SMQT-based Tone Mapping Operators for High Dynamic Range Images

Mikael Nilsson

Centre of Mathematical Sciences, Lund University, Lund, Sweden

Keywords:

Tone Mapping Operation, High Dynamic Range, Successive Mean Quantization Transform, Processing Speed.

Abstract:

In this paper, tone mapping operations based on the nonlinear Successive Mean Quantization Transform

(SMQT) are proposed in order to convert high dynamic range images to low dynamic range images. A SMQT-

based tone mapping applied on the luminance channel is derived as well as a SMQT-based method working

directly on all RGB channels. Both methods are compared to other state-of-the-art methods and produce visu-

ally similar results. The processing speeds of the SMQT-based methods are discussed and found to be some

of the fastest reported on a single CPU. Furthermore, additional improvement regarding the processing speed

and its impact on image quality is investigated.

1 INTRODUCTION

The real world scenes we experience in our daily life

have a very wide range of luminance values. The

human visual system is capable of perceiving scenes

over ﬁve orders of magnitude and can gradually adapt

to scenes with dynamic ranges of over nine orders

of magnitude (Duan and Qiu, 2004). While humans

can perceive scenes over ﬁve orders the current con-

sumer products today typically has display and acqui-

sition technology ranging from two to three orders of

magnitude. Hence, pursuing High Dynamic Range

(HDR) images is of interest in order to reduce the

discrepancy between consumer products and human

perception. Recent trends in HDR imaging research

involves design of HDR imaging sensors, HDR im-

age generation techniques, encoding methods for efﬁ-

cient transmission and algorithms designed to display

HDR images on Low Dynamic Range (LDR) devices

(Bandoh et al., 2010; Barakat et al., 2008; Lu et al.,

2009). Tone Mapping Operation (TMO) is the pro-

cess of converting an HDR image to an LDR image.

The task of such a TMO needs to address the issue of

ﬁnding a good balance between emphasizing all fea-

tures in the image as well as presenting a good con-

trast while producing the LDR image. Several recent

proposed TMOs can be found in the literature (Chen

et al., 2005; Duan and Qiu, 2004; Liu et al., 2010;

Lee et al., 2010; Qiu et al., 2010; Kuang et al., 2007;

Meylan and Susstrunk, 2006; Reinhard et al., 2002;

Reinhard and Devlin, 2005; Mantiuk et al., 2008; Du-

rand and Dorsey, 2002; Drago et al., 2003; Pattanaik

et al., 2000).

TMOs can generally be divided into two broad

categories: global and local tone mapping (Reinhard

et al., 2005). Global tone mapping techniques utilize

a single, and typically highly nonlinear, spatially in-

variant mapping function. In many cases the nonlin-

ear functions are combinations of logarithmic and/or

exponential operators (Reinhard et al., 2002; Drago

et al., 2003; Reinhard, 2011). Global TMOs tend to

preserve the subjective perception of the scene and

have the advantage of being simple and fast. How-

ever, global processing may cause a loss of contrast,

which is apparent in the loss of detail visibility (Zhang

and Kamata, 2008). Local TMOs utilize local neigh-

borhood around a pixel in the mapping. This implies

that two different HDR image pixels with the same

intensity can be mapped to different LDR image val-

ues. This can make the local TMOs bring out more

details compared to a global method, but usually at a

cost of longer processing time. However, local meth-

ods may also cause “halo” effects or ringing artifacts

in the resulting LDR image (Reinhard et al., 2002).

The processing time of a TMO is also an issue; sev-

eral of the existing methods are computationally ex-

pensive. Hence, utilizing Graphics Processing Unit

(GPU) (Zhao et al., 2008) or design of hardware ar-

chitecture (Wang et al., 2007) for existing methods

are of interest unless the TMO method used can run

at acceptable times on a single CPU.

In this paper, new global TMOs are proposed uti-

lizing the nonlinear Successive Mean Quantization

Transform (SMQT) (Nilsson et al., 2005b; Nilsson

Nilsson M..

SMQT-based Tone Mapping Operators for High Dynamic Range Images.

DOI: 10.5220/0004228700610068

In Proceedings of the International Conference on Computer Vision Theory and Applications (VISAPP-2013), pages 61-68

ISBN: 978-989-8565-47-1

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

et al., 2005a). To the best of the author knowledge no

prior tone mapping operation of high dynamic range

images based on the SMQT has been proposed or in-

vestigated. The paper will show that the SMQT is

a good choice for mapping HDR images to LDR. In

particular, it will be shown that the method is fast,

and gives reasonable visual results comparable to the

state-of-the-art.

Two versions of the tone mapping operations are

considered here, one working on luminance and one

version working directly on all RGB channels. The

framework of the luminance approach is in line with

other works (but they do not use or propose the use of

the SMQT). The presented all channel approach is to

the best of the author knowledge novel. It should be

emphasized that, in order to get a general framework,

the derivation, experiments and processing speeds are

conducted using numbers in double precision describ-

ing the HDR image. Hence, if RGB histograms of

the HDR image is available, the processing described

could be performed on those histograms and lead to

further speed improvements.

The paper is organized as follows. In the next sec-

tion formal description of the SMQT is revisited. Sec-

tion 3 presents how the SMQT TMO works on lumi-

nance values as well as the all channel RGB image

and makes a comparison. In section 4 the processing

speed is investigated and a comparison to other state-

of-the-art TMOs is performed. Finally, conclusions

are presented.

2 DESCRIPTION OF THE SMQT

In general, a data point x in a set D consisting of

|D| = D data points are the input to the transform.

The value of a data point is denoted by V(x). Note

that the data structure can be arbitrary, that is D can

be a vector, a matrix or some arbitrary form. In this

paper, the set D is a HDR image of size D = M × N

if gray-scale (luminance) and D = M × N × 3 if color.

The SMQT has only one parameter input: the

level L (indirectly, it will also have the number of data

points D as an important input). The output set from

the transform is denoted M . It has the same form as

the input, that is D could be a color HDR image of

size M × N × 3 then M is also a color image of size

M × N × 3 but with different range of values. The

transform of level L from D to M is denoted

SMQT

: D → M . (1)

The SMQT

function can be described by a binary

tree where the vertices are Mean Quantization Units

(MQUs). A MQU consists of three steps: a mean cal-

culation, a quantization and a split of the input set.

The ﬁrst step of the MQU ﬁnds the mean of the

data, denoted V, according to

V =

|D|

∑

x∈D

V(x). (2)

The second step uses the mean to quantize the values

of data points into {0, 1}. A comparison function is

deﬁned as



V(x),





1, if V(x) >

0, else.

(3)

denotes concatenation, then

U =

x∈D



V(x),



(4)

is the mean quantized set. The set U is the main out-

put from a MQU. The third step splits the input set

into two subsets:

= {x | V(x) ≤

V,∀x ∈ D}

= {x | V(x) >

V,∀x ∈ D},

(5)

where D

propagates the left and D

propagates the

right of the binary tree, see Fig. 1.

MQU

MQU MQU

MQU

MQU MQUMQU MQU

Figure 1: The operation of one Mean Quantization Unit

(MQU).

The output set U from a MQU is not a value or a

similarity coefﬁcient as in the linear transforms. In-

stead, U can be interpreted as the structure of D.

Hence, the MQU is independent of the gain and bias

adjustments of the input.

The MQU constitutes the main computing unit for

the SMQT. The ﬁrst level transform, SMQT

, is based

on the output from a single MQU, where U is the

output set at the root node. The outputs in the bi-

nary tree need extended notation. The output set from

one MQU in the tree is denoted U

(l,n)

, where l =

1,2,...,L is the current level, and n = 1,2,...,2

(l−1)

is the output number for the MQU at levell, see Fig. 2.

Weighting of the values of the data points in the

(l,n)

sets is performed and the ﬁnal SMQT

is found

VISAPP2013-InternationalConferenceonComputerVisionTheoryandApplications

MQU

MQU MQU

MQU

MQU MQU

MQU

MQU MQU

MQU

MQU MQU

MQU

MQU MQU

MQU

MQU MQU

MQU

MQU MQU

MQU

Level 1: 2

L−1

Level 2: 2

L−2

Level 1: 2

L−1

Level 3: 2

L−3

Level 2: 2

L−2

Level 3: 2

L−3

(1,1)

MQU

(2,1)

MQU

(2,2)

MQU

(3,1)

MQU

(3,2)

MQU

(3,3)

MQU

(3,4)

MQU

Figure 2: The Successive Mean Quantization Transform

(SMQT) as a binary tree of Mean Quantization Units

(MQUs).

by adding the results. The weighting is performed by

L−l

at each level l. Hence, the result for the SMQT

can be found in the following way

M = {x | V(x) =

∑

l=1

∑

l−1

n=1



(l,n)



· 2

L−l

∀x ∈ D, ∀u

(l,n)

∈ U

(l,n)

(6)

As a consequence of this weighing, the number of

quantization levels, denoted by Q

, for a structure of

level L will be Q

= 2

. Since the main aim here is to

produce low dynamic range images the most natural

choice is L = 8.

3 SMQT-BASED TONE MAPPING

OPERATIONS

Most color imaging systems today use a single image

sensor and a Color Filter Array (CFA) to capture full

color images. A color ﬁlter array enables each pixel

to capture the intensity of light with different color

spectrum. The most common design of CFA is the

GRGB Bayer pattern (Bayer, 1976) which consists of

two greens, one red, and one blue component. A CFA

image is then interpolated via a demosaicing algo-

rithm and produces a ﬁnal RGB color image. Hence,

in most cases color image are initially in RGB format

from which the proposed TMOs are derived.

Let a RGB HDR image be denoted I

HDR

(i, j, k)

where i = 0,1,...,M − 1 is the row index, j =

0,1,...,N − 1 the column index and k = 0,1,2 the

color channels red, green and blue. Addition-

ally, let R

HDR

(i, j) = I

HDR

(i, j, 0),∀i, j, G

HDR

(i, j) =

HDR

(i, j, 1),∀i, j and B

HDR

(i, j) = I

HDR

(i, j, 2),∀i, j

be the RGB matrices for the HDR image. Same nota-

tions will follow for a LDR image, but with subscript

LDR. To simplify notation, the indices i, j and k are

dropped unless speciﬁcally required.

In general, a TMO can be seen as a 3-D matrix

mapping

LDR

= f(I

HDR

) (7)

where f(•) is the general tone mapping. One ap-

proach commonly adopted for tone mapping is to con-

vert the RGB to luminance, L

HDR

, as

HDR

= 0.299R

HDR

+ 0.587G

HDR

+ 0.114B

HDR

(8)

and perform a mapping L

LDR

= g(L

HDR

) on the lumi-

nance only. To ﬁnd the LDR color channels, the desat-

urated color-to-luminanceratios can be used (Schlick,

1994; Mantiuk et al., 2009)

LDR



HDR



LDR



HDR



LDR



HDR



LDR

(9)

where s controls color saturation. Other techniques

may be employed in order to correct the color result

(Mantiuk et al., 2009). Note that TMO utilizing the

mapping g(·) rely on luminance only, implying color

space conversion and that color information is later

adjusted to achieve the ﬁnal result.

Given an HDR image in red, green and blue for-

mat, I

RGB

, a TMO aims at ﬁnding a good balance

between image features, contrast and color ﬁdelity.

The SMQT has been shown to have desirable proper-

ties in achieving a balanced contrast enhancement for

LDR gray-scale images (Nilsson et al., 2005b; Nils-

son et al., 2005a). Note that the SMQT can be seen as

a nonlinear compression of data points with a higher

number of bits to a deﬁned new, and lower, quan-

tization level L set by the user. Hence, the SMQT

can be used directly on gray-scale HDR images and

one possibility for HDR tone mapping is to apply it

in luminance space, see Fig. 3. However, a different

HDR

LDR

HDR

Eq. (8)

HDR

SMQT

(·) Eq. (9)

Figure 3: HDR to LDR image using the SMQT on lumi-

nance channel as a tone mapping operator.

approach is also proposed here, the full RGB image

(all channels) will be used to ﬁnd a mapping func-

tion h(·) using the SMQT which then is employed

on the channels independently as R

LDR

= h(R

HDR

LDR

= h(G

HDR

) and B

LDR

= h(B

HDR

). Thus, no

color space transformation needs to be employed (if

given an image already in RGB), see Fig. 4.

SMQT-basedToneMappingOperatorsforHighDynamicRangeImages

(a) Tone mapping result by SMQT on luminance. (b) Tone mapping result by SMQT over all RGB channels.

Figure 5: Comparison between luminance SMQT TMO, processing as in Fig. 3, and all RGB channel SMQT TMO, processing

as in Fig. 4. The parameters used are L = 8, γ = 1/2.2 and s = 0.8.

HDR

LDR

HDR

SM QT

(·)

Figure 4: HDR to LDR image using the SMQT on all RGB

channels as a tone mapping operator.

An exempliﬁed comparison between the lumi-

nance version and all channel RGB SMQT-based

TMO can be found in Fig. 5, to the right of each image

the log-luminance of the HDR intensity is plotted ver-

sus the mapped intensity of the LDR image for each

color channel. Note that a property following from

the SMQT applied on all channel RGB, as well as the

luminance mapping according to Eq. 9, is that the or-

der of intensity values in R, G and B for a pixel will

be the same in input and output since the channels use

the same monotone mapping, see Fig. 5.

4 EXPERIMENTAL RESULTS

The proposed luminance SMQT and all channel RGB

SMQT based TMO are implemented in Matlab



with parts of the SMQT operation rewritten in ANSI

C and wrapped to a mex ﬁle in order to gain speed.

The processing speed for the processing chains found

in Fig. 3 and Fig. 4 (note that it includes gamma cor-

rection) for HDR images of various size can be found

in Fig.6. The processing speed between the lumi-

nance and all channel RGB method are very similar,

but the all channel RGB is somewhat faster. This im-

plies that SMQT on M×N×3 data points is similar to

SMQT on M × N data points with additional color to

luminance found in Eq. 8 and producing color output

found in Eq. 9. Hence, if the SMQT processing speed

can be reduced the all channel RGB TMO is expected

0 1 2 3 4 5 6 7 8

HDR image size in megapixels

FPS

720p, FPS: ~4.1

1080p, FPS: ~1.9

640 × 480, FPS: ~11.9

5MP, FPS: ~0.8

all channel RGB SMQT, L=8

luminance channel SMQT, L=8

Figure 6: FPS for different sizes of HDR images. Circles

with text indicate FPS for the SMQT-based all channel RGB

TMO.

to increase its FPS more compared to the luminance

version. For a timing comparison with other work,

Mantiuk et al. implemented a TMO in Matlab and re-

ported a processing speed of 1.7 seconds (0.59 FPS)

on 2.6GHz CPU for a 1M-pixel image (Mantiuk et al.,

2008). The proposed luminance SMQT-based TMO

achieves 3.60 FPS and the all channel RGB SMQT-

based TMO 3.80 FPS on a 2.13GHz CPU for a 1M-

pixel image. However, GPU and hardware architec-

ture solutions of TMOs naturally report higher frame

rates (Zhao et al., 2008; Wang et al., 2007). A vi-

sual comparison to other state-of-the-art TMOs can

be found in Fig. 7. The SMQT-based methods use the

parameters L = 8, γ = 1/2.2 and s = 0.8 and the other

TMOs use the default parameters deﬁned in the Lu-

minance HDR software

. Note that the SMQT-based

TMOs, similar to other state-of-the-art TMOs, pro-

duce naturally looking LDR images.

Luminance HDR version 2.2.1 from http://

tpfsgui.sourceforge.net/

VISAPP2013-InternationalConferenceonComputerVisionTheoryandApplications

A B

D E F

(a) HDR image Stanford memorial church.

A B

D E F

(b) HDR image Nancy church 2 from MPI.

A B

D E F

A B

D E F

(d) HDR image Garage from RIT MCSL High Dynamic Range Image

Database.

A B

D E F

(e) HDR image Racecar from RIT MCSL High Dynamic Range Image

Database.

A B

D E F

(f) HDR image Snow from MPI.

A B

D E F

(g) HDR image MPI Atrium 1 from MPI.

Figure 7: Tone mapped HDR images. TMO by (A) Reinhard et al. (Reinhard et al., 2002), (B) Durand and Dorsey (Durand

and Dorsey, 2002), (C) Drago et al. (Drago et al., 2003), (D) Mantiuk et al. (Mantiuk et al., 2008), (E) the proposed

luminance channel SMQT-based method and (F) the proposed all channel RGB SMQT-based method. Zooming in the pdf

images is recommended for detail studies.

SMQT-basedToneMappingOperatorsforHighDynamicRangeImages

L = 1 2

5 6

Figure 9: Example of image quality on Stanford memorial for different levels L. Top is SMQT-based all channel RGB tone

mapping operation. Bottom is SMQT-based luminance channel tone mapping operation.

1 2 3 4 5 6 7 8

FPS

all channel RGB SMQT

luminance channel SMQT

Figure 8: Processing speeds on a one megapixel image in

Frames Per Second (FPS) on a 2.13GHz CPU. The param-

eters used are γ = 1/2.2 and s = 0.8.

4.1 Improving Processing Speed

While the processing speed for the proposed SMQT

TMOs are some of the fastest reported on a single

CPU, with regard to implementation on embedded

systems, it is still desirable to achieve better process-

ing speeds. The choice of the level used so far is

L = 8, simply due to the fact that the aim is eight

bit images. However, selecting a level L lower can

be a direct way to reduce processing speed but with

reduced image quality. Note that the ﬁnal output is

still desired to be eight bits and selecting L as a lower

number results in L bit output. Hence, a direct way to

again produce a eight bit result from any selected L is

to multiply the result from Fig. 3 or Fig. 4 with 2

8−L

resulting in an eight bit image

8 bit LDR

= I

LDR

· 2

8−L

. (10)

As mentioned, it is expected that the all channel

RGB will beneﬁt more than the luminance version in

a reduction of the SMQT processing speed, see Fig. 8.

The all channel RGB method beneﬁts more from the

reduction in processing speed of the SMQT, for ex-

ample at L = 5 the speed is more than 30% higher

in FPS compared to the luminance method on a one

megapixel image.

Naturally, the image quality decreases as the level

is decreased, see Fig. 9. A subjective observation

from the resulting images constructed with different

levels is that around L = 4 and L = 5 acceptable re-

sults can be achieved. In order to objectify this state-

ment the Peak Signal to Noise Ratio (PSNR) is cal-

culated for the luminance of images and as reference

the eight bit image is used. The seven images found

in Fig. 7 are used and the mean PSNR is calculated,

see Fig.11(a). Selecting a threshold at 30 dB, which

has been found to be suitable from a psychophysical

viewpoint (F. Xiao, 2005), coincide with choosing a

level around four for both methods. Additionally, the

quality mapped to mean opinion scores, Q

MOS

, from

HDR-VDP-2 (Mantiuk et al., 2011) is investigated.

The settings for Q

MOS

calculation are color encoding

selected as sRGB-display and pixels-per-degreeas 30.

The seven images found in Fig. 7 are used and the

mean Q

MOS

is calculated, see Fig.11(b). Note that

around L = 5 the Q

MOS

starts dropping and PSNR

drops below 30 db at around L = 4, hence this coin-

cides well with the initial subjective statement from

observing Stanford memorial, see Fig. 9. Further-

more, the all channel RGB SMQT keeps Q

MOS

higher

compared to luminance channel SMQT at L < 5.

Hence, a reasonable conclusion from this analysis is

that using L = 5 could be a fair choice in order to

reduce computation speed while retaining decent im-

age quality. A comparison of processing speed using

L = 5 can be found in Fig. 10.

VISAPP2013-InternationalConferenceonComputerVisionTheoryandApplications

1 2 3 4 5 6 7

PSNR [dB]

all channel RGB SMQT

luminance channel SMQT

(a) PSNR for different levels using level eight as reference.

1 2 3 4 5 6 7

100

MOS

all channel RGB SMQT

luminance channel SMQT

(b) Q

MOS

quality measure for different levels using level eight as reference.

Figure 11: Peak Signal to Noise Ration (PSNR) and quality measure (Q

MOS

) for different choices of level L. The parameters

used are γ = 1/2.2 and s = 0.8.

0 1 2 3 4 5 6 7 8

HDR image size in megapixels

FPS

720p, FPS: ~5.6

1080p, FPS: ~2.6

640 × 480, FPS: ~16.1

5MP, FPS: ~1.1

all channel RGB SMQT, L=5

luminance channel SMQT, L=5

reference, L=8

Figure 10: FPS for different sizes of HDR images and L=5.

Reference is average FPS from the two curves found in

Fig. 6. Circles with text indicate FPS for the SMQT-based

all channel RGB TMO.

5 CONCLUSIONS

Two novel global tone mapping operations based on

the nonlinear Successive Mean Quantization trans-

form (SMQT) have been proposed and investigated.

One method is based on applying the SMQT on lu-

minance channel and another is based on performing

the SMQT on all RGB channels. The methods were

compared to other state-of-the-art methods and pro-

duce visually similar results. Regarding the process-

ing speed, they are some of the fastest reported on

a single CPU and can run close to 12 FPS on VGA

(640 × 480) with a 2.13 GHz computer in default

operation. The methods were further investigated

and it was demonstrated that the all channel RGB

has more desirable properties compared to the lumi-

nance method considering processing speed reduction

and associated image degradation. It is found, using

PSNR and Q

MOS

, that a reasonable image degradation

which allows speedup can be achievedat the choice of

level L = 5 in the SMQT. Utilizing L = 5 compared

to the default operation, the all channel RGB method

can run at around 16 FPS while the luminance chan-

nel method achieves 12.5 FPS, on a VGA size image

and a 2.13 GHz computer.

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