.

ACKNOWLEDGEMENTS

This work was partially supported by the FIRB

project no. RBNE039LLC and by a grant of the Uni-

versity of Trieste. The Ancient tapestry of Figure 9

belongs to the Museo Civico Sartorium of Trieste.

A. Restrepo is on leave of absence from the dpt. de

Ing. Electrica y Electronica, Universidad de los An-

des, Bogota, Colombia, (arestrep@uniandes.edu.co).

REFERENCES

A. Restrepo, A. Naranjo, M. V. M. D. and de la Vega, R.

(1995). Designing osed’s (order statistic edge detec-

tors). Proc. IEEE ICIP 1995, II:173–176.

Debevek, P. and Malik, J. (1997). Recovering high dy-

namic range radiance maps from photographs. SIG-

GRAPH’97, pages 369–378.

Drago, F., M. K. A. T. and Chiba, N. (1997). Adaptive log-

arithmic mapping for displaying high contrast scenes.

EUROGRAPHICS 2003, 22(3):419–427.

Kroon, D. (2008). http://www.mathworks.com/ matlabcen-

tral/ﬁleexchange/.

Mardia, K. and Jupp, P. (2000). Directional Statistics. Wi-

ley, Chichester.

Meylan, L., Alleysson, D., and Susstrunk, S. (2007).

Model of retinal local adaptation for the tone map-

ping of color ﬁlter array images. J. Opt. Soc. Am. A,

24(9):2807–2816.

Meylan, L. and Susstrunk, S. (2006). High dynamic range

image rendering with a retinex-based adaptive ﬁlter.

IEEE trans. on Image Processing, 15(9):2820–2830.

Naka, K. and Rushton, W. (1966). S-potentials from colour

units in the retina of ﬁsh (cyprinidae). J. Physiol,

185:536–555.

Pridmore, R. W. (1999). Bezold-brucke hue-shift as func-

tions of luminance level, luminance ratio, interstim-

ulus interval and adapting white for aperture and ob-

jects colors. Vision Research, 39:3873–3891.

Restrepo, A., Marsi, S., and Ramponi, G. (2008). Chro-

matic enhancement for virtual restoration of art works.

EVA 08, Florence, April 2008, V. Cappellini and J.

Hemsley, eds.(Pitagora, Bologna):94–99.

Restrepo, A. and Ramponi, G. (”2008”). Word de-

scriptors of image quality based on local dispersion-

versus-location distributions. EUSIPCO 08, Lau-

sanne, Switzerland, August 25-29, 2008.

Restrepo, A., Rodriguez, C., and Vejarano, C. (2007). Cir-

cular processing of the hue variable: a particular trait

of image processing. Procs. VISSAP -Second Int.

Conf. on Computer Vision Theory and Applications,

Barcelona, March, 2007, 1(1):1.

Velde, K. (1999). Multi-scale color image enhancement.

IEEE Int. Conf. on Image Processing, 3:584–587.

HSV-DOMAIN ENHANCEMENT OF HIGH-CONTRAST IMAGES - Power Laws and Unsharp Masking for Bounded

and Circular Signals