DCT based Multi Exposure Image Fusion

O. Martorell, C. Sbert and A. Buades

Department of Mathematics and Computer Science & IAC3, University of Balearic Islands,

Cra. de Valldemossa km. 7.5, 07122 Palma, Illes Balears, Spain

Keywords:

Multi-exposure Images, Image Fusion, DCT Transform.

Abstract:

We propose a novel algorithm for multi-exposure fusion (MEF). This algorithm decomposes image patches

with the DCT transform. Coefﬁcients from patches with different exposure are combined. The luminance and

chrominance of the different images are fused separately. Details of the fused image are ﬁnally enhanced as

a post-processing. Experiments with several data sets show that the proposed algorithm performs better than

state-of-the-art.

1 INTRODUCTION

Multi-exposure fusion (MEF) is a technique for com-

bining different images of the same scene acquired

with different exposure settings into a single image.

The natural light has a large range of intensities which

a conventional camera cannot capture. By keeping the

best exposured parts of each image, we can recover a

single image where all features are well represented.

High Dynamic Range (HDR) imaging from a ex-

posure sequence is usually confused with MEF. In

HDR, the irradiance function of the image has to be

built, and in order to do so, the camera response func-

tion has to be estimated. Most methods use the al-

gorithm by Malik and Devebec (Debevec and Malik,

2008). Finally, to be displayed, the estimated HDR

function has to be converted into a typical 8 bit im-

age. This problem is known as tone-mapping (Rein-

hard et al., 2005).

All proposed MEF algorithms combine the set of

images, somehow choosing for each pixel the one

with better exposition. State of the art methods ex-

press this choice as a weighted average depending on

common factors as exposure, saturation and contrast,

e.g. Mertens et al. (Mertens et al., 2009). The pixel

values or their gradient might be combined. In the

case that pixel gradient is manipulated, a ﬁnal esti-

mate has to be recovered by Poisson editing (P

erez

et al., 2003). Robustness of methods is achieved by

using pyramidal structures or working at the patch

level instead of the pixel one.

We propose a multi-exposure image fusion algo-

rithm inspired by MEF Mertens’s algorithm (Mertens

et al., 2009) and the Fourier Burst Accumulation

(FBA) algorithm proposed by Delbracio and Sapiro

(Delbracio and Sapiro, 2015). Instead of combining

gradient or pixel values, we fuse the DCT coefﬁcients

of the differently exposed images. The algorithm de-

composes the image into patches and computes the

DCT. The coefﬁcients of patches at the same location

but different exposure are combined depending on its

magnitude. This strategy is used to combine patches

of the luminance. The chrominance values are fused

separately as a weighted average at the pixel level.

The novel method for the fusion of the luminance

images is presented in section 3.1. The chrominance

fusion algorithm is described in section 3.2. Section

3.3 proposes a detail extraction technique to enhance

the fused result. Finally, in section 4 some results and

comparisons with other image fusion algorithms are

presented.

2 RELATED WORK

There exists an extensive amount of research in MEF.

The ﬁrst distinction among MEF algorithms is wether

they combine pixel color values or pixel gradients.

Secondly, pixel-wise algorithms may be regularized

or made robust by using multi-scale pyramids or patch

based strategies. Finally, the fusion method might be

applied directly to RGB channels, to a decomposi-

tion of luminance and chrominance, or a decompo-

sition into basis and detail images. This latter case

permits to additionally apply an enhancement of the

detail part.

Martorell, O., Sbert, C. and Buades, A.

DCT based Multi Exposure Image Fusion.

DOI: 10.5220/0007356701150122

In Proceedings of the 14th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2019), pages 115-122

ISBN: 978-989-758-354-4

115

Pixel-wise methods, directly applied to RGB com-

ponents, compute a weighted average

u(x) =

∑

k=1

(x)I

(x) (1)

where K is the number of images in the multi-

exposure sequence, I

(x) is the input value at x po-

sition in the k-th exposure image and w

(x) is the k-th

weight at this position. The weight map w

measures

information such as edge strength, well-exposedness,

saturation, etc. Mertens’s algorithm (Mertens et al.,

2009) is the widely used algorithm in this class. It

computes three quality metrics:

• Contrast C: the absolute value of the Laplacian

ﬁlter applied to the grayscale of each image.

• Saturation S: measures the standard deviation of

R, G and B channels.

• Well-exposedness E: measures the closeness to

the mid intensity value.

These metrics are combined into a weight map for

each image

(x) =

(x)

∑

j=1

(x)

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

Other methods compute fusion by a weighted av-

erage, but with a different conﬁguration to the pro-

posed one by Mertens et al. For example, Liu et al.

(Liu and Wang, 2015) propose to use the SIFT de-

scriptor at each pixel to compute the weights, which

are later reﬁned and merged by a multiscale proce-

dure.

The second type of methods use the gradient of

the images, and then recovers the solution by Pois-

son image editing (P

erez et al., 2003). For several

algorithms, just the most convenient gradient is cho-

sen, for example Kuk et al. (Kuk et al., 2011). Other

methods combine all gradients, for example (Raskar

et al., 2005; Zhang and Cham, 2012; Gu et al., 2012;

Sun et al., 2013). Sun et al. (Sun et al., 2013) addi-

tionally ﬁlter the weight maps to make fusion more

robust. Ferradans et al. (Ferradans et al., 2012) ﬁrst

apply an optical ﬂow algorithm to register the images

before combining the gradient.

Paul et al. (Paul et al., 2016) fuse differently the

luminance and the chrominance values, the YCbCr

(Gonzalez and Wood, ) color space is used. The lu-

minance is combined by using gradient based fusion.

However, chromatic components are fused by direct

pixel-wise averaging, where weight depends on how

far is a pixel from a gray value.

Pixel wise methods are regularized by using pyra-

midal structures or working at the patch level. Burt

and Adelson (Burt and Adelson, 1983) proposed the

Laplacian pyramid decomposition for image fusion.

This decomposition was adopted by Mertens et al.

(Mertens et al., 2007) algorithm. The weight maps

are decomposed into a Gaussian pyramid G(w

)

and

the input images into a Laplacian pyramid L(I

)

, l

denotes the level in the pyramid decomposition. For

each level l the blended coefﬁcients of the Laplacian

pyramid are computed as

L(u)

(x) =

∑

k=1

G(w

)

(x)L(I

)

(x). (2)

Finally, the pyramid L(u)

(x) is collapsed to obtain

the fused image u.

Patch based methods use as minimal unity small

image windows. The decision is more robust than

pixel wise algorithms since much more values are

involved. The ﬁrst patch based algorithm was pro-

posed by Goshtasby (Goshtasby, 2005). The image is

divided into several non-overlapping blocks and the

ones with the highest entropy are selected. Block-

ing artifacts are reduced by a blending function. In

(Zhang et al., 2017a), Zhang et al. use patch correla-

tion to detect motion and deﬁne the average distribu-

tion, which is applied with a multi-scale procedure.

Zhang et al. (Zhang et al., 2017b) use super-pixel

segmentation to detect motion. This detection per-

mits to replace non corresponding parts by the speci-

ﬁed reference image. Finally, a multi-scale approach

uses gradient magnitude of each pixel to deﬁne av-

erage conﬁguration. Recently Ma et al. (Ma et al.,

2017) proposed to decompose the image patches into

three components: signal strength, signal structure

and mean intensity. Then, they fuse each component

separately. Moreover, the direction of the signal struc-

ture provides information for deghosting.

3 PROPOSED FUSION

ALGORITHM

We propose a novel algorithm for multi-exposure fu-

sion adopting the Fourier aggregation model (Delbra-

cio and Sapiro, 2015) as main tool. Compared to most

existing MEF algorithms, we apply a different proce-

dure for the luminance and chrominance components

of the images. We use the YCbCr (Gonzalez and

Wood, ) color transformation for this separation. The

luminance channel (Y ) contains most geometry and

image details while the chrominance (Cb, Cr) chan-

nels carry information about color.

VISAPP 2019 - 14th International Conference on Computer Vision Theory and Applications

116

3.1 Luminance Fusion

For the Fourier transform, it is well known that

the magnitude decay of coefﬁcients is related to the

smoothness of the function. That is, the sharpness of

detail information of an image is related to the amount

of signiﬁcant Fourier coefﬁcients.

A local interpretation of the decay of the Fourier

or DCT transform, indicates that under/over exposed

patches will have Fourier coefﬁcients of smaller mag-

nitude, due to the lack of high frequency information.

For shake removal, one supposes the existence of a

true spectrum, modiﬁed in each image by a different

kernel. For MEF, one can fuse the DCT coefﬁcients

in order to recover the full transform.

We locally apply a weighted average of each fre-

quency depending on its magnitude, permitting to

recover the most signiﬁcant ones, and thus the ex-

posed details. This strategy does not apply to the

zero frequency Fourier coefﬁcient, i.e. the mean.

Large zero frequency coefﬁcients correspond to over-

exposed images, then applying the same weighted

combination would simply overexpose the whole im-

age. We use the Mertens algorithm (Mertens et al.,

2009) to set the zero frequency coefﬁcient.

Let assume we have a multi-exposure sequence

of image luminances, supposed to be pre-registered,

which we denote by Y

, k = 1, 2, . . . , K. Since each

image might contain well exposed areas, we apply

the combination locally. We split the images Y

into

partially-overlapped blocks of b × b pixels, {B

}, l =

1, . . . , n

, n

the number of blocks. We propose to fuse

the non-zero frequencies of each block as follows:

(ξ) =

∑

k=1

(ξ)

(ξ), ξ 6= 0, l = 1, 2, . . . , n

(3)

where

denotes the DCT transform of the block B

and the weights w

(ξ) are deﬁned depending on ξ as,

(ξ) =

(ξ)|

∑

n=1

(ξ)|

, ξ 6= 0. (4)

The parameter p controls the weight of each Fourier

mode. If p = 0 the fused frequency is just the arith-

metic average, while for p → ∞ each fused frequency

takes the maximum value of the frequency in the se-

quence.

For ξ = 0, which corresponds to the mean in-

tensity of the block B

, the application of such a

procedure would correspond to average those blocks

with highest mean and therefore an over exposed im-

age. Let YM be the luminance of the result of ap-

plying Mertens’s algorithm (Mertens et al., 2009) to

the multi-exposure image sequence. We split it into

blocks BM

, l = 1, . . . , n

and deﬁne the zero fre-

quency mode of each block as

(0) = BM

l = 1, . . . , n

(5)

where BM

denotes the mean value of the block BM

Finally, if F

−1

denote the inverse Fourier trans-

form we obtain the fused blocks,

(x) = F

−1

(

(ξ)), l = 1, . . . , n

. (6)

Since blocks are partially overlapped, the pixels in

overlapping are averaged to produce the ﬁnal image.

3.2 Chrominance Fusion

We adopt a similar strategy to (Paul et al., 2016),

and directly combine for each pixel, the values of the

Cb, Cr channels at the same coordinates. The Cb, Cr

components have a range from 16 to 240, being 128

the absence of color information. That is, if both

chromatic components are equal to 128, the image

is gray. In order to maximize the color information,

color components further from 128 are privileged.

Let us denote the chrominance channels of the

input multi-exposure sequence by Cb

and Cr

, k =

1, 2 . . . , K. The fused chrominance channels are rep-

resented as follows

Cb(x) =

∑

k=1

(x)Cb

(x), Cr(x) =

∑

k=1

(x)Cr

(x)

(7)

We will use a non linear weight on the difference

to the gray. We use an exponential kernel,

(x) =

exp



(Cc

−128)



− 1

∑

j=1



exp



(Cc

−128)



− 1



, c ∈ {b, r}.

(8)

The value of σ is set to σ = 128.

3.3 Enhancement

Recent methods (Li et al., 2012; Singh et al., 2014;

Li et al., 2017) perform an additional enhancement to

the fused details. This is achieved by ﬁrst decompos-

ing the images into a base and detail images. These

components are fused independently and when com-

bined an additional parameter permits to enhance the

detail part.

We apply the detail enhancement separately of

the MEF fusion chain. We use the screened-Poisson

equation (Morel et al., 2014a; Morel et al., 2014b), to

separate the details.

λu(x) − ∆u(x) = −∆ f (x) x ∈ Ω (9)

DCT based Multi Exposure Image Fusion

117

(Mertens et al., 2009) (Raman and Chaudhuri, 2009) (Gu et al., 2012) (Li et al., 2012)

(Li and Kang, 2012) (Li et al., 2013) (Ma et al., 2017) Ours

Figure 1: Exposure fusion comparison. From top to bottom and left to right: Mertens et al. (Mertens et al., 2009), Raman et

al. (Raman and Chaudhuri, 2009), Gu et al. (Gu et al., 2012), Li et al. (Li et al., 2012), Li et al. (Li and Kang, 2012), Li et al.

(Li et al., 2013), Ma et al. (Ma et al., 2017) and our result.

with homogeneous Neumann boundary condition. In

(Morel et al., 2014a), the authors show that the so-

lution of the screened Poisson equation (9) acts as a

high-pass ﬁlter of f when λ increases, containing the

details of f . The difference f − u contains the basis

image, responsible for the geometry.

Let f denote the fused image by applying the

method introduced in sections 3.1, 3.2. The proposed

detail enhancement consists in solving the equation

(9), and thus splitting the image into a detail u and ge-

ometry f − u parts. By recomposing the fused image

with an additional detail enhancement we obtain

f (x) = f (x) − u(x) + αu(x) = f (x) + (α − 1)u(x).

(10)

4 EXPERIMENTAL RESULTS

In this section we compare the proposed method with

state of the art algorithms for exposure fusion. We

compare with Mertens et al. (Mertens et al., 2009),

Raman et al. (Raman and Chaudhuri, 2009), Gu et

al. (Gu et al., 2012), Li et al. (Li et al., 2012), Li et

al. (Li and Kang, 2012), Li et al. (Li et al., 2013)

and Ma et al. (Ma et al., 2017). All results except

for the last method were taken from the dataset pro-

vided in (Zeng et al., 2014) and (Ma et al., 2015). This

database (Zeng et al., 2014; Ma et al., 2015) contains

seventeen input images with multiple exposure levels

(≥ 3) together with fused images generated by eight

state-of-the-art image fusion algorithms. The results

from Ma et al. (Ma et al., 2017) were computed with

the software downloaded from the author’s page. In

all cases, default parameter settings are adopted.

Our results were computed using the same param-

eters for all tests in this section. The parameters for

the weighted average of the Fourier modes and the

chrominance channels are set to p = 7 and σ = 128 re-

spectively. Finally for the enhancement we set λ = 0.5

and α = 1.5.

Figure 1 displays the results of all methods in the

”Belgium House” data set. A zoomed detail of these

images is displayed in Figure 2. The results by Ra-

man et al. (Raman and Chaudhuri, 2009) and Gu et

al. (Gu et al., 2012) are quite dark and blurred. The

fused image by Li et al. (Li et al., 2013), having a

better luminance than the two previous methods, it

has large regions with a darker value than expected,

as for example in the wall below the painting. The

rest of the methods have a good global illumination.

However, looking closer to the details in Figure 2, we

might observe that many outdoor details in Mertens et

al. (Mertens et al., 2009), Li et al.(Li et al., 2012) and

Ma et al. (Ma et al., 2017) are overexposed, loosing

its deﬁnition. We might also observe that details in Li

et al. (Li et al., 2012) are excessively enhanced, mak-

ing them look like unnatural. Our result seems to be

the best compromise having a natural look and a good

deﬁnition of details.

Figure 3 and 5 respectively display the results with

the ”House” and ”Cadik” tests and corroborate obser-

vations on previous ﬁgure. Figures 4 and 6 shows

zoomed details of ﬁgure 3 and 5, respectively. For

the ”House” set, it must be noted the excessive detail

and color enhancement of Ma et al. (Ma et al., 2017),

the poor luminance balance of Li et al. (Li and Kang,

2012) and the detail blur in Li et al. (Li et al., 2013).

For the ”Cadik” set, let note that only Li et al. (Li

et al., 2013) and our result are able to correctly avoid

VISAPP 2019 - 14th International Conference on Computer Vision Theory and Applications

118

(Mertens et al., 2009) (Raman and Chaudhuri, 2009) (Gu et al., 2012) (Li et al., 2012)

(Li and Kang, 2012) (Li et al., 2013) (Ma et al., 2017) Ours

Figure 2: Detail of images in Fig. 1. We observe that many outdoor details in Mertens et al. (Mertens et al., 2009), Li et al.(Li

et al., 2012) and Ma et al. (Ma et al., 2017) are overexposed. Details in Li et al. (Li et al., 2012) are excessively enhanced,

making them look like unnatural. Our result looks natural and details are well deﬁned.

(Mertens et al., 2009) (Raman and Chaudhuri, 2009) (Gu et al., 2012) (Li et al., 2012)

(Li and Kang, 2012) (Li et al., 2013) (Ma et al., 2017) Ours

Figure 3: Exposure fusion comparison. From top to bottom and left to right: Mertens et al. (Mertens et al., 2009), Raman et

al. (Raman and Chaudhuri, 2009), Gu et al. (Gu et al., 2012), Li et al. (Li et al., 2012), Li et al. (Li and Kang, 2012), Li et al.

(Li et al., 2013), Ma et al. (Ma et al., 2017) and our result.

saturation near the lamp’s light. However, details on

Li et al. (Li et al., 2013) are excessively blurred.

5 CONCLUSION

We have presented a novel fusion algorithm for multi-

exposure images. The block based method uses

the DCT coefﬁcient instead of the traditional gra-

dient combination. Moreover, we propose to apply

an enhancement to the fused image by applying the

screened Poisson equation.

Experiments have shown the improvement of the

proposed algorithm compared to state of the art.

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