Intenational Achives of Photogammety, Remote Sensing and Spatial Infomation Sciences, Vol. XXXVIII, Pat 5 Commission V Symposium, Newcastle upon Tyne, UK. 3D MODELING OF SMALL OBJECTS USING MACRO LENS IN DIGITAL VERY CLOSE RANGE PHOTOGRAMMETRY H. Yanagi a, H. Chikatsu b a Achitectue, Civil and Building Envionmental Engineeing, Gaduate School of Advanced Science and Technology, Tokyo Denki Univesity, Hatoyama, Hiki-gun, Saitama 35-394, JAPAN - 7uda@ms.dendai.ac.jp b Depatment of Civil and Envionmental Engineeing, Tokyo Denki Univesity, Hatoyama, Hiki-gun, Saitama 35-394, JAPAN - chikatsu@g.dendai.ac.jp Commission V, WG V/ KEY WORDS: Maco lens, Zoom lens, Digital vey close ange photogammety, 3D modeling, TIN, Small object ABSTRACT: Recently, the documentation and visualization of vaious cultual assets have been eceiving attention. Fo example, a small Buddha less than cm in height and located in the womb of a lage Buddha is consideed as a cultual asset. In this study, the authos have consideed the use of maco lens to pefom digital vey close ange photogammety fo small objects. It was demonstated that a maco lens is suitable fo the documentation of small objects. In ode to evaluate 3D modeling in digital vey close ange photogammety, tiplet images of a dime (diamete: 7. mm) wee taken using a maco lens. This pape pesents the ability of a maco lens fo 3D modelling in digital vey close ange photogammety.. INTRODUCTION Recently, digital documentation of cultual assets has been eceiving attention. Small objects such as an extemely small Buddha that was located in the womb of a cm tall Buddha ae categoized as cultual assets. In ode to document small cultual assets, convenient 3D measuements ae equied. Theefoe, we have concentated on the development of convenient 3D measuement softwae called 3DiVision by using consume gade digital cameas (Chikatsu et al., 6). A steeomicoscope has been used in dental eseach (Mitchell et al., 989), and an enlaged image was captued using a non-metic camea with an extension tube (Hintz et al., 987). Howeve, a zoom lens o a maco lens has geneally been used fo ecoding cultual assets o fo industial measuement. In geneal, zoom lenses ae used fo captuing enlaged images. Howeve, thee ae still poblems elated to the use of a zoom lens in the digital documentation of small objects. These poblems include the instability of camea calibation that occus as a esult of the changes in the focal length and shap imaging, which is caused by the depth of field. On the othe hand, maco lenses have the ability to captue a shap image of a small object fom the viewpoint of the woking distance. In ode to evaluate the effectiveness of maco lenses in digital vey close ange photogammety, a maco lens and a zoom lens wee mounted on a digital single lens eflex camea. A compaative evaluation of the zoom lens and the maco lens has been discussed at the beginning of this pape. In geneal, halation is an impotant issue in 3D modeling. Theefoe, 3D modeling using a maco lens is discussed in the latte pat of this pape with espect to halation.. EXPERIMENT Table lists the specifications of the zoom lens and the maco lens that wee used in this investigation. These lenses wee mounted on Canon EOS D. Camea Zoom Lens Maco Lens Canon EOS D 8. megapixels; CMOS Senso size:.5 5 mm EF4-5 mm F4L IS USM Focal length: 4~5 mm F: 4 EFmm F.8 MACRO USM Focal length: mm F:.8 Table. Specifications of camea and lenses The white squae in Figue shows the aea that was consideed in this study. The black cicula tagets wee manufactued with an accuacy of ±.5 mm. The diamete of each cicula taget was cm, and the tagets wee aanged at intevals of 4 mm. The height of the cental tagets (3 ows in the cente) was 5 mm. GCPs (gound contol points) and check points wee aanged as shown in Figue. The pixel coodinates fo these points wee obtained as the aea gavity by using image pocessing pocedues. Figue. Test taget 67
Relative accuacy 相 対 精 度 Intenational Achives of Photogammety, Remote Sensing and Spatial Infomation Sciences, Vol. XXXVIII, Pat 5 Commission V Symposium, Newcastle upon Tyne, UK. / 55 / 5 / 45 / 4 GCPs Check points Figue. GCPs and check points 3. CAMERA CALIBRATION The following 7th polynomial function with decenting distotions is a well-known lens distotion model known as the Bownian model (Bown, 97). Howeve, it is also well known that k and k 3 in a zoom lens do not show significant influence (Wiley & Wong, 995). Futhemoe, the decenting distotion is esolved as pincipal point offsets (Fase & Al- Ajlouni, 6). Theefoe, the 3d polynomial function, which is shown in equation (), is used in this investigation. x 3 5 7 x x ( k k k3 ) p( x ) p x y y 3 5 7 y y ( k k k3 ) p ( y ) px y x y whee x and y ae the coected image coodinates; x' and y', image coodinates; k, k, and k 3, coefficients of adial distotion; and p and p, coefficients of decenting distotion. is the adial distance fom the pincipal points. x 3 x x k y 3 y y k 4. VERIFICATION OF ZOOM AND MACRO LENSES 4. Relationship between apetue value and accuacy The depth of field depends on the pincipal distance and the apetue value of the lens. Fo the 3D modeling of cultual assets, in paticula, it is impotant to adjust the depth of field fo each obtained image. Howeve, appopiate imaging modes can be used to achieve supeio imaging. In this study, the following thee imaging modes wee consideed: + P mode (pogam auto exposue): Apetue value and shutte speed ae set automatically depending on the bightness. + AV mode (apetue value): Apetue value can be changed manually. + A-DEP mode (auto-depth of field): Apetue value is set automatically depending on the AF (auto focus) fame. The apetue value in the AV mode must be set manually. In ode to decide the appopiate apetue value, five steeo images wee taken at diffeent apetue values with a base height atio of.34, altitudes of.3 m (zoom lens) and.5 m (maco lens), and a focal length of mm. () () Figue 3 shows the elationship between apetue values and elative accuacies. It can be seen that the elative accuacy impoved with an incease in the apetue value and that the elative accuacy exhibited the highest accuacy at F fo both lenses. Howeve, accuacy degadation was obseved ove 5F in the case of the maco lens. Theefoe, in this study, the apetue value in the AV mode was set at F. Table shows the expeimental esults. In tems of the accuacy fo each mode, the AV mode exhibited the highest accuacy fo both lenses. Howeve, the accuacies fo the A-DEP mode wee simila to those of the AV mode. Theefoe, it can be said that the A-DEP mode, which does not involve an adjustment of the depth of field, is a suitable imaging mode. Zoom lens Imaging mode Relative Right σx(mm) σy(mm) σz(mm) Left Image accuacy Image P 96 7.76.55.57 /3797 A-DEP 58 65.78.43. /43493 AV 57 65.75.6.87 /4379 Standad eo.85.85.353 /35448 Maco lens / 35 / 3 Imaging mode Relative Right σx(mm) σy(mm) σz(mm) Left Image accuacy Image P 7 7.44.45.79 /43463 A-DEP 7 7.64.5.7 /5497 AV 7 6.59.37.9 /5795 Standad eo.96.96.4 /35448 4. Enlaged imaging Zoom.8 4 5.6 8 6 5 9 3 Apetue 絞 り 値 (F) value (F) Table. Expeimental esults Maco Figue 3. Relationship between apetue value and elative accuacy Relative accuacy = X Y Z whee H is the altitude; σ X, σ Y, and σ Z ae the oot mean squae eos. H H H X Y p Z p (4) f f B whee σ X, σ Y, and σ Z ae the standad eos; H is the altitude; f is the focal length; B is the baseline; and σ P is the pointing accuacy (estimated to be. pixels (Schaefe & Muai, 988)). H In ode to obtain enlaged images of small objects, it is necessay to physically appoach an object. Theefoe, in ode to evaluate the elationship between enlaged imaging and the stability of the zoom lens and the maco lens, five tiplet images wee captued at five diffeent focal lengths (6 mm, 7 mm, 8 mm, 9 mm, and mm) at an altitude of.3 m fo the zoom lens. In case of the maco lens, five tiplet images wee captued at diffeent exposue (3) 68
Position of pincipal point (pixel) 主 点 位 置 (Pic) Position of pincipal point (pixel) 主 点 位 置 (Pic) Changing atio 変 動 率 安 定 性 stability Changing atio 変 動 率 Intenational Achives of Photogammety, Remote Sensing and Spatial Infomation Sciences, Vol. XXXVIII, Pat 5 Commission V Symposium, Newcastle upon Tyne, UK. stations (54 mm, 5 mm, 78 mm, 69 mm, and 5 mm) because the maco lens had a fixed focal length. It should be noted that images that wee taken unde diffeent focal length o diffeent exposue station conditions appeaed to be of the same size on the monito..5.5.5 ω φ κ R x x y y f a a a a kk 3.5 3..5 Zoom Maco 58.5.5..5..5. 7 7 7 9 6mm 7mm 54mm 5mm 4 7 8 8mm 9mm 78mm 69mm 7 mm 5mm focal 焦 点 距 length 離 altitude 撮 影 高 度 -.5 -.5 3 3 4 5 反 復 回 数 Figue 5. Ratios of calibation paametes in iteation (zoom lens).5 Figue 4. Stability NA X i Y i Z i R i R 6 X 6 Y 6 Z6 (5).5 whee NA (Nomalized Accuacy) is the stability; σ Xi, σ Yi, and σ Zi ae the oot mean squae eos fo each focal length and at each altitude; σ X6, σ Y6, and σ Z6 ae the oot mean squae eos fo the focal length of 6 mm and the altitude of 54 mm in the case of the maco lens; R i is the aveage of the iteation numbe fo each focal length and each altitude; and R 6 is the aveage of the iteation numbe fo the focal length of 6 mm and the altitude of 54 mm in the case of the maco lens. The stability of the changes in the focal length setting (zoom lens) and of the changes in the exposue altitude setting (maco lens) was evaluated using equation (5). Figue 4 shows the stability. Futhemoe, the numbes in Figue 4 epesent the iteation numbes of the camea calibation fo both the lenses. As a esult, it was deduced that the maco lens was moe stable than the zoom lens because the iteation numbe fo the maco lens was almost constant iespective of the diffeent altitudes. Howeve, the iteation numbe fo the zoom lens had extemely unstable values. 4.3 Geometic stability In ode to confim the stability that was mentioned above with espect to the oientation paametes, five cente images fo the diffeent focal lengths (zoom lens) and diffeent altitudes (maco lens) wee investigated. Figues 5, 6, 7, and 8 show the esult of the expeiment. Figues 5 and 6 show the changing atios of the calibation paametes in the camea calibation with a focal length of mm. The atio was computed by dividing the values of the calibation paametes in each iteation by the values of the final calibation paametes. Theefoe, a atio lage than implied a significant change in the camea calibation. Figues 7 and 8 show the distance fom the cente of an image to the pincipal point that was obtained fo each iteative computation fo diffeent focal lengths (zoom lens) and diffeent altitudes (maco lens). Fom this expeiment, it was obseved that in the case of the zoom lens, the shifting value of the attitude angle (ω, φ) and the pincipal point (x, y ) wee lage and that the amplitude attenuated exponentially, as shown in Figue 7. Additionally, it was obseved that the iteation numbe fo the camea ω φ κ R x x y y f ω φ κ R x x y y f a a a a kk -.5.5.5 3 4 Iteation 反 復 回 numbe 数 Figue 6. Ratios of calibation paametes in iteation (maco lens).5.5 -.5 69 whee ω, φ, and κ ae the attitude angles; R is the changing atio of the camea position fo the oiginal point; x and y epesent the pincipal point; f is the focal length; a and a ae the scale and shea factos; and -.5 k is the coefficient of adial distotion. 8 3 mm 9mm 8mm 7mm 6mm 6 4 8 6 4 3 4 5 反 復 回 数 Figue 7. Relationship between changing pincipal point and focal length (zoom lens) 7 6 5 4 3 3 4 反 復 回 数 H=5mm (f = mm (fmm coesponding) 相 当 ) H=69mm (f = 9mm (f9mm coesponding) 相 当 ) H=78mm (f = 8mm (f8mm coesponding) 相 当 ) H=5mm (f = 7mm (f7mm coesponding) 相 当 ) H=54mm (f = 6mm (f6mm coesponding) 相 当 ) Figue 8. Relationship between changing pincipal point and focal length (maco lens)
Woking distance (cm) ワーキングディスタンス(cm) Intenational Achives of Photogammety, Remote Sensing and Spatial Infomation Sciences, Vol. XXXVIII, Pat 5 Commission V Symposium, Newcastle upon Tyne, UK. calibation of the zoom lens and the position of the pincipal point wee significant depending on the long focal length in Figues 5 and 7. On the othe hand, in the case of the maco lens, the shifting value of each paamete was small, and it was obseved that the iteation numbe of each altitude fo the camea calibation of the maco lens was small fo each of the paametes shown in Figues 6 and 8. Theefoe, it was infeed that the maco lens was stable. Figues and show the image of Figue pocessed by using a Wallis filte and a Canny filte, espectively. 4.4 Woking distance Woking distance is defined as the length fom the top of the lens to the object. In ode to captue an image of a small object, it is necessay to physically appoach the object. Howeve, when the woking distance is small, the image is influenced by the shadow and by the depth of field. The maco lens is capable of captuing a lage image than the zoom lens, theeby making it is unnecessay to appoach the object. This was confimed though an expeiment. 8 6 4 マクロレンズ Maco lens Zoom ズームレンズ lens Figue. A dime 8 6 4 5.cm 5.5cm 5 5 5 3 被 写 体 の 大 きさ(mm) Object size (mm) Figue 9. Woking distance fo captuing an image of an object Figue 9 shows the elationship between the woking distance and the size of an object. In the case of the maco lens, the image of an object of size 5 mm was captued at the woking distance of 5 cm. Howeve, the zoom lens was only capable of captuing an image of an object of size 65 mm at a woking distance of 5.5 cm. Theefoe, it can be infeed that the maco lens is capable of taking lage images than the zoom lens. Figue. Image pocessed by using a Wallis filte 5. 3D MODELING Fom these esults, it can be concluded that maco lenses ae efficient at captuing images of small objects. Theefoe, in ode to investigate the adaptability of the maco lens fo the 3D modeling of a small object, tiplet images of a dime (Figue ) wee taken by Canon EOS D with a maco lens and at an altitude of 365 mm. In addition, 3DiVision was used fo the 3D measuement of the coin. 5. Image pocessing In this study, the featue points fo the 3D modeling of the coin wee obtained by steeo matching using the left and the ight images of the tiplet images. Howeve, it is difficult to obtain the featue points of the coin because the suface of the coin is appoximately flat. Theefoe, the featue points wee inceased by image pocessing using a Wallis filte (Jazayei & Fase, 8) and a Canny filte (Canny, 986). The Wallis filte has the chaacteistics of enhancing the contast of an image, and the Canny filte has the chaacteistics of extacting the edges fom an image. Figue. Image pocessed by using a Canny filte 6
Intenational Achives of Photogammety, Remote Sensing and Spatial Infomation Sciences, Vol. XXXVIII, Pat 5 Commission V Symposium, Newcastle upon Tyne, UK. 5. TIN Geneally, TIN (Tiangulated Iegula Netwok) is used fo 3D modeling. The constuction of TIN models has been investigating fo impoving efficiency in vaious fields. In the field of compute geomety, fo example, the flip algoithm that changes a diagonal line in a convex ectangle (Fotune, 995), the incement algoithm that adds the point and econstuct tiangulations (Fotune, 995), and the sweep line algoithm that constucts tiangulations while scanning a plane vetically fom the bottom to the top (Fotune, 987) have been investigated. In stuctual mechanics, the constuction of constained TIN models that do not have tiangulations in cavity aeas has been investigated (Okuda, 985). On the othe hand, halation is an impotant issue with espect to the captuing of an image of a cultual asset and industial measuement, and the featue points ae not obtained in a pat of the halation. Theefoe, the shapes aound the pats of the halation in the 3D model ae constucted vaguely. Theefoe, in this study, a constained TIN model that does not have tiangulations in a pat of the halation was constucted by efeing to the method poposed by Okuda and following the steps given below: Step. Extaction of halation aeas Pats of the halation extacted by image pocessing and the outlines of the extacted pats ae obtained. Figue 5 shows the constained TIN model of a dime; this model was constucted by following the above steps. Figue 6 shows the 3D model with textue, and Figue 7 shows a contou image of the 3D model with intevals of.5 mm. Fom these figue, it can be concluded that the 3D modeling of the dime was caied out without using pats of the halation. Figue 5. Constained TIN model fo the one dime coin Step. Constuction of inclusion line An inclusion line is constucted by using the featue points that wee obtained by steeo matching and the outlines that wee obtained in Step. Step 3. Constuction of tiangulations () Tiangulations ae constucted fom a side of the inclusion line, and at the same time, tiangulations ae constucted fom a side of the outlines that wee obtained in Step (Figue 3). Step 4. Constuction of tiangulations () Tiangulations ae constucted fom a side of the tiangulations that wee constucted in Step 3. The constained TIN model is constucted by the epetition of Step 4 (Figue 4). Figue 6. 3D model of the one dime coin with textue Figue 3. Constuction of tiangulations fom one of the sides Figue 4. Constained TIN model Figue 7. Contou lines 6
Intenational Achives of Photogammety, Remote Sensing and Spatial Infomation Sciences, Vol. XXXVIII, Pat 5 Commission V Symposium, Newcastle upon Tyne, UK. 6. VERIFICATION OF 3D MODELING In ode to veify the accuacy of 3D modelling, the lengths of the dime and the 3D model wee measued. Figue 8 shows a pat of the measuements of the coin and the 3D model. Refeences: Chikatsu, H., Ohdake, T., 6. Ubiquitous digital photogammety by consume gade digital camea, The Intenational Achives of the Photogammety, Remote Sensing and Spatial Infomation Sciences, Vol. XXXVI, Pat 5, ISSN 68-75 (CD-ROM). Mitchell, H. L., Chadwick, R. G., McCabe, J. F., 989. Steeomicoscope photogammety fo the measuement of small objects, Photogammetic Recod, Vol. 3, No. 74, pp. 89-99. Hintz, R. J., Sodeholm, K. J., Saett, D. C., 987. Tooth mophology quantification using non-metic photogaphy in an Analytical System, Technical Papes of the ASPRS-ACSM Annual Convention, 7, pp. 7-78. Bown, D. C., 97. Close-ange camea calibation, Photogammetic Engineeing, Vol. 37, No. 8, pp. 855-866. Wiley, A. G., Wong, K. W., 995. Geometic calibation of zoom lenses fo compute vision metology, photogammetic Engineeing & Remote Sensing, Vol. 6, No., pp. 69-74. Figue 8. Pat of the measuements Measuing pat 3D model A dime 7.34 mm 7.4 mm Table 3. Results of the measuements Fom the esults of the measuements of the dime, it can be concluded that the accuacy fo the 3D model is almost the same value of a dime. 7. CONCLUSION 7. mm Fom the esults pesented in this pape, it can be concluded that a maco lens is efficient fo small object imaging in digital vey close ange photogammety. Futhe, the 3D modeling of an extemely small object was achieved using a maco lens. With espect to the captuing of images with light, halation is an impotant issue. Howeve, a 3D model was constucted by using a constained TIN model that does not constuct vague shapes aound pats of the halation. Fase, C. S., Al-Ajlouni, S., 6. Zoom-dependent camea calibation in digital close-ange photogammety, Photogammetic Engineeing & Remote Sensing, Vol. 7, No. 9, pp. 7-6. Schaefe, H., Muai, S., 988. Automated taget detection fo eal-time camea calibation, Poceeding of 9th Asian Confeence on Remote Sensing, pp. H.-4 -H.-4-8. Jazayei, I., Fase, C. S., 8. Inteest opeatos in close-range object econstuction, The Intenational Achives of the Photogammety, Remote Sensing and Spatial Infomation Sciences, Vol. XXXVII, Pat B5, pp. 69-74. Canny, J., 986. A computational appoach to edge detection, IEEE Tansaction on Patten Analysis and Machine Intelligence, Vol. PAMI-8, No. 6, pp. 679-698. Fotune, S., 995. Voonoi diagams and delaunay tiangulations, computing in euclidean geomety, Wold Scientific, pp. 5-65. Fotune, S., 987. A sweepline algoithm fo voonoi diagams, Algoithmica,, pp. 53-74. Okuda, O., 985. Automatic tiangula mesh geneation of abitay plana domains utilizing the node-patten fo finite element analysis, Jounal of the Japan Society of Pecision Engineeing, 5(4), pp. 8-88. 6