for Spectral and Glossiness Recording

Transcription

1 Imrovement in Accurac of Flat-bed Scanning Stem for Sectral and Gloine Recording Maki Yokoama a, Takahiro Takiguchi b, Keiichi Ochiai b, Norimichi Tumura b, Tohia Nakaguchi b, and Yoichi Miake c a Deartment of Information and Image Science, Chiba Univerit, b Graduate School of Science and Technolog, Chiba Univerit, c Reearch Center for Frontier Medical Engineering, Chiba Univerit, Abtract In thi aer, we evaluate the accurac of etimation for urface roughne and ecular reflectance arameter in a flat-bed canning tem that we have rooed revioul for recording the ectral and gloine information of variou heet (Abe et al. 006). The normal vector of an object i etimated uing a hae from hading algorithm, and urface roughne and ecular reflection arameter are etimated uing the etimated normal vector. The etimated normal vector, roughne and ecular reflectance arameter can be ued to reroduce variou aearance of target object b uing the comuter grahic technique. However, reroduction of object i not accurate becaue of the low accurac of etimation for the normal vector uing a hae from hading algorithm. In thi aer, we imrove the accurac of etimation for the normal vector b increaing the number of the light ource of canning tem. Firt, baed on a comuter imulation, we evaluated the accurac of etimation for the normal vector, roughne and ecular reflectance arameter in increaing the number of the light ource. Secondl, we erformed eeriment uing a real object, and reroduced the object uing the etimated arameter under arbitrar illuminant. Introduction With the wide read of broad-band internet in the world, internet mueum i come into ractical ue. On internet mueum, object uch a art work are tored a digital data and a databae of thee data i made for digital archive. Acro network, the digital data i delivered and we can browe variou art work at an time and an lace. For accurate reroduction of the original object, it i necear to record the hae, color, and gloine of the object accuratel. In general, digital camera are ued for recording 3D-object, however in the cae of heet like object, it i ea to acquire image uing image canner. In a conventional image canner tem, the gloine information i not recorded becaue an object i illuminated from onl ingle direction. Gardner et al. develoed the linear light ource aaratu to record reflectance arameter of heet like object, b acquiring a erie of image uing a digital camera a a linear light ource move. However, the tem take a long time and high cot to ue the digital camera. To record the ectral and gloine information of variou heet eail and at low cot, we have rooed a flat-bed canning tem uing two image taken under different light ource direction. In thi tem, however, it i not accurate to record gloine of object becaue of the low accurac of etimation for the normal vector uing a hae from hading algorithm. Therefore we need to imrove the accurac of etimation for the normal vector. In thi aer, we evaluate the accurac of three te of method for the normal vector etimation of object, baed on a comuter imulation. Firt, a hae from 8 Coright 007

2 hading algorithm 3 ued in reviou canning tem i a technique to etimate the normal vector uing a ingle diffue reflection image. We ue the Zheng and Chellaa aroach 4 for the etimation of the normal vector. Second, hotometric tereo method uing two light ource 5 i a technique to etimate the normal vector uing two diffue reflection image taken under the geometr that the two light ource are laced mmetricall to the viewer direction. Lat, hotometric tereo method uing three light ource 6 i a technique to etimate the normal vector uing three diffue reflection image taken under the different geometrie of illuminant. In addition, we erform eeriment uing a real object and reroduce the object under arbitrar illuminant uing the etimated arameter. The aer i organized a follow. Section decribe the three te of geometr for canning tem. In Section 3, the canning tem rooed revioul i elained. Section 4 introduce the three te of technique for etimation of the normal vector, ued in our eeriment. Baed on a comuter imulation, the evaluation of accurac for etimating the normal vector, roughne arameter and ecular reflectance arameter i elained in Section 5, and eeriment uing a real object are hown in Section 6. Finall, we conclude thi work in Section 7. Geometr of canning tem In thi ection, we decribe the three te of geometr of canning tem. Figure (a) how the geometr of the revioul rooed canning tem. The canning tem conit of the linear light ource, the reflector, the line enor, and the laten gla. The target object i ut on the laten gla and illuminated b the linear light ource or the reflector. The reflected light of the object i catured b the line enor. For recording the gloine information, we take two image of the object illuminated b the linear light ource and the reflector reectivel. The image of an object illuminated from the linear light ource of 45 degree including onl the diffue reflection comonent i ued to etimate the normal vector. The image of an object illuminated from the reflector of 0-δ degree including the diffue reflection Platen gla Object Reflector 線光源 Light ource Line enor (a)shae from hading (b) Photometric tereo uing (c)photometric tereo uing two light ource. three light ource. Figure. Geometr of the canning tem. comonent and ecular reflection comonent i ued to etimate roughne arameter and ecular reflectance arameter of the object. The light angle δ i effective to revent the trong ecular reflection from the laten gla. To al three different method of etimation for the normal vector to the canning tem, a hae from hading algorithm i erformed in the revioul rooed geometr. Photometric tereo method uing two light ource can be ued in the tem added b a linear light ource to the revioul rooed geometr a i hown in Figure (b). Two image of the object illuminated from each linear light ource include onl the diffue reflection comonent and the are ued for etimating the normal vector. To ue hotometric tereo method uing three light ource, comlicated geometr i required uch a a tem uing oint light ource in lace of a linear light ource a i hown in Figure (c). Three diffue reflection image obtained b varing the oition of the light ource are ued for etimating the normal vector. In all three method, roughne arameter and ecular reflectance arameter are etimated from the image of the object illuminated from the reflector. The 9th International Smoium on Multiectral Colour Science and Alication 83

3 3 Previoul rooed gloine canning tem In thi ection, we decribe the roce of recording the gloine information in the canning tem rooed revioul. A the firt te of the roce, the reflectance of the object i etimated from the image of the object illuminated from 45 degree and the light ource direction b uing the hitogram of the iel value on the homogeneou reflectance area. A the econd te, the normal vector i etimated from the image of the object illuminated from 45 degree with the conideration of the light ource direction. A the third te, the roughne and ecular reflectance arameter of the object are etimated b uing the above etimated normal vector and the image of the object illuminated from 0-δ degree. Finall, the obtained normal vector and ecular reflectance arameter and roughne arameter are ued to reroduce the variou aearance of the object under arbitrar illuminant. In thi aer, we comare with the accurac of etimation for the normal vector of the three te of method mentioned above. 3. Reflectance etimation The image of the object illuminated from 45 degree include the diffue reflection comonent. Uing thi image, the reflectance can be etimated for the object. Figure how one eamle of flat and ractical lane and their hitogram for each iel value. The hitogram of the ractical lane change with variance of roughne becaue the ractical lane ha different normal vector at each iel. The normal vector of the iel at the eak of the hitogram can be conidered to be vertical to the object. Therefore, the reflectance of the object i etimated from the iel value at the eak of the hitogram. 3. Shae from hading A hae from hading algorithm i a wa to etimate the hae of the object from a hading image. In thi aer, we ue the Zheng and Chellaa aroach 4 for the etimation of the normal vector. In the Zheng and Chellaa aroach, the intenit gradient contraint i ued for and their energ function E i a follow, E = F(, q, Z ) dd () Number of iel Normal vector 素素数数画素値画数画素値画Piel value (a)flat lane. Number of iel Normal vector Piel value (b)practical lane. Figure. One eamle of lane image and hitogram. where F(, q, Z) = μ [ R(, I (, ) ] + μ [ R (, + Rq (, q I (, ) ] [ R (, + Rq (, q I (, ) ] [( Z ) + ( q Z ) ] + μ + μ3 + μ S(, ) [( ) + ( q q ) ]. 4 () In the above equation, the arameter and q are gradient and Z i a height of a iel. The reflectance function i denoted a R and the intenit of a iel of coordinate (,) i denoted a I. The firt term of equation () come from the erfect diffue reflection. The econd and third term come from the moothne contraint. The fourth term come from the integrabilit contraint. The lat term i a new term we added uing ecular reflection comonent. The ecular reflection comonent of a iel (,) i denoted a S(,). The arameter, q are gradient of the iel which include the ecular reflection comonent. μ i a weighting factor. 3.3 Roughne from ecular The image of the object illuminated from 0-δ degree include the ecular reflection comonent and diffue reflection comonent of an object. Since we have alread obtained the reflectance and the normal vector at each oint a i decribed revioul, the diffue reflection comonent of the image of the object illuminated from 0-δ degree i eail comuted b Lambertian roert of the diffue reflectance comonent. Therefore, the ecular reflection comonent can be etracted from the 0-δ degree image b ubtracting the calculated diffue reflection comonent, baed on Dichromatic reflection model 7 84 Coright 007

4 b Y a a b = = ln X σ k o lotted data, and the arameter σ and k are obtained from the fitted line. equation (). Figure 3. The leat-quare method. The roughne and ecular reflectance arameter of Torrance Sarrow reflection model 8 are etimated b uing thi ecular reflection comonent. Equation () how the imlified Torrance Sarrow reflection model 9 for ecular reflection comonent. Figure 4. Reflectance ma with two light ource. 4 Increaing the number of light ource for etimating normal vector In thi ection, we decribe two method of etimation for the normal vector. In ection 4., hotometric tereo method uing two light ource 5, and in ection α 4., hotometric tereo method uing three light e * σ I = k () ource 6 are mentioned. coθ where I denote the ecular comonent, θ i the degree between the normal vector and the viewer vector, α i the degree between the normal vector and the halfwa vector. The halfwa vector i biecting the angle between the light ource vector and the viewer vector, σ i the urface roughne arameter and k i the ecular reflectance arameter. Equation () can be linearized b taking the logarithmic oeration a follow, 4. Photometric tereo method uing two light ource In the cae that the reflectance of the object i known, there are everal iel that we could etimate the normal vector from two image 5. Figure 4 how a reflectance ma with two light ource. The iel that have the iel value = i the interection oint of two equal luminance curve and the normal vector of each iel i n, n. In the cae of the geometr that α two light ource are laced mmetricall to the ln k = ln I + ln coθ +. () * σ viewer direction, the onl normal vector n can be B defining the X, Y a: etimated becaue two curve come in contact with each other. The oint fill the multile root condition X = α (3) of the irradiance equation. The multile root condition Y = ln I + ln coθ (4) i given b the equation a follow, equation (4) can be re-written a follow, ρ = () Y = - X + ln k (5) σ where and are the unit vector of the light ource where the arameter σ and the arameter k are unknown arameter to be olved. The X and Y are obtained from the etimated normal vector and etracted ecular reflection comonent at each iel. vector, ρ i the reflectance of the object, and are the iel value of each image. We can etimate clearl the normal vector of a iel filling equation () in the cae that the reflectance of the object i known. The leat-quare method i ued to olve the equation ( ) ( ) () ρn = + (5) for arameter σ and k from man iel in the homogeneou area. The leat-quare method a i hown Figure 3 i ued to fit the equation (5) into the where n i the normal vector of the interection oint of two equal luminance curve and it i obtained from q n n n The 9th International Smoium on Multiectral Colour Science and Alication 85

5 4. Photometric tereo method uing three light ource Photometric tereo method uing three light ource 6 i a technique to etimate the normal vector uing everal image taken under the linearl indeendent geometrie of the light ource. A iel value can be decribed uing the unit of normal vector and the light ource direction, n and, the intenit of the light l, and the reflectance of the object ρ, a follow, T T = ρ l( n' ' ). () Subtituting ρn =n and l=, equation () can be re-written a follow, T = ( n ) () where the reflectance of the object and the intenit of the light are ρ= n and l= reectivel becaue n and are the unit of each vector. We etimate the normal vector uing three image obtained b varing the oition of the light ource that i linearl indeendent. Each light ource direction i =[,, z ] T, =[,, z ] T, 3 =[ 3, 3, 3z ] T. Each iel value i decribed a follow, 3 T n = n n z T z z 3 3 3z Thi can be decribed a matri a follow,. (3) = n T S (4) The normal vector i comuted b multiling equation (4) b invere matri of S. B uing the etimated normal vector, roughne arameter σ and ecular reflectance arameter k are etimated a i hown in Figure 6. The abcia ai of the grah decribe the variance of hae. The reult are comared with the ground truth. In the ideal cae, the etimation value i on the broken line. From Figure 6, we can ee the accurac of etimation for roughne arameter and ecular reflectance arameter b uing a hae from hading algorithm i the lowet and the accurac of hotometric tereo method uing three light ource i the highet. Figure 7 how the reult of the etimation for ecular reflectance arameter and roughne arameter in the cae of changing each arameter when ~we modeled object in the comuter. A mentioned above, in the ideal cae, the etimation value i on the broken line. The accurac of etimation for roughne arameter b uing hotometric tereo method uing three light ource i the mot accurate, and that i the lowet b uing hae from hading. For the etimation of ecular reflectance arameter, the accurac i nearl accurate with all three te of method. In comuter imulation, it i high that the accurac of etimation for the normal vector and roughne arameter with hotometric tereo method uing three light ource and hotometric tereo method uing two light ource. 5 Evaluation of accurac in comuter imulation In thi ection, we erform the comuter imulation for evaluation of etimating the normal vector. In the comuter, we modeled hae of target object baed on the Gauian ditribution which i hown in Figure 5. Table how the error of etimation for the normal vector uing the object modeled in comuter. We take an average of error at each hae. Photometric tereo method uing two light ource and hotometric tereo method uing three light ource have about 5 degree error with true value and a hae from hading algorithm ha about 0 degree error with true value. Figure 5. Shae modeled in comuter. Table. Error of normal vector etimation. Number of Average value Ma value uing image of error( ) of error( ) Shae from hading Photometric tereo uing two light ource Photometric tereo uing three light ource Coright 007

6 Photometric tereo uing two light ource Photometric tereo uing three light ource Ground truth σ Shae from hading (a)shae from hading read of wave(gauian deviation) (a) Roughne arameter σ. Photometric tereo uing Photometric tereo uing three light ource two light ource Ground truth k (c)photometric tereo uing two light ource. three light ource. Figure 9. Etimated normal ma uing three different method. Shae from hading 5 (b) Photometric tereo uing read of wave(gauian deviation) 30 Table. Reult of arameter etimation. (b)secular arameter k. Roughne arameter Secular reflectance arameter Shae from hading Photometric tereo uing two light ource Photometric tereo uing three light ource Ground truth Figure 6. Reult of arameter etimation. Photometric Stereo uing two light ource Shae from hading Etimation value Etimation value Photometric tereo uing three light ource Photometric tereo uing two light ource Shae from hading 0. Photometric tereo uing three light ource Ground truth Ground truth (a)roghne arameter σ. (b)secular arameter k. Figure 7. Reult of arameter etimation. (a)shae from hading. Figure 8. Gold ticker. 6 Eeriment uing real object Figure 8 how a gold ticker that we ued for eeriment. Uing the above-mentioned the three te of method for etimating the normal vector, we erformed the etimation for the normal vector of the real object. The obtained normal ma are hown in Figure 9. Normal ma are image that tore normal vector directl in the RGB value of an image. The real value of the roughne arameter of the object we ued for eeriment i 0.57 and that of the ecular reflectance arameter i 0.4. Thee value are obtained b fitting the ecular reflection comonent (b)photometric tereo uing (c)photometric tereo uing two light ource. three light ource. Figure 0. Reult of reroduced image. of the multile image to the imlified Torrance Sarrow reflection model9 mentioned above. The multile image are obtained b varing the oition of the light ource from -40 degree to 40 degree at 5 degree interval. Table how each reult of ecular reflectance arameter and roughne arameter obtained uing the three te of method. We can ee that the accurac of etimation for the The 9th International Smoium on Multiectral Colour Science and Alication 87

7 ecular reflectance arameter and roughne arameter with hotometric tereo method uing three light ource i the highet in the three method. Uing the etimated normal vector and ecular reflectance arameter and roughne arameter of the object, we reroduced the object under arbitrar illuminant on the comuter grahic. Figure 0 how the reult of reroduced image. 7 Concluion We evaluated the accurac of etimation for urface roughne and ecular reflectance arameter in a flat-bed canning tem that we have rooed revioul for recording the ectral and gloine information of variou heet. A hae from hading algorithm i ueful for a canning tem becaue onl a ingle diffue image i required, but the accurac of etimation for the normal vector i the lowet in the three method. In contrat, the accurac of etimation for the normal vector with hotometric tereo method uing three light ource i the highet in the three method, but it i not ueful for a canning tem becaue the comlicated geometr i required a mentioned revioul. Therefore, hotometric tereo method uing two light ource that can be erformed b adding a linear light ource to the revioul rooed canning tem i ueful for a canning tem. In thi aer, we don t make conideration for ectral information becaue we have ued the object that ha uniformit of color and material. Therefore, in the future work, we need to lit the region of the object that have non-uniformit of color and material. Acknowledgement The author are thankful to Dr. F. Nakaa, Dr. H. Ichikawa and Dr. Y. Minato of Fuji Xero Cororation for everal ueful comment.. T. Takiguchi, S. Abe, N. Tumura, T. Nakaguchi, F. Nakaa, H. Ichikawa, Y. Minato, K. Miata, Y. Miake, Deigning flat-bed canning tem for ectral and gloine recording, Proceeding of SPIE Volume 606.DI-DII (996). 3. R. Zhang, P. S. Tai, J. E. Crer and M. Shah, Shae from Shading: A Surve, IEEE Tranaction on Pattern Anali and Machine Intelligence, vol., no.8, (999). 4. Q. Zheng and R. Chellaa, Etimation of Illumination Direction, Albedo, and Shae from Shading, IEEE Tranaction on Pattern Anali and Machine Intelligence, 3(7), (99). 5. K. Shinmoto, T. Honda, S. Kaneko, A Formalization of Photometric Stereo Method Uing Two Light Source and It Alication to Recontruction of Human Skin relica, The Intitute of Electronic, Information and Communication Engineer Tranaction, Jaanee, Vol.J8-D-II No..0-8(999). 6. R, J. Woodham, Photometric method for determining urface orientation from multile image, Otical Engineering 9, (980). 7. S. A. Shafer, Uing color to earate reflection comonent, COLOR Reearch and alication Vol.0, No.4,.0-8 (985). 8. K. E. Torrance and E. M. Sarrow, Theor for Off-Secular Reflection From Roughned Surface, J. Ot. Soc. Am Vol.57 No.9,.05-4 (967). 9. Y. Sato, K. Ikeuchi, Reflectance Anali for 3D Comuter Grahic Model Generation, Grahical Model and Image Proceing, Vol. 58 No.5, (996). Reference. A. Gardner, C. Tchou, T. Hawkin, P. Debevec, Linear light ource reflectometr, ACM Tranaction on Grahic (TOG), Volume, Iue (003). 88 Coright 007