GENERATION OF HDR IMAGES IN NON-STATIC CONDITIONS

BASED ON GRADIENT FUSION

Sira Ferradans

, Marcelo Bertalm´ıo

, Edoardo Provenzi

and Vicent Caselles

Centre De Recherche en Math´ematiques de la D´ecision UMR CNRS 7534, Universit´e de Paris Dauphine,

Place du Mar´echal De Lattre De Tassigny, 75775, Paris Cedex 16, France

Department of Information Technology, Universitat Pompeu Fabra, C/ T`anger 122-140, Barcelona, Spain

Keywords:

High Dynamic Range Images, Gradient Fusion, Registration, Optical Flow.

Abstract:

We present a new method for the generation of HDR images in non-static conditions, i.e. hand held camera

and/or dynamic scenes, based on gradient fusion. Given a reference image selected from a set of LDR pictures

of the same scene taken with multiple time exposure, our method improves the detail rendition of its radiance

map by adding information suitably selected and interpolated from the companion images. The proposed

technique is free from ghosting and bleeding, two typical artifacts of HDR images built through image fusion

in non-static conditions. The advantages provided by the gradient fusion approach will be supported by the

comparison between our results and those of the state of the art.

1 INTRODUCTION

Radiance in natural scenes can span several orders

of magnitude, yet commercial cameras can capture

only two orders of magnitude and reproduce Low Dy-

namic Range (LDR) photographs, often affected by

saturated areas and loss of contrast and detail. Dur-

ing the last ﬁfteen years, many techniques have been

studied and proposed in order to expand the dynamic

range of digital photographs to create the so-called

High Dynamic Range (HDR) images, i.e. matrices

whose entries are proportional to the actual radiance

of the scene. For a thorough overview of the HDR

imaging we refer the interested reader to the excellent

book (Reinhard et al., 2005). HDR images have been

widely used to capture scene illumination, but also

for a realistic scene representation. That is to say, the

wider dynamic range of HDR images allow to better

capture details and color differences. This high preci-

sion is the reason why most photographers nowadays

use cameras with a wider dynamic range than two or-

ders of magnitude.

Two main problems remain to be solved in HDR

imaging. First, while the technique proposed by De-

bevec and Malick (Debevec and Malik, 1997) can be

considered as the ‘de facto standard’ for the creation

of HDR images in static conditions, i.e. with perfectly

still camera and without moving objects in the scene,

no standard is available when these condition fail.

Second, HDR images cannot be entirely displayed

or printed on the majority of commercial screens or

printers, hence a so-called ‘Tone-Mapping’ transfor-

mation is needed to properly reduce their range with-

out losing details and respecting as much as possible

the original color sensation.

In this paper we deal only with the ﬁrst problem,

i.e. we study HDR image generation in non-static

conditions, which are, by far, the most common. As

we will explain in more detail later on, standard HDR

image creation algorithms assume perfect alignment

for the input images and no motion, the price to pay

when this assumption fails is the generation of arti-

facts, in particular those called ‘ghosts’, i.e. objects

with a translucent appearance induced by an incoher-

ent image fusion, and ‘bleeding’, i.e. the diffusion of

an artiﬁcial color over a ﬂat image region, see Fig-

ure 1. To avoid this and other problems that we will

discuss in more detail later, instead of synthesizing a

new HDR image from the original sequence of LDR

images, we will select just one of them to be the ref-

erence and then we will improve the associated radi-

ance map by adding as many details as possible with-

out introducing artifact. In doing this, a fundamental

role will be played by gradient fusion, which has sev-

eral advantages with respect to intensity fusion in this

case. As we will show in Section 5, the results of the

proposed technique compare well to the state of the

art.

Ferradans S., Bertalmío M., Provenzi E. and Caselles V..

GENERATION OF HDR IMAGES IN NON-STATIC CONDITIONS BASED ON GRADIENT FUSION.

DOI: 10.5220/0003840700310037

In Proceedings of the International Conference on Computer Vision Theory and Applications (VISAPP-2012), pages 31-37

ISBN: 978-989-8565-03-7

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

Figure 1: From top to bottom: an example of ghost and

bleeding artifacts, respectively.

2 STATE OF THE ART IN HDR

IMAGE CREATION

For the sake of readability, it is worthwhile to begin

this section by introducing some concepts and nota-

tion that will be used throughout the paper. We deﬁne

the radiance E(x) to be the electromagnetic power per

unit of area and solid angle that reaches the pixel x of

a camera sensor with spatial support Ω ⊂ R

. The

camera response function f is the non-linear map-

ping f : [0, +∞) → {0, . . . , 255} that transforms the

radiance E(x) acquired in the time ∆t into I(x), the

intensity value of the pixel x, i.e. f(E(x)∆t) = I(x). f

is assumed to be semi-monotonically increasing, i.e.

its derivative is supposed to be non-negative, since

the digital values stored by the camera remain con-

stant or increase as the radiance increases. In par-

ticular, the graph of f remains constant to 0 (black)

for all the radiance values that do not overcome the

sensibility threshold of the camera sensor and to 255

(white) for all those radiance values that exceed its

saturation limit. For values that lie inside these two

extremes, f is invertible and so we can use its inverse

−1

: {0, . . . , 255} → [0, +∞) to pass from image in-

tensity values I(x) to the corresponding radiance val-

ues E(x): f

−1

(I(x)) = E(x)∆t. The camera response

function can be built in controlled conditions by tak-

ing photos of a uniformly illuminated Macbeth chart

with patches of known reﬂectance.

However, in many practical cases, the camera re-

sponse function is not known, thus various techniques

for recovering f or its inverse without a Macbeth chart

havebeen developed. These methods are called chart-

less and are all based on the same principle: since

the camera sensor is limited by its sensibility thresh-

old and saturation limit, in order to detect the whole

scene radiance one has to take N ≥ 2 shots with dif-

ferent time exposures ∆t

, j = 1, . . . , N. The next

step consists in using the redundant information about

the scene provided by the set of N digital images

to recover the inverse camera function f

−1

. This

is the only step that distinguishes the various algo-

rithms proposed in the HDR imaging literature that

we will brieﬂy recall later. Let us for the moment sup-

pose that we have indeed computed f

−1

, then we can

construct the j-th partial radiance E

(x) as follows:

(x) ≡ f

−1

(x))



∆t

, j = 1, . . . , N. Notice that we

use the adjective ‘partial’ when referring to the radi-

ances E

because they are built by applying f

−1

to I

thus E

cannot be considered a faithful representation

of the entire radiance range, but only of the part cor-

responding to clearly visible details in the j-th image.

Finally, in order to compute the set of ﬁnal radiance

values {E(x), x ∈Ω} that will constitute the HDR im-

age of the scene, one performs a weighted average of

the partial radiances:

E(x) =

∑

j=1

w(I

(x))E

(x)

∑

j=1

w(I

(x))

, (1)

where the weights w take their maximum in 127, the

center of the LDR dynamic range, and decrease as the

intensity values approach 0 or 255, when the infor-

mation provided by I

is imprecise. If one deals with

color images, then this procedure must be repeated

three times in order to recover three radiance func-

tions relative to the red, green and blue spectral picks

of the scene radiance.

As we have said, the algorithms for HDR im-

age generation in static conditions are practically dis-

tinguished only for how they recover inverse cam-

era response function f

−1

. Mann and Picard (Mann

and Picard, 1995; Mann, 2000) were the ﬁrst to ad-

dress this problem, they postulated a gamma-like an-

alytical expression for f

−1

and solved a curve ﬁt-

ting problem to determine the most suitable param-

eters. Mitsunaga and Nayar (Mitsunaga and Nayar,

1999) improved Mann and Picard’s work by assum-

ing f

−1

to be a polynomial and determining its co-

efﬁcients through a regression model. Debevec and

Malik (Debevec and Malik, 1997) worked with log-

arithmic data and did not impose any restrictive an-

alytic form to f

−1

, yet they required it to be smooth

by adding a penalization term proportional to the sec-

ond derivative of f

−1

to the following optimization

VISAPP 2012 - International Conference on Computer Vision Theory and Applications

problem: Minklog f

−1

(x)) −logE(x) −log∆t

Their method is fast and gives reliable results, for this

reason it has become the de facto standard in the ﬁeld

of HDR imaging with static conditions.

Let us now consider non static conditions, i.e. im-

ages taken with hand held camera and/or of dynamic

scenes. In this case, a motion detection step must be

added to register the set of input LDR images and

a more careful fusion process must be considered to

avoid artifacts.

Let us begin with registration: Ward (Ward, 2003)

proposes to use multi-scale techniques to register a set

of Median Threshold Maps (MTB), which are a bi-

narization of the images with respect to their median

value. Although this approach is independent of the

exposure time, it dependson noise and histogram den-

sity around the median value. Grosch (Grosch, 2006)

bases a local registration method on Ward’s MTBs

and Jacobs et al. (Jacobs et al., 2008) proposed an

improvement of Ward’s work by estimating motion

with an entropy based descriptor. These methods give

good results for the case of small movements gener-

ated by a hand held camera, but they tend to produce

artifacts when dealing with large object motion, as

e.g. people walking through the scene. Tomaszewska

and Mantiuk (Tomaszewska and Mantiuk, 2007) and

Heo et al. (Heo et al., 2011) propose to compute a

global homography using RANSAC with SIFT de-

scriptors which are based on gradients. Finally, Kang

et al. (Kang et al., 2003) propose to use the camera

function to boost the original images in order to facil-

itate the registration process.

Let us consider nowthe methods that focus mainly

on a suitable improvement of the fusion step. As

we have said before, if we assume a perfect corre-

spondence among pixels in non-static conditions and

perform a weighted average of radiances, then ghosts

artifacts appear in areas where motion has occurred.

Many methods in the state of the art, e.g. (Khan et al.,

2006), (Heo et al., 2011), (Granados et al., 2010),

(Grosch, 2006) and (Jacobs et al., 2008), focus on

avoiding ghost formation by modifying eq. (1) in or-

der to reduce the inﬂuence of pixels corresponding to

moving objects in the process of intensity fusion to

generate the HDR image. These methods may be ro-

bust to pixel saturation and small misalignments, but

the areas that appear only in one image will be copied

while the other image areas will be averaged from dif-

ferent images, thus new boundaries could be created

in the process. In order to deal with these artifacts,

Gallo et al. (Gallo et al., 2009) propose to create

a vector ﬁeld by copying patches of gradients from

the best exposed areas that match a reference image.

Then they blend the borders of neighboring patches

and integrate the vector ﬁeld. The resulting images

are ghost free but artifacts appear on the patch borders

and ﬂat regions. Finally, let us report that gradient-

based methods can deal with the radiance differences

among the image sequence but are sensitive to mis-

alignments and can produce color bleeding as Eden et

al. (Eden et al., 2006) have pointed out.

3 THE PROPOSED ALGORITHM

The method that we propose has several steps in cas-

cade, before describing in detail all the steps it is

worthwhile to give a brief summary of the whole al-

gorithm. Firstly, as done in the static scenario, we ap-

ply the inverse camera function to every LDR image

of the bracketing of pictures taken with different time

exposures, obtaining the partial radiance map for each

one of them. These radiance maps are radiometrically

aligned using the camera function with the exposure

time of the reference image. These modiﬁed images

are used to compute a dense correspondence ﬁeld, us-

ing the optical ﬂow algorithm of Chambolle and Pock

(Chambolle and Pock, 2011), for every image with

respect to the reference one. These correspondences

are subsequently ﬁltered using a reﬁnement step: for

every pair of images, we compensate the motion be-

tween them and compute the absolute value image

difference. The histogram of this image difference is

modeled as a mixture of Gaussians, which allows us

to distinguish between correct and erroneous corre-

spondences. Finally, we use the corrected correspon-

dences to obtain a gradient ﬁeld that we integrate by

solving a Poisson equation. To avoid color bleeding

and other color artifacts we set a randomly selected

group of points as Dirichlet boundary conditions. The

intensity values of these points are computed through

the Debevec-Malikintensity fusion of the aligned pix-

els.

The ﬁrst step of the algorithm has already been de-

scribed in the previous section, we present and discuss

the following steps in separated subsections.

3.1 Radiance Registration

As previously declared, the goal of our method is to

increase the detail rendition of the reference radiance

map in the areas where the original LDR reference

image was over/under exposed. The aim is to obtain

these missing details from other images of the brack-

eting without creating artifacts produced by merging

motion pixels. Thus, we need to distinguish motion

pixels that we do not want to fuse from details that

appear in other images (but not in the reference one)

GENERATION OF HDR IMAGES IN NON-STATIC CONDITIONS BASED ON GRADIENT FUSION

that we actually want to fuse. To explain the problem

let us consider the two HDR radiance maps shown in

Figure 2.

Figure 2: Radiance maps of two pictures shown

with the software HDRshop (available online at

http://www.hdrshop.com/) useful to exemplify the ra-

diance registration process (images courtesy of O.Gallo).

From the two images in Figure 2 we take the right

one as reference. In this case we would like to intro-

duce the detail of the texture on the wall present in

the left image, avoiding the girls that cover it, given

that we want to maintain the scene of the reference

image. A registration algorithm based on intensity

or geometry comparison cannot distinguish between

wall details and people passing by, thus we need to

modify the radiance maps before operating the regis-

tration, in such a way that the pixels corresponding to

wall details are matched for fusion but not those cor-

responding to the girls. More generally, we need a

pre-registration step that modiﬁes the radiance maps

so that the registration process will match the most

precise details, i.e. those coming from dark areas of

overexposed images and from bright areas of under-

exposed images.

Our tests have shown that the more efﬁcient ra-

diometric modiﬁcation for this scope is given by the

application of the camera response function with the

(ﬁxed) time exposure of the reference image, to each

radiance map, as also observed by (Kang et al., 2003).

Thus instead of I

we work with the modiﬁed im-

ages f(∆t

ref

(x)). Notice that the reference image

remains unchanged while for the others the transfor-

mation amounts to a normalization of the exposure

time. Notice that, since the range of f is {0, . . . , 255},

after this process the radiance maps become a new set

of LDR images. The advantage of this transformation

is that the intensity levels become closer and that the

image areas corresponding to the over/under-exposed

values of the reference image also appear saturated in

the other radiometrically aligned images.

After this pre-registration step, we can apply any

optical ﬂow method over the new set of LDR images.

We used the method of Chambolle and Pock (Cham-

bolle and Pock, 2011) which provides dense corre-

spondences between pixels. Although the matchings

are accurate, the method can produce errors on the

boundaries of moving objects and the areas where ob-

jects disappear due to motion. Thus a reﬁnement step

is needed to check whether the correspondences are

correct or not.

3.1.1 Reﬁnement Step

Let us assume that we have two radiometrically

aligned images I

ref

, I

, j = 1, . . . , N, without motion.

The pixel-wise distance between them deﬁnes the dif-

ference image kI

ref

(x) −I

(x)k that depends on their

noise. If we model this noise as additive and Gaus-

sian, then the difference image histogram will be

highly populated close to zero. As the motion (or mis-

matches) among the images increases, more modes

appear in this histogram. We therefore propose mod-

eling this difference histogram as a set of Gaussians

using a Gaussian Mixture Model (GMM) where the

most probable Gaussian is associated to the prop-

erly matched pixels and the other Gaussians represent

matchings that are not correct. Let the most proba-

ble Gaussian be characterized by a median µ and a

standard deviation σ. We deﬁne as a mismatch those

correspondences with a distance from µ given by ασ,

where α is a parameter of the algorithm. After the re-

ﬁnement step, a pixel of the reference radiance map

can have a set of correspondences in pixels of the

other images of the sequence or no correspondence at

all if the pixel belongs to an object that appears only

in the reference image.

4 GRADIENT FUSION

After the steps previously discussed we know which

pixels can be fused without generating artifacts in the

ﬁnal HDR image. Here we examine the process that

will add details to the reference radiance map from

the others in the set. Let us begin by observing that

in general we do not have correspondences between

all pixels of the reference image and pixels in all the

other images of the bracketing, thus an intensity fu-

sion can create artiﬁcial edges, as can be seen in Fig-

ure 3.

Note that the people are moving along the se-

quence, thus, their intensity values are being copied

from the reference image to the ﬁnal image while

the other areas are computed by a weighted average

among the corresponding pixels. This difference gen-

erates new edges around the subjects in motion. In

order to avoid this problem, we propose using gradi-

ent fusion techniques in the Log-scale. Let us set for

this scope

= log

), j = 1, . . . , N.

VISAPP 2012 - International Conference on Computer Vision Theory and Applications

Figure 3: Detail of a result obtained by building radiance

maps with an intensity fusion process, it can be seen that

artiﬁcial edges appear (in particular around the moving peo-

ple). Image (courtesy of O. Gallo) shown with HDRShop at

a ﬁxed time exposure.

Poisson Editing (P´erez et al., 2003) allows mod-

ifying the features of an image without creating new

edges or artifacts in the LDR domain. The idea is

to copy a target gradient ﬁeld in a region Ω

′

of the

image domain which is then integrated by solving a

Poisson equation. Thus, the problem is to properly

choose the target gradient ﬁeld. To do that, recall that

our aim is to improve the detail rendition of the ﬁ-

nal HDR image, so we must give more importance to

gradients with largest norm. As discussed in (Piella,

2009), if we consider the weighted second moment

matrix G

(x):

(x) =







∑

j=1



(x)

∂

∂x



∑

j=1

(x)

∂

∂x

∂

∂x

∑

j=1

(x)

∂

∂x

∂

∂x

∑

j=1



(x)

∂

∂x









(2)

where the partial derivatives are com-

puted at the point x = (x

, x

) and s

(x) =

k∇

(x)k



∑

i=1

k∇

(x)k

, then the predom-

inant gradient direction is given by the largest

eigenvector of G

(x) and the corresponding eigen-

value gives its norm. In this process the sign of the

gradient is lost. In our experiments, we have seen that

the best results are achieved when we restore the sign

to be that of the gradient with maximum modulus.

We can now deﬁne the target vector ﬁeld for Pois-

son editing as follows: given a pixel x in the reference

image, from all gradients of the bracketing of images

at x, we select the gradient with largest modulus. Let

us denote it by M(x). Then the target vector V in x is

deﬁned as:

V(x) =

√

λε(x)θ, (3)

where λ is the largest eigenvalue of G

(x), θ its asso-

ciated eigenvector, and

ε(x) =

(

−1 if hθ, M(x)i ≤0;

1 otherwise.

We stress that V(x) is not necessarily a conservative

vector ﬁeld and, as remarked by Tao et al. (Tao et al.,

2010) this can lead to bleeding effects along strong

edges. In order to stop the bleeding effect, we have

introduced Dirichlet boundary conditions at a set of

randomly chosen points of Ω taken from the set of

points for which there exist reliable correspondences.

For them we have set the intensity as the radiance ob-

tained with the Debevec-Malik intensity fusion.

5 RESULTS AND COMPARISONS

Now that the method has been described we can pro-

ceed to give some implementation detail. The op-

tical ﬂow method of Chambolle and Pock was ap-

plied to the luminance values of the radiometrically

aligned images. For the reﬁnement step we modeled

the histogram of image differences as a GMM (Gaus-

sian Mixture Model) with two components. A ﬁnal

step in the reﬁnement process is introduced to avoid

taking into account pixels on the boundaries: inter-

preting the mismatches as motion masks, we apply to

these masks a dilation ﬁlter with a 6×6 structuring

element (Gonzales and Woods, 2002). In the fusion

process we randomly select the 10% of the total image

area as possible Dirichlet points keeping only those

with matches. Finally, we solve the Poisson equation

using the Conjugate Gradient method for each color

channel independently.

Let us now discuss the results of our proposal.

Since HDR images cannot be represented on a LDR

display, to show the results obtained from our algo-

rithm we will show snapshots of the image provided

by the free HDRShop software, available online at

www.hdrshop.com, at a given exposure time. The

comparison with the state of the art will be done fol-

lowing the procedure used in other papers, that is, by

comparing the tone mapped versions of the HDR im-

ages.

First of all we would like to start by showing the

improvement obtained using our method. In Figure 4

we can see two original partial radiance maps com-

pared to our results. The enhancement is specially

obvious on the building wall (ﬁrst row), where our

method recovers texture and color, and also in the

trees, which show much more details (second row).

The parameter α controls the ﬂexibility in the se-

lection of matches in the registration process. Our

GENERATION OF HDR IMAGES IN NON-STATIC CONDITIONS BASED ON GRADIENT FUSION

Figure 4: Left column: original reference radiance map

at two different time exposures set in the HDRshop soft-

ware. Right column: corresponding enhanced image with

the method proposed in the paper. The parameter α was set

to 1.

experiments have shown that a value of α that gives

overall good performances is 0.5, for which we have

found no artifacts in the ﬁnal images. As we approach

1 we generate more details, but we might also create

artifacts, as can be seen in Figure 5.

Figure 5: From left to right: results of our algorithm ob-

tained by setting α = 0.5 (no artifacts) and α = 1 (artifacts

appear), respectively.

The selection of the reference image can also in-

ﬂuence the appearance of ghosts or artifacts. We have

in fact observed that when a moving pixel with a color

similar to the background is located in an area satu-

rated by the camera function, then the reﬁnement step

may fail to distinguish background from foreground

and color artifacts may appear. We can see an exam-

ple in Figure 6: in the ﬁrst row we present two images

of the bracketing that were used as two different ref-

erence images. The corresponding results are shown

in the second row. In both cases the parameter value

is α = 1. Note that the result shown on the left hand

side has an artifact on the puppet’s leg. The reason

is that the reference image is saturated in that area,

so the reﬁnement step cannot distinguish between the

puppet’s leg and the ball.

Finally, we show the comparison between our re-

Figure 6: First row: two different original images taken as

reference. Second row: output of our algorithm. It can be

noticed an artifact in the left hand image due to the failure

of the reﬁnement step explained in the text.

Figure 7: First row, from left to right: tone mapped results

of our HDR generation model and that of Gallo et al., re-

spectively. Second row: detail magniﬁcation of the pictures

above. The color difference is due to the different tone map-

ping operators used. We stress that the artifact visible in the

image of Gallo et al’s is not produced by the tone mapping

operator, but by their HDR formation model.

sults and those of Gallo et al. (Gallo et al., 2009)

who also use a gradient fusion technique. Since they

present their results using tone mapped versions of

their images, we also used a tone mapped version of

ours. In Figure 7 we can see that our method avoids

the generation of geometry artifacts as well as bleed-

ing.

VISAPP 2012 - International Conference on Computer Vision Theory and Applications

6 CONCLUSIONS

We have proposed a method for HDR image creation

in the non-static scenario where photographs have

been taken with a moving hand-held camera and/or

the scene to be captured is dynamic. Our method

is based on gradient fusion techniques that compares

well to the state of the art. We have computed re-

liable correspondences by analyzing the differences

of registered images using a GMM model. We have

pointed out the importance of using gradient-based

method instead of intensity-based methods. Finally,

we proposed a technique in which a suitable selection

of Dirichlet conditions permits to avoid or strongly

reduce the bleeding artifacts that may appear after the

integration of vector ﬁelds.

ACKNOWLEDGEMENTS

The authors would like to thank Dr. Orazio Gallo for

kindly providing his images. They would also like

to acknowledge partial support by PNPGC project,

reference MTM2006-14836, and by GRC refer-

ence 2009 SGR 773 funded by the Generalitat de

Catalunya. S. Ferradans was partially supported by

ERC Grant n279593 SIGMA-Vision. E. Provenzi ac-

knowledges the Ramo´on y Cajal fellowship by Minis-

terio de Ciencia y Tecnolog´ıa de Espa˜na. V. Caselles

also acknowledges ‘ICREA Acad`emia’ prize by the

Generalitat de Catalunya.

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GENERATION OF HDR IMAGES IN NON-STATIC CONDITIONS BASED ON GRADIENT FUSION