Multiple exposure fusion for high dynamic range image acquisition.bak

358 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 21, NO. 1, JANUARY 2012

Multiple Exposure Fusion for High DynamicRange Image Acquisition

Takao Jinno, Student Member, IEEE, and Masahiro Okuda, Member, IEEE

Abstract—A multiple exposure fusion to enhance the dynamicrange of an image is proposed. The construction of high dynamicrange images (HDRIs) is performed by combining multiple im-ages taken with different exposures and estimating the irradiancevalue for each pixel. This is a common process for HDRI acquisi-tion. During this process, displacements of the images caused byobject movements often yield motion blur and ghosting artifacts.To address the problem, this paper presents an efficient and accu-rate multiple exposure fusion technique for the HDRI acquisition.Our method simultaneously estimates displacements and occlusionand saturation regions by using maximum a posteriori estimationand constructs motion-blur-free HDRIs. We also propose a newweighting scheme for the multiple image fusion. We demonstratethat our HDRI acquisition algorithm is accurate, even for imageswith large motion.

Index Terms—High dynamic range image (HDRI), maximum aposteriori (MAP) estimation, multiple exposure.

I. INTRODUCTION

B Y ADAPTING TO lights in any viewing condition,the human visual system can capture a wide dynamic

range of irradiance (about 14 orders in log unit), whereas thedynamic range of charge-coupled device or complementarymetal–oxide–semiconductor sensors in most of today’s cam-eras does not cover the perceptional range of real scenes. Itis important in many applications to capture a wide range ofirradiance of natural scene and store it in each pixel.

In the application of CG, a high dynamic range image (HDRI)is widely used for high-quality rendering with image-basedlighting [1], [2]. Nowadays, HDR imaging technologies havebeen developed and some HDR sensors are commercially avail-able. They are used for in-vehicle cameras, surveillance in nightvision, camera-guided aircraft docking [1], [4], high-contrastphoto development [3], robot vision [5], etc.

In the last decade, to capture the HDRI, many techniqueshave been proposed based on the multiple-exposure principle, inwhich the HDRI is constructed by merging some photographsshot with multiple exposures. Many of the techniques assumethat a scene is static during taking photographs. The motion ofobjects causes motion blur and ghosting artifacts. Although in

Manuscript received August 12, 2009; revised April 28, 2011; accepted June04, 2011. Date of publication June 30, 2011; date of current version December16, 2011. This work was supported in part by the Grant-in-Aid for Young Sci-entists under Contract 14750305, by the “Invitation Fellowship Programs forResearch in Japan” of the Japan Society for the Promotion of Science, and bythe Human Media Creation Center. The associate editor coordinating the reviewof this manuscript and approving it for publication was Prof. Kiyoharu Aizawa.

The authors are with the Faculty of Environmental Engineering, The Univer-sity of Kitakyushu, Kitakyushu 808-0135 Japan.

Digital Object Identifier 10.1109/TIP.2011.2160953

some fields, such as video coding and stereo vision, many dis-placement (or motion) estimation methods are proposed; simplyapplying them into the multiple exposure fusion often fails sincethe intensity levels of the images are significantly different dueto the failure of camera response curve estimation, and more im-portantly, low and high exposure causes blackout and whiteoutto some regions of the images, respectively, in which corre-spondence between the images is hard to find. Moreover, in thecase of low exposure, noises such as thermal noise and darkcurrent sometimes make the displacement estimation difficult.None of the conventional methods [1]–[11] addresses all of theproblems.

In this paper, we propose an algorithm of the HDRI estima-tion based on the Markov random field (MRF) model. We canconstruct the HDRI by taking into consideration displacements,underexposure and overexposure (saturation), and occlusions.The displacement vectors, as well as the occlusion and the satu-ration, are detected by the MAP estimation. In our method, wedo not need to estimate accurate motion vectors but displace-ment to the pixel with the closest irradiance, whereas the con-ventional methods such as [9] try to accurately estimate the mo-tion. This relaxation improves the final quality of the HDRI. Theocclusion and the saturation are clearly classified and then sepa-rately treated, which results in the accurate removal of ghostingartifacts.

In the following section, we introduce a technique forcombining the multiple exposure images. We point out thatweighting functions used in the conventional methods have adrawback in a case of capturing a scene with movement andthen propose a new weighting function. A motion compensationtechnique is proposed in Section III. In Section IV, we showsome experimental results to confirm the validity of our work,in comparison with other methods, and then, we conclude thispaper in Section V.

II. MULTIPLE EXPOSURE FUSION

A. Overview

The HDRI is constructed by combining multiple images. Theprocedure for the HDRI acquisition is informally described asfollows.

1) The images are acquired with different exposure settings.In our method, we assume that the exposures are set bychanging shutter speed, while the aperture is fixed, and weobtain a set of ordinary low dynamic range images with8 bits/channel. In general, there is a nonlinear relationshipbetween the pixel values of the 8-bit images acquired by acamera and the values of actual irradiance. To compensate

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JINNO AND OKUDA: MULTIPLE EXPOSURE FUSION FOR HIGH DYNAMIC RANGE IMAGE ACQUISITION 359

for this nonlinearity, the photometric camera calibrationdescribed in Section II-B is performed for the input images.

2) We select a main image from the multiple exposure im-ages. For each of the other images, the displacement fromthe main image, which is mainly due to object movements,is found. In practice, we select an image with medium ex-posure as the main image in a default setting. Furthermore,the occlusions and underexposed and overexposed regionsare found for the images. This is done by the MAP-basedmotion compensation method in Section III.

3) To improve the accuracy for discriminating the occlusionand the saturation (i.e., underexposed and overexposed re-gions), we employ the postprocessing in Section III-D. Fi-nally, we combine the images to create the HDRI.

B. Photometric Camera Calibration

The relationship between irradiance and the amount of lightsthat we measure through some sensor can be expressed by

(1)

where is the exposure time (shutter speed).In many camera sensors, captured signal is recorded

at more than 8 bits in a so-called “raw image” format. Theraw image is nonlinearly transformed through some imageprocessing such as the gamma correction. Then, the pixel isquantized to 8 bits. We assume that the nonlinearly transformed8-bit images are obtained as an input. For convenience, we setthe range of to [0, 1]. To accurately retrieve the irradiance,we need to compensate for the nonlinearity by estimating thetransform. Here, we approximate it by a single curve and call it“camera response curve,” denoted by

(2)

If one uses the raw images and an image sensor has linearsensitivity characteristics, this photometric calibration can beskipped. To accurately retrieve the irradiance, a dequantizationprocedure is necessary. However, since we may assume thatthe image is densely quantized and the quantization errorhardly affects the quality of the HDR acquisition, we ignore thequantization effect.

Among the existing methods for the calibration problem, weadopt the method in [8] to find , in which the curve is approxi-mated by a low-order polynomial using multiple images and thevalues of exposure ratios between the images. Once the curve isestimated, the irradiance is derived from (1) and (2) as

(3)

In our method, the multiple exposure images are taken byvarying the exposure time of a camera with other settings fixed.Then, the images are merged to create the HDRI by

(4)

where is a value of the pixel of the th exposure image.is the number of images, is the exposure time of the th

Fig. 1. Two examples of weighting functions: (left) hat function and (right)Gaussian function.

Fig. 2. Weighting functions of five adjusted exposure images: (top) conven-tional weights and (bottom) our weights.

image, and is a weighting function. The weighting functionhas small values for the underexposed and overexposed pixels,and these pixel values are ignored. If a scene is completely staticand the images are aligned, we may safely combine the imagesby (4). However, if there is motion between images, ghostingartifact may appear in . The main goal of this paper is toaddress the ghosting problem.

C. Weighting Function

In (4), the weighting function is introduced because underex-posed or overexposed regions are much less reliable than the re-gions of middle intensities. Thus, in the conventional methods,the weight is specified to be small for pixel values near satu-ration values 0 and 1 and high for the middle intensities. Twoexamples for the weighting functions used in the conventionalmethods [6], [7] are shown in Fig. 1. The role of the weight isto discard saturated pixels. The region where the pixel valuesare close to 0 or 255 is backed up by other exposure with largerweight. In the conventional methods, the weighting functionsare built based on the assumption that middle intensities around0.5 have high reliability for irradiance estimation. From (1) and(2), one can denote the weighting function as the function of theirradiance . The Gaussian function in Fig. 1 (right) inthe irradiance domain is depicted in Fig. 2 (top), where five ex-posures are used . The conventional weighting in Fig. 2(top) have two drawbacks. First, in very dark area, all of the ex-posures have similar weights. This means that all the images aresummed up in some degree, even if the images with high expo-sure are completely underexposed or corrupted by dark currentnoises in the dark area. This results in noisy and ghosting arti-facts, as shown in Fig. 15. The other drawback is that much of



irradiance is covered by several images. If a scene remains com-pletely static during taking photographs, the weighting functionworks well. Otherwise, however, it yields ghosting artifacts asthe multiple images are combined in the overlapped region. Thisoverlap makes it easy to yield the ghosting artifacts. To addressthe problem, we rearrange the weighting function to

(5)

where is a parameter that controls the width of the functionand

The weighting functions in the case of are shown inFig. 2 (bottom). The functions relieve the overlap. Each expo-sure independently covers some region, which results in the re-duction of offset noise and ghosting artifacts. In particular, thedark area is supported only by the lowest exposed image, whichcan reduce the artifacts. Note that, even though the lowest andhighest exposures have large weights in the unreliable irradi-ance regions, the effect is minor since other exposures are lessreliable than these in high- and low-irradiance regions.

III. MOTION COMPENSATION

A. MRF Model

in (2) can be derived by only when pixels are notunderexposed or overexposed. Moreover, (4) is effective onlywhen a scene is static. Since moving objects cause the motionblur, it is required to compensate the displacement as muchas possible. The compensation is usually done by two steps,i.e., global motion and local displacement compensation steps.In our method, we assume that the global motion (e.g., mo-tion caused by camera shake) has been already compensatedby some image alignment algorithm [1]. Here, we focus on thelocal displacement compensation.

In our situation, the displacement estimation may fail due to1) occlusion, 2) saturation, that is, underexposure and overex-posure, and 3) differences in intensity caused by the failure ofthe camera response curve estimation. Fig. 3 illustrates an ex-ample of two exposures, where some regions of the high-expo-sure image is overexposed [white region in (a)] and underex-posed [black region in (b)]. There may be three types of regionswhere correspondence between the images is hard to find: 1)occlusion [marked by light gray in (c)]; 2) saturation (overex-posure marked by white); and 3) both of the two (dark gray).

In our approach, we simply search the closest value within awindow for the hole caused by the occlusion, whereas, in thesaturated area, we do not compensate for the motion (detail isfound in Section III-D). For the regions where pixel intensitiesvary between images due to failure of the camera response curveestimation, we treat them the same way as the occlusion. In theend, we need to estimate the following two classes, as well asthe displacement vectors: 1) Class I are regions that include theocclusion and intensity mismatch caused by the failure of thecamera response curve estimation, and 2) Class II are regions ofthe saturation, that is, underexposure and overexposure.

Fig. 3. Example of multiple exposure images: (a) high exposure, (b) low ex-posure, (c) occlusion (gray), and saturation (white).

Here, we introduce a probability model for the estimation ofthe displacement between two images and the regions of thetwo classes. Let us denote two measured images with differentexposure, i.e., and

(where is a discrete rectangular sampling lattice in ),which are considered to be samples from a random field. In thisframework, the exposure time of all the images are known, andimages and have been made linear to irradiance values bythe photometric camera calibration method in Section II-B. Thefield is defined on the sampling lattice .

Here, we introduce three random fields, i.e.,, , and, which correspond to the displacement,

the occlusion, and the saturation, respectively. The displace-ment is defined as the apparent motion vector of objectsbetween the two images. Although the displacement field inour framework is similar to the conventional motion vectorfields, they differ in that we try to find a pixel with the closestluminance but high-accuracy estimation (e.g., subpixel search)is not necessary.

is a binary random field that indicates whether each pixelbelongs to the occlusion. Random variable on each site

takes 0 or 1 according to the following rule:

if is in Class Iotherwise,

(6)

Binary process indicates the occlusion.The saturation is defined by the region of the underexposure

and overexposure in image . This is also a binary random fieldthat indicates the following saturation:

if is in Class IIotherwise,

(7)

In our method, instead of and , we estimate complement vari-ables and , which have “0” in the cases of Classes I and II,respectively.



Since all of these three fields mostly consist of some regionsof similar values, they can be considered as the MRFs. Our es-timation problem is to find the most likely fields , , and byusing observed images and , that is, maximizing the pos-terior probability . Applying the Bayes rule, theposterior probability is written by

(8)

Since the denominator of (8) is independent to variablesand , the problem to solve is stated as the maximization of thenumerator, that is, our MAP estimation is

(9)

Since , , and are modeled by the MRFs, probabilitycan be characterized by the Gibbs distribution

[12]–[14], i.e.,

(10)

where , , and are an energy function, a normalization con-stant, and temperature, respectively. Then, MAP estimation canbe replaced by the minimization problem of the energy function.From (9) and (10), we can formulate the following problem:

(11)

B. Formulation of Energy Functions

The term in (11) characterizes image with, , , and given. In most cases, such as [14]–[19], the func-

tion is defined by the -norm or -norm error between theblocks of and . In our case, since the difference in pixelvalues of and its corresponding pixels in sensitively af-fects the quality of the final HDRI while an accurate motionestimation is not necessary, we use the minimum value of thedifference as

(12)

where is a block of pixels around the center pixel . Weuse the block of 31 31. The above error assumes that pixeland its corresponding displaced pixel in ideally coincides. InClass I, however, it is not the case. Furthermore, since the valueof the luminance cannot be estimated in the areas of Class II,the assumption does not hold. Considering these, we define thefollowing energy function:

(13)

This equation excludes the occlusion and the saturation from thecost function.

The second term of (11) is a cost imposed on displacementvectors . Since the displacement generally occurs due to objectmovements, the displacement vectors should be smooth. Thus,we define the energy function as follows:

(14)

where is a block around center pixel . Note that we usedifferent notations for and since they have differentsets of sites on neighborhood. In practice, we use 3 3 blocks.

The third and forth terms in (11) are constraints on the regionof and . Since the occlusion mainly depends on objects andthe failure of the camera response curve do not happen in anisolated pixel, we impose a penalty on the isolated small regionsby

(15)

where is an operator that counts the number of value “1” inthe eight adjacent pixels and is the potential function thathas the minimum value at 0. The saturated area has the value ofeither 0 or 1. Again, the isolated small regions are penalized by

(16)

where

ifotherwise.

(17)

From (11)–(16), the energy function to minimize is definedas

(18)

where are weights.

C. Suboptimal Search

The nonlinearity of (18) makes the minimization problemhard to directly solve. To address the difficulty, some relaxationalgorithms have been proposed such as simulated annealing[12] and the mean field theory [16]–[18]. The former has highcomputational complexity. The latter can relieve the com-plexity, but it is not straightforward to apply it to our problem.



Fig. 4. Multiple exposure images. (Upper row) Input images. (Lower row) Histograms. (a) � . (b) � . (c) � (main image). (d) � . (e) � .

In our method, instead, we adopt a suboptimal approach similarto [15].

In our search, the estimations of the displacement, the oc-clusion, and the saturation are independently performed. In theestimation algorithm, we adopt a block-based search for the oc-clusion and the saturation, whereas a pixel-based search is per-formed for the displacement. In the displacement estimation,we simply search the closest value in block for each pixel.Given the disparity, we find blocks with large cost in (18) andthen set them as occlusions. Similarly, given the disparity andthe occlusion, we search the block with a high energy value in(16), and the saturation map is formed. These steps are iterateduntil cost (18) is unchanged. After all, the algorithm is stated asfollows.

[Estimation Algorithm]

1) (Initial setting) Search the pixels that have small valuesin the forth term of (18) and then set them as .Initial displacement vectors are found by searching thepixel with the closest pixel value in window , and set

if the value at the site is above a prescribedthreshold; otherwise, set .

2) For each pixel , search the corresponding pixel withminimum difference (12), and set the displacement to .

3) The blocks with high values in (18) are set as Class I, thatis, .

4) The blocks with high values in (16) are set as Class II,that is, .

5) Ifholds, then

stop (where is the number of iterations). Otherwise,go to Step 2.

D. Postprocessing

Using the above algorithm, we can determine the regions ofthe occlusion and the saturation and obtain the displacementvectors, except in these areas. Next, it is necessary to combinethe images using the information. Due to space limitation, here,we consider only the case where has lower exposure than .Thus, the underexposed area of is also underexposed in .When has higher exposure than , the underexposure andoverexposure are inversely treated in the following algorithm.

In the occlusion, we simply search the closest value withinthe window in for each pixel in and then set it as the corre-sponding pixel, whereas, in the overexposure region, we do notcompensate for the motion. In the estimation of Section III-C,we independently determine the saturation and the occlusion.However, since in the saturated region, there can be also occlu-sion [such as the dark gray region in Fig. 3(c)], we need to findthe occlusion in the saturated areas. We solve the problem by athresholding method as follows. Since we assume that we shootthe multiple exposure images with changing only the exposuretime, the amounts of light of the two images at some pixel arerewritten from (1) as

constant (19)

where is the exposure time of and is the difference ofthe exposure time of the two images.

Suppose that the dynamic range of the sensor is . Then,if is larger than 1 (that is overexposure), its measured valueis saturated to 1. Thus, the actual value for satisfies

(20)

Substituting this to the first equation in (19), we obtain

(21)

From these, we set the pixels satisfying (21) as the saturation,i.e., those less than as the occlusion.

IV. EXPERIMENTAL RESULTS

In order to evaluate the validity of the proposed algorithm, wehave conducted for two examples. Weights , , and usedin (18) are 0.003, 0.5, and 0.5, respectively. The selected blocksizes of and are 31 31 and 3 3 integer samplinglattices, respectively. The potential function used in (15), (16),and (18) is

where is a scaling factor.In the first experiment, we shot five photographs by changing

the shutter speed setting, while the aperture is fixed, and usethem as an input for our algorithm. The shutter speed settingsthat we used are 1/125, 1/80, 1/50, 1/30, and 1/20 (in seconds).



Fig. 5. Underexposure map. (a) � . (b) � . (c) � . (d) � .

Fig. 6. Overexposure map. (a) � . (b) � . (c) � . (d) �

Fig. 7. Occlusion map. (a) � . (b) � . (c) � . (d) � .

The input images and their histograms are shown inFig. 4. We select a single main image [ in Fig. 4(c)] from themand apply the methods in Sections III-C and III-D to the pair ofthe main and each of the other four images. Then, the modifiedimages are merged by (4).

In Figs. 5–7, we show the maps of the underexposure, over-exposure, and Class I, respectively. These are obtained by theMAP estimation, followed by the postprocessing, in which thewhite pixels are judged as the underexposure, overexposure, and

Fig. 8. Our result (it is tone mapped to displayable range)

Fig. 9. (From upper left to lower right) Motion blur in dark region: blockmatching, HDR video [9], ghost removal [1], and photomatix [23].

Fig. 10. (From upper left to lower right) Motion blur in highlights: blockmatching, HDR video [9], ghost removal [1], and photomatix [23]

Class I, respectively. Fig. 8 depicts the HDRI constructed by ourmethod (for displaying, its dynamic range is scaled and then



Fig. 11. Scene with large motion.

Fig. 12. Results: (left) photomatix and (right) our method.

Fig. 13. Noise in underexposure region: (left set) photomatix and (right set)our method

Fig. 14. Ghost: (left) photomatix and (right) our method.

compressed by a tone mapping). In the set of input images, theface moves in the dark area, while his left elbow moves fromthe bright region of the sky to the dark region of the pole. Itis shown in Fig. 8 that our algorithm reconstructs the irradiancewell and successfully removes the blur caused by these motions.In Figs. 9 and 10, we show some comparisons with four conven-tional methods: 1) a standard block matching algorithm; 2) an

Fig. 15. Two examples of scenes under the circumstances of day light and nightview. Note that we select the highest exposure as the main image in (a) forimproving visibility, whereas medium exposure is used for the other examples.(a) Night view. (b) Day light.

HDR video [9] with Lukas–Kanade optical flow estimation [20];3) ghost removal in [1]; and 4) the commercially available soft-ware Photomatix [23]. We implement 1 and 2 using OpenCVand are used in substitution for the method in Section III-C.Other processing, such as in Section III-D, remains unchanged.When implementing the conventional methods, if the motion



vectors are unreliable, they are set to 0 for the pixels (note thatwe have confirmed that a large error occurred when simply ap-plying the methods without these treatments). The results of 3and 4 are obtained using the software in [22] and [23]. Theseconventional methods often fail to compensate for the motiondue to the saturations and the noises, as is described in Section I.The block-matching-based algorithm often yields blocking arti-facts and is sensitive to luminance change caused by an inaccu-rate calibration of the camera response curve. The method in [9]fails particularly for the underexposed regions since the offsetnoises significantly affect the performance. The ghost removalin [1] performs worst among these methods. Photomatix tendsto cause large errors in highlights. We have tested some otherexamples and confirmed that our method performs best for allthe tests.

The advantage of our method is most evident when the mo-tion is large. For the second example, we create the HDRI fromthe three images (see Fig. 11) with large movements, and theresults are illustrated in Figs. 12–14. Here, we show only the re-sult of Photomatix among the four conventional methods sincethe qualities of the other three results are much poorer. In thesefigures, Photomatix (left) has some ghosting artifacts, whereasthe proposed method (right) does not because of accurate esti-mation and our new weighting function. We have tested someother examples and confirmed that our method performs bestfor all the tests. Fig. 15 shows additional examples with largemotions. The proposed method is superior to the conventionalmethods for most of the examples we have tested.

V. CONCLUSION

We have propose a method for the multiple-exposure fusion.In the method, the MAP-based method estimates occlusion,saturation, and displacements between input images and thenconstruct the HDRIs by removing the artifacts. While in theconventional work it is hard to eliminate the ghosting artifacts,particularly when large motion occurs, the proposed methodcan compensate for the effects of motion, the occlusion, andthe saturation and can obtain motion-blur-free HDRIs.

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Takao Jinno received the B.E. degree from The Uni-versity of Kitakyushu, Kitakyushu, Japan, in 2007.

He has been with the Graduate School of Environ-mental Engineering, The University of Kitakyushu.He is engaged in high dynamic range imageprocessing.

Masahiro Okuda received the B.E., M.E., andDr.Eng. degrees from Keio University, Yokohama,Japan, in 1993, 1995, and 1998, respectively.

He was with the University of California, SantaBarbara, and Carnegie Mellon University, Pittsburgh,PA, as a Visiting Scholar in 1998 and 1999, respec-tively. He has been with Faculty of The University ofKitakyushu, Kitakyushu, Japan, as an Associate Pro-fessor of environmental engineering since 2001. Hisresearch interests include filter design, vision/geom-etry coding, and multirate signal processing.


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Multiple exposure fusion for high dynamic range image acquisition.bak