Improving the Perceptual Uniformity of a Gloss Space

Transcription

1 Improving the Pereptual Uniformity of a Gloss Spae Adria Fores, 1 Mark D. Fairhild, 1 Ingeborg Tastl 2 1 Munsell Color Siene Laboratory, Rohester Institute of Tehnology 2 Hewlett-Pakard Laboratories Abstrat The pereptual gloss spae defined in Pellaini et al. [9] ould be used for quality ontrol appliations to bring similar benefits as seen in olor with the use of CIELAB. However, a distane metri to relate all the dimensions in the spae does not exist, and the spae was only validated with the materials used to define the spae. The urrent spae s distane metri does not allow relating differenes in lightness to the other dimensions: ontrast gloss and distintness of image gloss. The lightness pereption uniformity of the spae was first evaluated in a psyhophysial study, where the observers lightness disrimination was found to derease as lightness inreased. A funtion was derived to model the lightness pereption observed and it was inluded into the distane metri of the spae. The spae uniformity around sixteen positions in the gloss spae was evaluated in a seond psyhophysial study to assess the overall spae uniformity. The spae was found to be pereptually non-uniform outside the samples used when the spae was reated. Also, an improved gloss differene equation that takes into aount the non-uniformity of the spae is presented, showing a statistial signifiant improvement over the urrent gloss differene equation of the spae and reduing the STRESS value from to Introdution The CIELAB olor spae and the olor differene equations defined in it have been widely used for quality ontrol appliations and to haraterize input and output devies taking into aount human olor pereption. When onsidering gloss pereption, pereptual attributes defined as ASTM features (distitness-of-image gloss, haze, bloom, et.) are used for quality ontrol appliations, and pereptual gloss spaes are disussed in the omputer graphis literature. The pereptual gloss spae defined in Pellaini et al. [9] ould be used for quality ontrol appliations to bring similar benefits as seen in olor with the use of CIELAB. For example, the ability to set toleranes aross multiple dimensions and the opportunity to have a single value to desribe the pereptual distane between two materials. However, some limitations still restrit the use of this pereptual gloss spae in that regard. The first limitation is the need to loate the position in the spae for a given real material, whih ould be aomplished by approximating material measurements with the underlying analytial model that defines the pereptual gloss spae. The seond limitation is the need to further haraterize the relation between different dimensions in the spae and to validate the spae s pereptual uniformity. This paper is going to fous on the uniform gloss spae defined in Pellaini et al. [9], by first adding lightness to the gloss differene equation of the spae, then the spae uniformity will be evaluated, and finally an improved gloss distane measure will be presented. The urrent spae s distane metri does not allow relating differenes in lightness to the other dimensions: ontrast gloss and distintness of image gloss. The lightness pereption uniformity of the spae was first evaluated in a psyhophysial study, where the observers lightness disrimination was found to derease as lightness inreased. Then, a funtion was derived to model the lightness pereption observed and it was inluded in the distane metri of the spae defined in Pellaini et al. [9]. It s important to note that the gloss pereption using a ommon LDR display is studied in this work, and similar experiments would need to be performed to study the gloss pereption of physial objets or when using HDR displays. The pereptual uniformity around sixteen positions in the gloss spae was evaluated in a psyhophysial study. The results of our study show that the spae is not pereptually uniform and improvements on the distane metri are needed to improve its uniformity outside the samples used to reate the spae. Finally, the results of the seond experiment are used to derive an improved gloss distane measure of the spae. To summarize, the main ontributions of this paper are: The inlusion of lightness to the gloss differene equation of the gloss spae defined in Pellaini et al. [9]. The validation of the gloss spae uniformity, finding that the spae is non-uniform outside the samples used to reate the spae in Pellaini et al [9]. The reation of an improved gloss differene equation that takes into aount the spae non-uniformity. Bakground In Pellaini et al. [9], a pereptual spae of glossy materials represented by the Ward BRDF model [15] was presented. Two different experiments were performed to find the dimensionality of the gloss spae for a set of samples, and then to pereptually sale the axes to obtain a uniform spae. Two dimensions were found to be enough to desribe the gloss pereption: ontrast gloss (), whih desribes the relation between the diffuse omponent and the speular peak, and distintness of image gloss (d), whih defines the sharpness of the refletions. Lightness (L ) was added to define the diffuse omponent, and the mapping from the Ward BRDF model parameters to the pereptual parameters was defined as: = 3 ρs + ρ d /2 3 ρ d /2 (1) d = 1 α (2)

2 L = f (ρ d ) (3) where ρ d and ρ s are the diffuse and speular refletane, respetively, α is the Ward BRDF model parameter, and f orresponds to the CIELAB lightness funtion. The results of the experiment were also used to define a pereptual distane metri in the spae: D i, j = [ i j ] 2 + [8(d i d j )] 2 (4) where D i, j is the pereptual distane between the samples i and j represented with the and d spae oordinates. This spae has suessfully been used to evaluate the material disrimination dependene on the objets shape and for different materials [14]. In Vangrop and Dutré [13], the shape dependene was modeled and orreted, then being able to math the gloss appearane of two objets with different shapes. The pereptual spae is a remapping of the Ward BRDF model [15], whih is defined by the following equation: f (ω i,ω o,α) = 1 (n ωi )(n ω o ) e tan2 δ/α 2 4πα 2 (5) where ω i and ω o are the inident and outgoing light diretions, respetively, n is the surfae normal, δ is the angle between the surfae normal and the half-way vetor ( ω i+ω o 2 ), and α is the Ward BRDF parameter that ontrols the width of the lobe. A limitation of this work is that the spae is only defined for the Ward BRDF model, thus limiting its appliability to materials defined by that model, and the fat that the pereptual uniformity was only valid for the materials used to reate the spae. In this paper the pereptual uniformity of the spae is being evaluated. Another pereptual spae for gloss was introdued in Wills et al. [16]. In this ase, 55 measured materials from the MERL database [8] were used to define the spae. A two dimensional spae was found by using multi dimensional saling (MDS) to analyze the pairwise omparison by first estimating the dimensionality of the data, and then onstruting the embedding spae [1]. The main limitation of that spae is the lak of pereptual axes, and the need to repeat part of the psyhophysial experiment and rebuild the spae every time a new material is added. Experiments Two experiments were performed in order to (1) Determine pereptual lightness differenes in the Ld spae, and to (2) Evaluate the gloss uniformity of the Ld spae. The method of onstant stimuli was used together with a two-alternative fored hoie (2AFC) design. Figure 1 shows the interfae used in the different experiments, where two pairs of images were presented for eah trial to the observers. The standard pair of images was on the left, and the test pair was on the right. The test pair was omposed of a given gloss enter and a test sample. The upper/lower position of the images for the test pair were randomized for eah trial. The gloss enter sequene and the test samples for eah gloss enter were randomized for eah observer. The question that the observers had to answer for eah of the trials was the following one: Whih pair of images is more similar?. Observers were instruted to judge the overall material appearane differene, i.e. taking into aount both lightness and gloss differenes. The left and right arrow keys on the keyboard Figure 1. User interfae of the experiment developed with Psyhtoolbox, showing the two pairs of images to be ompared. were used to selet the pair of images onsidered to be more similar. Twenty-one observers with normal olor vision and normal or orreted to normal visual auity partiipated in eah experiment. The experiment was onduted in the dark and eah observer performed a total of 1097 judgements for both experiments. In order to maximize the material disrimination in the experiment a blob-like shape and the Eualyptus Grove light probe from Paul Debeve were used. This geometry gave the best material disrimination auray in Vangorp et al. [14] and this environment map was found to be the environment map with real world statistis providing the best material disrimination in Fleming et al. [3], respetively. A 30-inh HP ZR30w display was used for the experiment and was haraterized using a PR-655 spetroradiometer and the Day method [2]. A good display s additivity was observed, and a mean CIEDE2000 of 0.33 was found when displaying the olors of the 24 pathes of the Mabeth Color Cheker. The Physially Based Ray Traer (PBRT) [10] was used to generate the syntheti images presented to the observers. The pfstools framework [7] was used to apply the Reinhard et al. [12] global tone mapping operator (key= 0.18 and φ = 1.0) to a tiled image ontaining all the images used for eah experiment. Then, the resulting CIE Y was linearly mapped to the display s dynami range. Next, the olor for eah pixel was set to be neutral by saling its X and Z omponents: X = Y X wp Y wp, Z = Y Z wp Y wp, being XY Z wp the display s white point. Finally, the inverse of the display model was used to onvert from XYZ to display digital ounts. Experiment 1: Adding lightness to the spae s distane metri The goal of the first experiment is to add a funtion for L to the gloss distane measure seen in Equation 4. The Ld spae differene equation presented in Pellaini et al. [9] does not define how the differenes in lightness are related to differenes in the other dimensions of the spae, and d. For that reason, differenes between materials with different lightness an t be resolved using the urrent equation. The experimental design explained in the previous setion was used to understand and model the behavior of L in the Ld spae. The standard pair was defined to only vary in a single dimension (d = {0.9, }), while having onstant lightness and ontrast (L = 30, = 0.25). The distane between the standard pair was equal to D i, j = 0.05 in the uniform spae desribed in Equation 4. Several gloss enters were studied to better understand the

3 pereption of lightness differenes aross the spae. Five positions in the d plane were seleted to study if there was a lightness pereption differene depending on the position on that plane (d = {0.2,0.85}, {0.3,0.9}, {0.4,0.95}, {0.1,0.8}, {0.15,0.925}). Then, a gloss enter was defined at L = {10,20,40,60,80} for eah of the d positions. Eleven test samples were defined for eah gloss enter, varying only in L. They spanned the range [L 10,L + 10] with an interval of 2 when the gloss enter was at L = 10, and the range of [L 20,L +20] with an interval of 4 for gloss enters defined at other L. The materials desribed above that given its ontrast () and lightness (L ) would not enfore energy onservation were not evaluated. Results Experiment 1 L* Mean Threshold at 50% Probability d={0.2,0.85} d={0.3,0.9} d={0.4,0.95} d={0.1,0.8} d={0.15,0.925} y = 0.122*x More different than the standard pair More similar than the standard pair L* gloss enter Figure 2. distane. L approximation funtion, being D i, j = 0.05 the standard pair For eah test sample, the frequeny of observers judging it to be loser to the gloss enter than the standard pair was first alulated. Next, a gaussian funtion was fitted for eah gloss enter to the frequeny of its test samples. The gaussian funtion was then used to obtain the lightness differene probability at 0.5, 0.75, and 0.25 from the gloss enter, shown as, lower, and upper error bars in Figure 2, respetively. The L pereption was found to be independent of the d position and the lightness differenes were approximated with a linear funtion. Care should be taken when using the funtion outside the range studied [10,80]. The lighter the gloss enter is, a greater hange in lightness is needed for observers to pereive the test pair as more different than the standard pair. Meaning that the observers lightness disrimination dereases as lightness inreases. Thus, the pereption of lightness differenes depends on the lightness of the samples. The approximation obtained in Figure 2 an be used in the following form to ompute the pereived lightness differene in the Ld spae: L i L j f L (L i,l j ) = L i where the 0.05 is the distane D i, j of the standard pair (whih orresponds to the magenta line in Figure 2). Note that in this ase (6) f L (L i,l j ) f L (L j,l i ) and are must be taken to use the gloss enter as L i. Another option is to use the mean ( L i+l j 2 ) instead of L i in the denominator to ompute the distane in the point loated in the middle of the two samples, thus obtaining a symmetri funtion. The revised distane funtion one lightness is added to the Ld spae is the following: Ld = [ i j ] 2 + [8(d i d j )] 2 + f L (L i,l j ) 2 (7) Disussion Experiment 1 In this gloss spae L is used to define the material appearane of an objet, and that appearane representation is later used to generate syntheti images. In this work, as in Pellaini et al. [9] where the original spae was defined, a LDR display is used, whih requires the tone mapping of the images before being displayed. Tone mapping operators mostly ompress the luminane of the sene, and this ompression is probably being represented in the funtion obtained in Figure 2. As future researh, it would be interesting to study if there is a relation between the lightness differene funtion and the tone mapping operator used. At the same time, if the Ld spae is to be used to judge the pereived gloss differenes between real objets, a similar experiment to the one performed in this work should be performed using either real samples or a high dynami range display, as it is known that limiting the image dynami range does hange the apparent gloss of surfaes depited in images [11]. Another reason why a funtion is required for L might be related to the same need as in the CIEDE2000 olor differene equation. Experiment 2: Gloss uniformity validation The goal of the seond experiment is to validate the uniformity of the Ld spae presented in Pellaini et al. [9]. The positions 1-5 in Table 1 were used as gloss enters for this experiment. Those positions are the approximation of 5 materials of the MERL database [8] (pearl-paint, gold-paint, olorhanging-paint3, nikel, and silver-metalli-paint) into the Ld spae using the projetion defined in Fores et al. [4], and an be seen in Figure 3. Only variations in the d plane were onsidered for the test samples in order to evaluate the urrent weights of the d dimensions in Equation 4. At the same time, the number of trials to perform was greatly redued by only sampling two of the three dimensions of the Ld spae. To sample around eah gloss enter the Equation 4 was taken into aount in order to have six pereptually equal steps in eah dimension (step size = and d = 0.033/8) entered in the gloss enter. Also, the gloss enter itself was used as a test sample. As the test samples only varied in the d plane, the standard pair for this experiment only varied in L and had L = {20,15} and d = {0.2,0.85}. Results Experiment 2 The same idea of the MaAdam ellipses or olor toleranes in CIELAB spae will be used to evaluate the spae uniformity. The gloss spae will be uniform in a region if the differene of the standard pair to the test samples around the gloss enter defines a irle, and the spae will be non-uniform if an ellipse is obtained. To ompute eah ellipse, the test samples that were seleted by the observers to be more similar than the standard pair with

4 Figure 3. Gloss Centers 1-5 used to evaluate the spae uniformity. Gloss Center L d Table 1. Ld oordinates of the gloss enters studied. a frequeny of 0.5 or higher were first seleted. Then, a ovariane matrix was defined with those test samples. Finally, the 95% onfidene interval ellipse was obtained for the given ovariane matrix and sample mean. As the sampling was seleted to be uniform in the gloss spae, the test samples were equally spaed. The ellipses obtained for eah gloss enter and the samples used to reate the spae in Pellaini et al. [9] an be seen in Figure 4. In this ase, the standard pair had a Ld = when using Equation 7. Disussion Experiment 2 Cirles would have been obtained instead of ellipses for eah gloss enter if the d spae was uniform. The ellipse determines the 95% onfidene interval where 50% of the observers seleted that the test pair was more similar than the standard pair. Consequently the Ld spae defined in Pellaini et al. [9] is non-uniform for the gloss enters tested. It s interesting to note that the original distane metri of the spae seen in Equation 4 is only pereptually uniform around the top left gloss enter studied, while being non-uniform for the rest of the gloss enters evaluated. In fat, the top left gloss enter studied is the only one loated between the samples used to define the gloss spae in Pellaini et al. [9] (see Figure 4). This finding agrees with the laim that the spae only aurately predits the appearane for materials in the range of the samples used to reate the spae, as stated by the authors [9]. From the small number of gloss enters evaluated in this experiment a trend an roughly be seen when looking at Figure 4. Figure 4. Gloss Centers studied Pellaini saling Pellaini d saling Pellaini MDS Ellipses obtained from the 5 gloss enters, showing the nonuniformity of the spae outside the samples used to reate the gloss spae in Pellaini et al. [9]. A ompression in the dimension might be needed with inreasing, as depited by looking at the right-most ellipses. While a rotation and an additional ompression in the d dimension for materials on the lower left quadrant might also be needed. It s also important to note that the different gloss enters have different lightness, as seen in Table 1, and lightness might also need to be onsidered when trying to improve the spae uniformity. Experiment 2.1: Sampling extra gloss enters In this experiment the spae uniformity around additional gloss enters throughout the spae was evaluated. This experiment was designed to better understand the non-uniformity of the spae found in the seond experiment, to see if the same trends seen in Figure 4 are maintained, and to aid the development of an improved gloss differene equation. Eleven new gloss enters (6-16 in Table 1) were defined aross the spae with the goal to better understand the nonuniformity of the spae, to evaluate materials with higher ontrast and the ones loser to the boundaries of the spae ( = 0 and d = 1), and to evaluate some d positions at different L planes to analyze the relation of lightness with the other dimensions of the spae. The spae uniformity around two different d positions was evaluated at three L planes (gloss enters (7,8,9) and (12,13,14) in Table 1). To maximize the lightness range studied the L planes evaluated for eah d position were different, as to enfore energy onservation materials with lower ontrast () an reah higher

5 lightness than high ontrast materials. The experiment proedure was the same performed in the seond experiment. The only differene was the sampling rate used for the gloss enters loser to the boundaries (15 and 16), being 4x8 ( x d) for the gloss enter loser to = 0 and 8x4 for the sample loser to d = 1. The same step size used in the seond experiment was used. 1.8 Pellaini saling Pellaini d saling Pellaini MDS Figure 5. Ellipses obtained from the 16 gloss enters showing the spae non-uniformity and the original samples used to reate the spae in Pellaini et al. [9]. The ellipses are olor-oded with its lightness plane. Results Experiment 2.1 The same proedure used to obtain the ellipses in the seond experiment was performed for the new gloss enters evaluated. The ellipses obtained are shown in Figure 5 together with the original samples used to reate the spae in Pellaini et al. [9]. An inreased elongation in the d plane is observed as L inreases, as an be seen in the two d positions evaluated at three lightness planes. Only two of the three different gloss enters at the d = {0.65,0.93} position an be seen in Figure 5. This happens beause the same test samples were seleted by the observers with a frequeny higher than 50% for the gloss enters 12 and 14, thus resulting with the same overlapping ellipse. At the same time, all the test samples available aross the dimension were seleted for those two samples, meaning that a probably even larger horizontal elongation is pereived. Disussion Experiment 2.1 The addition of eleven new gloss enters to the evaluation of the spae uniformity allowed to onfirm the trend seen in the seond experiment, where there seems to be an elongation in the dimension with inreasing, an elongation on d as d inreases, and the orientation of the ellipses points out that there might exist a rotation point. The inreased elongation in the d plane seen as L inreases indiates that the observer disrimination dereases as L inreases. The same effet was seen in the first experiment, where the lightness disrimination also dereases with lightness. However, a more omplex interation between L and the d dimensions is apparent from the results obtained, as the elongation is dependent on the d position of the sample. For the samples in the d = {0.2,0.875} position, the spae goes from being uniform to show an inreased elongation as L inreases, and for the samples in the d = {0.65,0.93} position the spae is already strethed at low lightness and it strethes even more as L inreases. It s interesting to note that ellipse size of the gloss enter with lowest lightness (L = 5) with high ontrast (d = {0.65,0.93}) has almost the same size as the ellipse with mid ontrast (L = 50) in the low ontrast region (d = {0.2,0.875}). A further evaluation is probably needed to better understand and be able to model the d dimensions dependene on L. At the same time, it would also be interesting to further validate the uniformity of the region where the samples used to reate the spae in Pellaini et al. [9] are loated and in addition evaluate that region at multiple lightness planes. Improved gloss differene equation In this setion an improved gloss differene equation will be derived using the results from the psyhophysial experiments desribed above. The standardized residual sum of squares (STRESS) metri, presented in Garia et al. [5] and ommonly used in the Color Siene ommunity to evaluate olor differene equations, will be used to evaluate the performane of existing and developed gloss differene equations. STRESS values measure the deviation between visual differenes ( V ) and numerial differenes (e.g. Eab ), while at the same time allowing to make statistial inferenes of two different equations. For eah gloss enter, the distane from the pereived loation of the gloss enter in the spae ( in Figure 5) to eah point that defines the ellipse represents an equal visual differene, as the ellipse represents the materials that would have the same distane to the gloss enter as the distane between the samples in the standard pair. To ompute STRESS, the data for all gloss enters is used and ompared to a given numerial differene equation applied to eah pair of samples in the spae. Beause of the resemblane to its expressions and for easy understanding, referene to the olor differene equations will be used throughout the following explanation. First, the eulidian distane metri in the Ld spae ( Ed ) was omputed for the gloss enters and ellipses obtained in this work, giving a STRESS value of Then, the STRESS value using the gloss differene equation derived by Pellaini et al. [9] (Equation 4), was omputed and a STRESS of was obtained. Lower STRESS values indiate a lower deviation between visual differenes and numerial differenes, meaning that an improvement was obtained by saling the d dimension by 8. Spae Modeling The development of the improved gloss differene equation was guided by the goal to model the elongation in the and d dimensions, to model the rotation observed in the ellipses, and with the assumption that the spae is uniform in the region where the samples used to reate the spae are loated. The starting point of the modeling proess was Equation 4, as it is assumed that it provides a pereptual uniform spae where the samples used in Pellaini et al. [9] are loated. The use of ylindrial oordinates was a natural evolution in olor differene equations, where the distane from neutral and the rotation angle is used to desribe Chroma and Hue in CIELAB, respetively. The same approah was used in this work

6 to improve the gloss differene equation of the spae. In this ase, the rotation point is not as learly defined, neither oneptually nor as a point in the spae. Still, the orientation of most ellipses seems direted towards a point near the upper left limit of the spae, d = {0,8}. As we haven t found a oneptual meaning for the distane and rotation from the rotation point in terms of gloss, the same nomenlature, Chroma and Hue, as in CIELAB will be used for larity. Two optimization proesses were done to first find the rotation point of the spae, and then to model the inreased ellipse elongation seen in Figure 5 as the gloss enters are farther a part from the rotation point. For the first optimization proess, the rotation point (d) and the funtion for Chroma that will be desribed later were non-linearly optimized to minimize the STRESS value. The sixteen ellipses found experimentally were used and the rotation point obtained was Rot d = {0.004,86}. The rotation point represents the point in the spae that better aligns with the long axis of all the ellipses. Chroma Figure Experimental Data Syntheti data Sigmoid funtion Chroma Chroma vs Chroma for the 16 gloss enters obtained in our study, the four syntheti irles added to enfore the uniformity in the area where the Pellaini et al. [9] samples were loated, and the sigmoid used to approximate the data. One the rotation point was known, a seond optimization proess was performed to add a weighting funtion to Chroma. Chroma defines the distane from the rotation point and diretly relates to the inreased ellipse elongation as the gloss enters are farther a part from the rotation point. In this ase, four syntheti irles equal in size to the top left irle seen in Figure 5 were plaed in the region where the Pellaini et al. [9] samples are loated in order to enfore the spae uniformity in that area. That deision lead to the good performane of a sigmoid funtion, as an be seen in Figure 6. Chroma is the distane from the rotation point to the gloss enter (see Equation 8), and Chroma is the radius of the ellipse in the diretion of the rotation point from the enter of the ellipse. The four additional irles added and the sigmoid funtion that approximates both the experimental and syntheti data are also shown in Figure 6. For the seond optimization proess, the parameters of the sigmoid funtion were non-linearly optimized to minimize the STRESS value. In this ase, both the sixteen ellipses found experimentally and the four syntheti irles were used during the optimization proess. The sigmoid parameters obtained were the following: p = {0.87, 2.66, 0.15, }. Finally, the first parameter (p 1 ) was set to 1 in order to enfore the region uniformity where the Pellaini et al. [9] samples are loated. A STRESS value of was obtained when the sixteen ellipses found experimentally were evaluated, whih was found to be a statistially signifiant improvement when ompared to the Ed and the D i, j gloss differene equation from [9]. To ompute the gloss differene equation the distane from the rotation point for eah sample (Chroma) is first omputed: C 1 = [ 1 Rot ] 2 + [(8d 1 ) Rot d ] 2 (8) C 2 = [ 2 Rot ] 2 + [(8d 2 ) Rot d ] 2 (9) where the rotation point Rot d = {0.004,86}, and d are the oordinates of the two samples evaluated. Next, the Chroma and Hue differenes between those samples are omputed as in E 94 : = 1 2 (10) d = d 1 d 2 (11) C d = C 1 C 2 (12) H d = 2 + d 2 Cd 2 (13) The sigmoid funtion used in Figure 6 is the following one: p 2 p 1 S C = p [(p 3 C 1 )p 4 ] (14) where p = {1,2.66,0.15,3140.9} are the sigmoid parameters. Finally, the gloss differene equation is omputed: ( G d (Ld 1,Ld 2 ) = f L (L 1,L 2 ) 2 Cd + S C ) 2 + H 2 d (15) where Ld 1 and Ld 2 are the oordinates of the two samples, S C is used to weight C d, and Equation 6 is used to ompute f L. Figure Modeling Experimental data Ellipses obtained in the psyhophysial studies are visualized with dashed blak lines, and results obtained using the gloss differene equation G d developed are shown in red. The approximation of the experimental results with the derived gloss differene equation an be seen in Figure 7, where the resulting ellipses from the experiments are shown in dashed blak

7 lines, and the ellipses obtained with the G d are shown in red. In order to ompare the size and orientation, the same saling used to math the experimental data of the top left irle with the gloss differene equation was used for all the other ellipses. As C and H are independent from L, the results seen for the gloss enters studied at three different lightness planes are not represented, and the same ellipse is obtained in eah d position. Figure Ellipses displayed aross the d plane in order to show the funtion behavior aross the spae. Note that the d plane shown is independent of lightness. Figure 8 shows the behavior of the G d at different loations aross the d plane at any L level. The spae is uniform in the region where the samples used to reate the spae in Pellaini et al. [9] were loated, while outside this region the ellipses are elongated in respet to the rotation point. Conlusion and Future Work Two experiments were performed in this paper. The first one was used to evaluate the lightness pereption in relation to the ontrast gloss and distintness of image gloss dimensions of the spae. The lightness disrimination was found to derease as lightness inreased. The lightness pereption was then modeled and inluded into the distane metri of the gloss spae. The seond experiment was used to evaluate the spae s pereptual uniformity, finding that the spae is only uniform in the region where the samples used to reate the spae in Pellaini et al. [9] are loated. Then, the spae non-uniformity was modeled and an improved gloss differene equation was defined. A more detailed analysis is needed to better understand how L effets the spae uniformity of the d plane, and for that reason this interation was not inluded in the gloss differene equation presented. As a future work it will also be interesting to validate the uniformity of the gloss spae at different lightness planes in the region where the samples used to reate the spae are loated. It s important to note that this gloss spae might not be able to represent all real materials as the gloss spae is a remapping of the Ward BRDF model, whih has an impliit modeling of the inreased refletane towards grazing angles (Fresnel effet) and its distribution an not aurately represent ertain real materials [6]. Finally, the pereption of olor in relation to the gloss spae would be an interesting avenue of future work to obtain an overall material pereption spae inluding both pereptual attributes, olor and gloss. Referenes [1] Sameer Agarwal, Josh Wills, Lawrene Cayton, Gert Lankriet, David Kriegman, and Serge Belongie. Generalized non-metri multidimensional saling. In AISTATS, San Juan, Puerto Rio, [2] Ellen A. Day, Lawrene A. Taplin, and Roy S. Berns. Colorimetri haraterization of a omputer-ontrolled liquid rystal display. Color Researh and Appliation, 29: , [3] Roland W. Fleming, Ron O. Dror, and Edward H. Adelson. 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