A distortion-free data hiding scheme for high dynamic range imagesChung-Min Yu,Kuo-Chen Wu,Chung-Ming Wang ⇑Institute of Computer Science and Engineering,National Chung Hsing University,250Kuo Kuang Road,Taichung 402,Taiwan,ROCa r t i c l e i n f o Article history:Received 18December 2009Received in revised form 8February 2011Accepted 21February 2011Available online 27February 2011Keywords:High dynamic range images Data hiding Distortion-freeMessage embedding Steganographya b s t r a c tIn this paper we present a distortion-free data hiding algorithm which can embed secret messages into high dynamic range (HDR)images.Our scheme provides three significant benefits.First,it enables us to convey secret messages to produce a stego HDR image.When we operate the tone mapping technique to reduce the high contrast to a displayable range,no distortion is encountered between the tone-mapped cover and the stego images.A quantitative measure verifies that histograms of the cover and stego HDR images are correlated with linear dependency.To the best of our knowledge,our algorithm is the first approach in HDR literature that can provide capability of distortion-free data embedding.For the appli-cation of image annotation,the average capacity offered by our method is in the range of 0.12–0.29bits per pixel.Our scheme provides an average capacity in the range of 0.0010–0.0026bits per pixel for the application of image steganography where the stego HDR image preserves an HDR image encoding for-mat which does not cause any suspicion by eavesdroppers.Second,our algorithm performs with adaptive message embedding where pixels conceal different amounts of secret messages based on their homoge-neous representations.Quantitative analysis indicates that our algorithm offers an insignificantly small magnitude of the maximal pixel difference between the cover and stego HDR images.This feature and the histogram distribution of similarity between the cover and stego HDR images increase the difficulty of detecting whether any message is hidden in an HDR image.Third,our scheme is efficient.The time required for message embedding or extraction is in the range of several hundred milliseconds.Our approach belongs to a blind detection where the messages can be extracted without referring to the ori-ginal cover HDR image.We believe our proposed scheme is suitable for applications such as image anno-tation or image steganography.Ó2011Elsevier B.V.All rights reserved.1.IntroductionTransmission of private information through the internet in a secret manner is now more frequent due to the prevalence of com-puter science and the internet.This trend encourages researchers to investigate techniques for covert communication.Besides the system of cryptography,data hiding [11]provides an alternative solution to achieving the goal of covert communication.Data hid-ing is a way of secret communication carried out by using various digital multimedia to convey the critical messages,and therefore the major demand here is for both good imperceptibility and a high embedding capacity.Generally,the object in which we intend to embed the secret message is called the cover object indicating that the secret message has not yet been embedded [19].After it has conveyed the secret message,we refer to it as the stego object.While a variety of media,such as text [1],image [17],audio [8],video [10],3D models [2],or general multimedia [7],can serve as a cover object,the image is the most popular medium that is employed for data hiding.An image data hiding technique is usually evaluated in terms of visual quality and embedding capac-ity.The image data hiding algorithm should maximize the amount of messages that can be conveyed in the cover image,and mini-mize the distortion appearing in the stego image caused by the hidden message [17].In addition,data hiding algorithms can be developed to provide features of reversibility.These data hiding algorithms are referred to as reversible data hiding algorithms [14,18]which allow the receiver to extract the embedded data,and completely restore the cover image without losing any of the information.Going one step further,we can produce a stego image without incurring any image distortion which minimizes the distortion to the extreme.This kind of algorithm is referred to as a distortion-free data hiding algorithm.An intriguing feature of the distortion-free algorithm is camouflage of the stego image;consequently,the stego image will not attract much attention by eavesdroppers when it is delivered to the receiver through a public channel.This property makes it useful for data hiding applications such as medical or military image authentication where the quality of the stego image is strictly required,and/or image annotation where sensitivity of the secret message is strictly confidential.0141-9382/$-see front matter Ó2011Elsevier B.V.All rights reserved.doi:10.1016/j.displa.2011.02.004⇑Corresponding author.Tel.:+886422840497915;fax:+886422853869.E-mail addresses:phd9202@.tw (C.-M.Yu),phd9501@.tw (K.-C.Wu),cmwang@.tw (C.-M.Wang).In recent years,there has been an explosion of interest in high dynamic range(HDR)images[13].The‘‘dynamic range’’of a scene is the contrast ratio between its brightest and darkest parts.In con-trast to low-dynamic range(LDR)images,HDR images represent luminance values usingfloating-point numbers for a scene in order to accurately represent the wide range of intensity levels found in real scenes ranging from direct sunlight to deepest shadows.Fig.1 demonstrates the visual difference between LDR and HDR images. The scene has high contrast ratio because of outdoor as well as in-door landscape.When we directly display the LDR image,we lose the details of the outdoor scene because the luminance is out of the range that is supported in an ordinary device.Similarly,the detail in the indoor scene is not visible when we directly exhibit the HDR image.However,we can visualize both details when the HDR image is processed by the tone-mapping operator.Several image processing software and computer games are developed to support HDR images,and they are becoming increasingly popular in variousfields such as digital photography,computer graphics, movies,videogames,and medical imaging.Unfortunately,research in steganography has not kept pace with the advances of HDR images,even though they are expected to replace the low-dynamic range(LDR)images and become the new image standard.To the best of our knowledge,there has been only very limited data hiding work done on HDR images[3].This work produces stego images with high visual quality that is accept-able to human perception.However,an image distortion is inevita-ble due to the hidden messages.In this paper,we provide a new data hiding algorithm that em-beds secret messages into HDR images encoded with the radiance RGBE format[15].Our scheme takes advantage of encoding secret messages to homogeneous representations inherent in the radi-ance RGBE encoding format which has found widespread use in the image community.The scheme provides three significant ben-efits.First,it enables us to convey secret messages to produce a ste-go HDR image.The tone-mapped cover image and the stego images message embedding.The insignificantly small magnitude of the maximal pixel difference and the histogram distribution of similar-ity increase the difficulty of detecting whether any message is hid-den in an HDR image.Third,our scheme is efficient as the time required for message embedding or extraction is in the range of several hundred milliseconds.Our algorithm belongs to a blind detection where the messages can be extracted without referring to the original cover HDR image.Experimental results have verified the feasibility of our algorithm.This paper is organized as follows.In Section2,we review data hiding approaches for HDR images.We then put forward our algo-rithm in Section3.Experimental results are shown in Section4,fol-lowed by the Conclusion and Future Work in Section5.2.Related worksThis section surveys data hiding approaches for HDR images. We were surprised tofind only one paper in the current literature which presents information for HDR data hiding[3].Since that paper utilizes the radiance RGBE encoding as the cover image, we believe it can provide more insight for developing our proposed algorithm.For reference purposes we will briefly describe the ‘‘distortionless data hiding’’that is misleading in the low-dynamic range images,and the approach to producing distortion-free data embedding using permutation.In the following paragraphs we highlight the HDR format,and review the only HDR data hiding algorithm that we have found.A number of data hiding techniques were proposed which use the LDR image as the cover media to convey secret messages. One of these algorithms uses the title of‘‘distortionless data hid-ing’’[20].This causes misconception because the algorithm pro-vides the capability of‘‘reversibility’’which means that once the secret messages are extracted,the original cover image can be restored.Nevertheless,this type of algorithm generates a stegodifference between LDR and HDR images:the LDR image is directly displayed in thefirst column;the HDR image is directly displayed displays the tone-mapping result of the HDR image.226 C.-M.Yu et al./Displays32(2011)225–236encode an optimal message capacity of up to log2(n!)bits,where n is the number of elements to be arranged.The radiance RGBE encoding format[15],originally known as the Radiance picture format,wasfirst introduced as part of the Radiance lighting simulation and rendering system[16].This encoding format has found widespread use for HDR photography and image-based lighting.Other encoding formats include OpenEXR,LogLuv,etc.In the HDR format,the pixel’s color is pre-sented by four channels that include the red,green,blue,and expo-nent channels.This encoding leads to a feature indicating that the representation of a color is not unique.Therefore,we take this advantage to present a distortion-free data hiding algorithm in this paper.Cheng and Wang proposed an adaptive data hiding approach with authentication for a high dynamic range image[3].To the best of our knowledge,their scheme is thefirst such approach for HDR images using the radiance32-bit RGBE encoding.In the radiance format HDR image,the range of luminance intensity is decided by the8-bit exponent value E.Cheng and Wang’s method uses this advantage to classify the pixels into theflat and boundary areas.This pixel classification enables their scheme to remove the restrictions of afixed size of message embedding at each pixel in order to provide larger embedding capacity with little visual dis-tortion.In their reports,their algorithm achieves embedding capacity in the range of 5.13–9.69bits out of32bits of RGBE encoding.Although their algorithm causes image distortion between the cover and stego image,the PSNR values for the tone-mapped stego images are greater than the30dB that is acceptable to human perception.Our survey indicates that an HDR image data hiding algorithm was presented based on the use of the32-bit radiance RGBE encod-ing,and it causes image distortion because of the hidden message. Due to the advantages of data embedding with the distortion-free manner,we believe it is necessary to develop a distortion-free data hiding algorithm which takes this encoding into consideration.Our algorithm is detailed in the next section.3.Our proposed algorithmThis section presents our proposed methods for embedding a secret message into an HDR image without causing any distortion. The method is referred to as a concise fundamental method(CF). This method is simple and direct with an intuitive manner.The low-dynamic range(LDR)images use8bits to represent each of the primary colors,red,green,and blue,leading to a total of24bits of image representations.In an HDR image encoded with the radi-ance format,a pixel is represented by three primary channels fol-lowed by an exponent channel,resulting in a total of32bits of image representation.In each channel,8bits of storage are used so the value at each channel is in the range of0and255.Without loss of generality,let P(r,g,b,e)represent a pixel en-coded with the radiance format,where r,g,and b represent the pri-mary color channels and e indicates the exponent channel which is based on a power of two with the biased number of128.The color of this pixel is afloating point value which can be derived using the floating point conversion as shown in Eq.(1).Similarly,given a col-or in a pixel with thefloating values(R,G,B),we can convert the pixel into the radiance(r,g,b,e)encoding using the integer conver-sion,as shown in Eq.(2),where max(R,G,B)represents the maxi-mum value in the R,G,and B color components.R¼ððrþ0:5Þ=256ÞÂ2ðeÀ128ÞG¼ððgþ0:5Þ=256ÞÂ2ðeÀ128ÞB¼ððbþ0:5Þ=256ÞÂ2ðeÀ128Þð1Þe¼d log2½maxðR;G;BÞ þ128er¼bð256ÂRÞ=ð2eÀ128Þcg¼bð256ÂGÞ=ð2eÀ128Þcb¼bð256ÂBÞ=ð2eÀ128Þcð2ÞDue to the exponent channel that is introduced in the radiance format,we can derive that there is more than one representation todescribe the color of a pixel.For example,we can apply the divisionoperator with the divisor2for each color channel and increase1tothe exponent channel.Given an original pixel P(r,g,b,e),this divi-sion operator will produce a representation A(r/2,g/2,b/2,e+1)which would give nearly the samefloating-point color value andgive identical color after tone mapping for the original pixel pro-vided that components in the color channels,r/2,g/2,and b/2,stillobey the integer form.Similarly,we can apply the multiplicationoperator with the multiplier2for each color channel and subtract1from the exponent channel.This multiplication operator will pro-duce a representation B(2r,2g,2b,eÀ1)which will give nearly thesamefloating-point color value and also give identical color aftertone mapping for the original pixel provided that components inthe color channel,2r,2g,and2b,are within the legal range be-tween0and255.Since each pixel may contain a number of differ-ent representations,the concise fundamental method we proposetakes advantage of this feature to convey the secret message with-out producing any image distortion.We detail this method in thefollowing paragraphs.3.1.Our embedding methodGiven an arbitrary pixel P(r,g,b,e),we define the homogeneous representation group(HRG)for this pixel as a set of representationswhere every element in HRG describes the pixel color identical toP(r,g,b,e).We use the HRG P with the suffix‘‘P’’to denote thehomogeneous representation group for the pixel P.We define thehomogeneity value(HV P)for this pixel as the number of elementsin the homogeneous representation group.We sort every elementin the HRG according to the value represented in the exponentchannel using the ascending order,and assign each sorted elementan index.This allows us to define a homogeneity index(HI)forevery sorted element in HRG where the HI has the range from0to(HV p)À1.As an example,let P(24,160,52,127)represent a pix-el.Then,the homogeneous representation group of this pixel HRG Pcontains three elements as shown in Table1,where the HRG is ex-pressed as HRG P={(24,160,52,127),(12,80,26,128),(6,40,13,129)}.This pixel has the homogeneity value of3(HV P=3),andthe element(24,160,52,127)is assigned to the smallest homoge-neity index of0(HI P=0)because it has the smallest value in theexponent channel.Accordingly,the element(6,40,13,129)hasthe homogeneity index of2(HI P=2).Note that the blue channelin the element(6,40,13,129)contains an odd value of13whichterminates the possibility of applying the division operator.We re-fer to the blue channel as the dominated channel for this pixel.Depending on particular values of a pixel,there are two special cases that we do not determine a pixel’s corresponding HRG formessage embedding.For a pixel P(r,g,b,e),thefirst case is whenthe pixel values in the primary color and exponent channels areTable1An example of a pixel P has four sorted elements in the homogeneous representationgroup(HRG)with the homogeneity value(HV P=3).Pixel P Homogeneityvalue(HV P)Sorted elementsin HRG PHomogeneityindex(HI P)P(24,160,52,127)3(24,160,52,127)0(12,80,26,128)1(6,40,13,129)2C.-M.Yu et al./Displays32(2011)225–236227all zeros,i.e.,P(r,g,b,e)=(0,0,0,0).We refer to this type of pixel as the‘‘null’’pixel.Note that it might be possible for us to apply the division operator255times to produce the homogeneous repre-sentation group,HRG p={(0,0,0,0),(0,0,0,1),...,(0,0,0,255)}, which has the homogeneity value of256allowing us to embed up to8bits of secret message.However,the embedding will pro-duce a relatively large pixel difference after the message embed-ding(see the analysis of pixel difference described in Section 3.3).Therefore,our method does not embed any secret messages when encountering the‘‘null’’pixel.The second special case occurs when the pixel values in the pri-mary color channels are power of2,or one or two of pixel values is/ are zeros,i.e.,P(r,g,b,e)=(2k||0,2k||0,2k||0,e)where k is an integer satisfying the range of06k67and||represents or nota-tion.We refer to this type of pixel as the‘‘neutral’’pixel.Note that the pixel values cannot be all zeros in three channels,because we have defined this kind of pixel as the‘‘null’’pixel.Note again that if the exponent e is less than or equal to248,we can apply the divi-sion operator up to eight times in order to produce the homoge-neous representation group with the homogeneity value of8.For example,when P(r,g,b,e)=(128,128,128,248),there are eight elements in the HRG p where HRG p={(1,1,1,255),(2,2,2,254), (4,4,4,253),...,(128,128,128,248)}.It might be possible for us to adopt this HRG p to embed3bits of secret message.Unfortu-nately,the embedding will produce a much larger pixel difference which becomes evident from the analysis of pixel difference de-scribed in Section 3.3.Consequently,our method excludes the ‘‘neutral’’pixel from message embedding.It is not difficult to determine the homogeneity representation group for a given pixel.In particular,wefirst apply the multiplica-tion operator with the multiplier2to the extreme before we apply the division operator with the divisor2to the extreme.When applying the multiplication rule,the extreme in the multiplication operator means that the components in the color channel are lar-ger than the maximum value of255.The extreme in the division operator,however,means that the components in the color chan-nel have changed to be with thefloating point form.If we operate MU(multiplication)times of multiplication and DI(division)times of division operator,then the homogeneity value of a pixel P is HV P=MU+DI+1.As an example,given a pixel K(20,16,60,127), we consider the color channel(20,16,30)and apply the multipli-cation operator,at most,two times(MU=2)producing two ele-ments,(40,32,120,126)and(80,64,240,125).We cannot apply the multiplication operator anymore because if we do so,the component480will be larger than the maximum value of255. Similarly,we apply the division operator for two times only (DI=2),producing two elements(10,8,30,128)and(5,4,15, 129).We cannot apply the division operator anymore,because if we do so,the component2.5and7.5are with thefloating point forms.The homogeneous representation group of the pixel K is HRG K={(80,64,240,125),(40,32,120,126),(20,16,60,127), (10,8,30,128),(5,4,15,129)}and the homogeneity value of the pixel K will be HV K=2+2+1=5.Note that the homogeneity value of a pixel has the maximal value of7because the component in the color channel must be in the range of0and255.This also means that the homogeneous representation group contains,at most, seven elements.The homogeneity value of a pixel has the minimal value of1indicating that there is an element in the homogeneous representation group which is the pixel itself.Once we have determined the homogeneous group and the homogeneity value of a pixel K,HV K,we can compute the pixel capacity in bits and denote it as C K,as shown in Eq.(3).The pixel capacity indicates how many bits of secret messages that this pixel can offer to convey secret messages.Certainly,the pixel capacity depends on how many elements are in the homogeneous represen-tation group.C k¼b log2ðHV KÞcð3ÞThe embedding process for the cover pixel K(r,g,b,e)can befacilitated using the homogeneity index table(HIT)as shown in Table2.Given a cover pixel K,we can determine the homogeneity value HV K.Depending on this value,thefirst column of Table2lists numbers of bits that can be conveyed.In the third column,we de-scribe the associate bit pattern of the secret message that can be concealed with respect to different homogeneity indices.By refer-ring to the HIT,we can alter the cover status C(HV K,HI K)which re-cords the status of the cover pixel to the stego status S(HV K,HI0K), indicating that a desired bit pattern of the secret message has been conveyed by the stego pixel.The embedding process is best illustrated by an example shown below.Given a cover pixel K(20,16,60,127),following the exam-ple shown above,we can produce the homogeneous representation group for this cover pixel.Table3shows the sortedfive elements in the group where HRG K={(80,64,240,125),(40,32,120,126),(20, 16,60,127),(10,8,30,128),(5,4,15,129)}.Clearly,the cover sta-tus C(HV K,HI K)=C(5,2)because the cover pixel has the homogene-ity value of HV K=5and,according to the sorted elements in HRG K, it has the homogeneity index of HI K=2.Note that since HV K=5,this cover pixel can embed2bits of se-cret message based on the expression shown in Eq.(3).In particu-lar,by altering the cover status C(HV K,HI K)=C(5,2)to S(HV K,HI0K)=S(5,0),appearing in thefirst row third column,we embed two bits of secret message‘‘01.’’In other words,in order to convey two bits of the secret message‘‘01,’’the stego pixel which we should select is the element in the homogeneous representation group HRG K that has the homogeneity index of HI K=0.Conse-quently,the stego pixel is K’(80,64,240,125).As another example, if we intend to embed two bits of the secret message‘‘10,’’we alterC(HV K,HI K)=C(5,2)to S(HV K,HI0K)=S(5,1)in the second row indi-cating that the stego pixel will be K’(40,32,120,126)which has the homogeneity index of HI K=1.We do not need to take any ac-tion if we intend to embed the secret message‘‘11’’because the cover pixel C(HV K,HI K)=C(5,2)happens to have the homogeneity index of HI K=2,which means that C(HV K,HI K)=C(5,2)and S(HV K,HI0K)=S(5,2).Consequently,the stego pixel is exactly the same as the cover pixel.Note that we will not change the cover status C(5,2)to the stego status(5,4)appearing in thefinal row.This is because,though the cover pixel has the homogeneity value ofTable2Homogeneity index table used to embed secret message into a cover pixel K with different homogeneity values HV K.Number ofbitsconveyedHomogeneityvalue(HV K)Homogeneity index0123456 01NP––––––12‘‘0’’‘‘1’’–––––13‘‘1’’‘‘0’’NA––––24‘‘00’’‘‘01’’‘‘10’’‘‘11’’–––25‘‘01’’‘‘10’’‘‘11’’‘‘00’’NA––26‘‘10’’‘‘11’’‘‘00’’‘‘01’’NA NA–27‘‘11’’‘‘00’’‘‘01’’‘‘10’’NA NA NATable3An example of embedding2bits of secret message into a cover pixel K(80,64,240, 125)with the homogeneity value of HV K=5and cover status C(5,2).Sorted elements inHRG KHomogeneityindex(HI K)Status of stegopixelConveyedmessage (80,64,240,125)0S(5,0)‘‘01’’(40,32,120,126)1S(5,1)‘‘10’’(20,16,60,127)2S(5,2)‘‘11’’(10,8,30,128)3S(5,3)‘‘00’’(5,4,15,129)4S(5,4)NA228 C.-M.Yu et al./Displays32(2011)225–236HV K=5,we assign four patterns to represent two bits of secret message.As a result,we denote‘‘NA’’in thefinal row to indicate that we do not assign any bit pattern.We have described the secret message embedding by referring to the homogeneity index table through an example described above.Observing the homogeneity index table shown in Table2 again,the symbol‘‘NP,’’appearing in thefirst row,means that it is not possible to embed the secret message if a pixel has one homogeneity index.The‘‘–’’symbol represents that the homoge-neity index is out of range.Taking the second row as an example, if a pixel K has two elements in its homogeneous representation group,the homogeneity value of this pixel is HV K=2and the pixel has two homogeneity indices,either HI K=0or HI K=1.Homogene-ity indices that are greater or equal to2are certainly out of range. Similar to the embedding example shown in Table2,the‘‘NA’’symbol means that we do not assign any bit pattern.It is worth mentioning that the secret message of the bit pattern associated with the homogeneity index is not identical even though the same numbers of bits are conveyed with different homogeneity values.For example,(HV K,HI K)=(4,0)in the fourth row third column,and(HV K,HI K)=(5,0)in thefifth row third col-umn,all can convey two bits of secret message;however,the for-mer indicates the secret message with the bit pattern‘‘00,’’but the latter depicts the secret message with the bit pattern‘‘01.’’The benefit of adopting the diverse bit pattern is in order to avoid coin-cident alternation of the homogeneity index when embedding the same amounts of secret messages.Another benefit is that the di-verse bit pattern will reduce changes encountered in the histogram distributions(at red,green,and blue color channels)for the stego HDR image.This avoids the attack of histogram inspection that is commonly employed in the steganalytic technique.We will pres-ent a quantitative measure of the histogram distribution in the experimental results which will demonstrate that our proposed algorithm produces a similar histogram distribution even though a number of secret messages have been conveyed in the stego HDR image.Finally,the homogeneity index table is a necessity both in the message embedding and the extraction.Therefore, we can use a secret key,Key-1,to increase the security,thereby avoiding the attack of eavesdroppers.Given an HDR image with a resolution of MÂN,the message embedding in the concise fundamental method is operated using the following four steps:Step1:We examine every pixel according to a secret key,Key-2, which determines the embedding order of the secret message.For the examined pixel,such as K,we determine the corre-sponding homogeneous representation group(HRG K)and calcu-late the homogeneity value(HV K)of the HRG K.Step2:For the examined pixel,the pixel capacity C K is com-puted using Eq.(3).If the homogeneity value(HV K)is less than or equal to1,this pixel cannot convey any secret message.We go back to Step1and process the next pixel.Otherwise,we read in C K bits of secret messages accordingly.Step3:We compute the current cover pixel status C(HV K,HI K).Based on the secret message,C(HV K,HI K),we determine thedesired stego pixel status S(HV K,HI0K)by referring to C(HV K, HI K),the Homogeneity Index Table,and the secret message.Step4:We alter the current cover pixel K to become the stego pixel K0by selecting an appropriate element in HRG K that hasthe homogeneity index of HI0K.Once this has been done,we can process the next pixel starting from Step1.The total embedding capacity(TMC)of an HDR image can be computed by examining the homogeneity value of each pixel,as shown in Eq.(4).TMC¼XMÂNi¼1b log2ðHV iÞcð4ÞThe extraction of the secret message is straightforward.Given a stego HDR image,we examine every pixel in a specific order de-rived by using the secret key,Key-2.For each stego pixel,such as K0,which we inspect,we compute the homogeneity value HV K0 for this stego pixel.If HV K0is less than or equal to1,then this pixel conveys no secret message.We then process the next pixel in a specific order.Otherwise,we produce the homogeneous represen-tation group,HRG K0for this stego pixel and calculate how many bits of secret message,say SM,are concealed in the cover pixel K0using Eq.(3).By comparing the cover pixel K0with all of the elements in HRG K0,we can determine the homogeneity index of the cover pixel,HI K0,and produce the status of the stego pixel S(HV K,HI0K).Given the secret key,Key-1,we can produce the homogeneity index table (HIT).Finally,we can extract SM bits of secret message by referringto HIT and S(HV K,HI0K).This ends the extraction of a stego pixel K0, and we can proceed to extracting the secret messages concealed in the next stego pixel.3.2.Pixel categories classificationThe proposed method embeds secret messages into the HDR images.In this section,we further discuss the issue of pixel classi-fication in order to provide an insight for the pixel distribution in a single HDR image.In addition,the pixel classification can illustrate pixels that are eligible for message embedding.We classify the pixels in an HDR image into totally seven cate-gories,as shown in Table4,where max(r,g,b)represents the max-imal values of a pixel for the three channels.Whenever possible, we illustrate an example of a pixel in each category.Based on its features,a pixel is classified into either‘‘regular’’or‘‘irregular’’pixels,as shown in Table4.The‘‘regular’’pixel affirms that the maximal values of a pixel for the three channels,abbreviated as max(r,g,b),is equal to or greater than128.In contrast,the‘‘irreg-ular’’pixel represents that max(r,g,b)6127.Note that a pixel can belong to one of these two categories(‘‘regular’’or‘‘irregular’’),but not both.Based on the point of view of message embedding,a pixel can be classified intofive categories.Pixels belonging to thefirst twoTable4The categories of pixels based on two classification bases in an HDR image encoded by the RGBE format.Classification basis Pixel category Satisfied conditions Example of a pixel P(R,G,B,E)Pixel features Regular max(r,g,b)P128P(12,19,132,131)Irregular max(r,g,b)6127P(127,43,64,133) Message embedding Embeddable26HV P67P(12,132,26,134)Promising max(r,g,b)=127(HV P=2)max(r,g,b)=254and r,g,b2even(HV P=2)P(43,127,56,125) P(254,142,38,129)Singular HV P=1P(129,124,122,130)Null r=g=b=0(HV P>8)P(0,0,0,128)Neutral HV P=8P(128,128,128,248)C.-M.Yu et al./Displays32(2011)225–236229。
