non-laser-based scanner for three-dimensional digitization of historical artifacts

Non-laser-based scanner for three-dimensionaldigitization of historical artifacts

Daniel V. Hahn, Kevin C. Baldwin, and Donald D. Duncan

A 3D scanner, based on incoherent illumination techniques, and associated data-processing algorithmsare presented that can be used to scan objects at lateral resolutions ranging from 5 to 100 �m (or more)and depth resolutions of approximately 2 �m. The scanner was designed with the specific intent to scancuneiform tablets but can be utilized for other applications. Photometric stereo techniques are used toobtain both a surface normal map and a parameterized model of the object’s bidirectional reflectancedistribution function. The normal map is combined with height information, gathered by structured lighttechniques, to form a consistent 3D surface. Data from Lambertian and specularly diffuse sphericalobjects are presented and used to quantify the accuracy of the techniques. Scans of a cuneiform tablet arealso presented. All presented data are at a lateral resolution of 26.8 �m as this is approximately theminimum resolution deemed necessary to accurately represent cuneiform. © 2007 Optical Society ofAmerica

OCIS codes: 150.6910, 100.2000, 100.5070, 110.6880, 120.2830, 120.6650.

1. Introduction

In recent years there has been a push to develop ameans of digitizing cuneiform tablets, the world’s old-est known writing system.1,2 Unlike most other formsof documentation, cuneiform is 3D in nature. The me-dia are rounded clay tablets (with writing often wrap-ping around the sides of the tablet), and the charactersare wedge impressions made when the clay was moist(Figure 7 below shows a photograph of a cuneiformtablet). The quest for digitization is fueled by severalfactors. Only a small fraction of the estimated 500,000tablets known to exist can be made available for publicdisplay.3 Even for cuneiform scholars, of which thereare few, access to worldwide collections is expensive,time-consuming, and can be politically difficult.1,4

The Cuneiform Digital Library Initiative,5 an in-ternational collaboration among many universitiesand museums, has utilized a flatbed scanner to aid

in abstracting pictographic symbols from cuneiformtablets.2 This approach, along with other 2D means ofpreservation, falls short of preserving much of theinformation resident on cuneiform tablets, such asthe tablet material properties, writing that wrapsaround the tablet, and author-dependent features in-cluding wedge depth or accent, and character size.6

Several researchers have utilized laser-based scan-ners to obtain a 3D digitization of cuneiform tablets.2,3

While superior in data content to 2D methods, laserscanners have their own shortcomings. Laser systemsare expensive3 and subject to error attributable tospeckle noise and multiple surface reflections in deepgrooves.4 In addition, there is an inherent trade-offbetween the depth of field and resolution of the scan.4Both Kumar et al.1 and Woolley et al.3 cite 50 �m asthe best attainable lateral resolution for a laser-based system; this is also the resolution achieved byAnderson and Levoy.2 Several scholars have indi-cated that 50 �m resolution is insufficient and arguethat a lateral resolution of at least 25 �m is re-quired.1,3,6

Holographic recording schemes have also beenused to obtain shape data on cuneiform tablets7,8;Dreesen et al.8 were able to obtain a lateral resolutionof 3 �m. However, this scheme still requires multipleholograms to capture all faces of the object, and theresulting holograms would quickly prove cumber-some for the sharing and storage of information. Most

The authors are with The Johns Hopkins University AppliedPhysics Laboratory, 11100 Johns Hopkins Road, Laurel, Mary-land, 20723-6099, USA. D. Hahn’s e-mail address is [email protected].

Received 3 October 2006; revised 2 January 2007; accepted 24January 2007; posted 24 January 2007 (Doc. ID 75751); published1 May 2007.

0003-6935/07/152838-13$15.00/0© 2007 Optical Society of America

2838 APPLIED OPTICS � Vol. 46, No. 15 � 20 May 2007

importantly, holograms are an analog storage me-dium. To alleviate the problem of data storage andsharing, as well as to aid in visualization and anysubsequent processing, the digitization of the surfaceinformation is of paramount importance. Digitizationusing a holographic technique would require record-ing of the interference pattern via a CCD.9 In addi-tion, computer intensive numerical reconstructionswould be required to visualize the object.

We present a 3D scanner, based on incoherent il-lumination, which is designed to digitize cuneiformtablets at lateral resolutions as small as 5 �m anddepth resolution of approximately 2 �m. The scannerutilizes a camera and telecentric lens to acquire im-ages of tablets under varying controlled illuminationconditions. Image data are processed using photo-metric stereo and structured light techniques to de-termine the tablet shape and surface reflectancecharacteristics, namely the bidirectional reflectancedistribution function (BRDF). Color information isreconstructed from primary color monochrome imagedata. A preliminary version of the scanner and asso-ciated data processing algorithms has been previ-ously detailed as a work in progress,4 but was lackingin several key regards. First, a Lambertian BRDFwas assumed; we now discuss a means by which tosolve for the actual BRDF of the tablet material, afeature that is important for proper shape reconstruc-tion and material identification. Second, we presentscans of test objects that validate the data and boundthe measurement error. In addition, several algorith-mic improvements are detailed.

2. Scanner Design and Operation

A diagram of the scanner is shown in Fig. 1. Thescanner uses fixed camera and object positions tomaintain image registration while varying the light-ing conditions by rotating the source about the objectand by projecting different illumination colors andpatterns (the polar angle of the source is fixed). Adigital projector was selected as the light source as itprovides excellent illumination uniformity, can easilyproject custom patterns, and, through the use of anadditional lens, provides adequate collimation. Theobject is imaged with a telecentric lens; it is the mag-nification factor of this lens and the pixel size of thecamera that determine the horizontal resolution ofthe scanner (current camera technology limits thisresolution to approximately 5 �m when using a tele-centric lens of unity magnification). Sharp image fo-cus is obtained by attaching a neutral density (ND)filter to the telecentric lens so that the iris of the lensis fully opened. A V block mounted on top of an ele-vation stage is used to position the object within theworking distance of the telecentric lens.

Scanner usage and associated data processingsteps are detailed in the flow chart shown in Fig. 2.Color information is obtained by illuminating the ob-ject with solid primary colors over various azimuthalangles. Shape information is obtained by combiningtwo techniques: the method of photometric stereo,10

which provides information that is locally accurate,and structured light analysis,11,12 which providesglobal accuracy. Photometric stereo methods are also

Fig. 1. Scanner design (Ref. 4).

20 May 2007 � Vol. 46, No. 15 � APPLIED OPTICS 2839

used to recover the surface BRDF.13 Each image isprocessed, upon acquisition, to correct for cameranoise, camera nonlinearity, and illumination nonuni-formity.14

A. Application of Photometric Stereo

The method of photometric stereo is used to obtain asurface normal map of the object and to determinethe surface BRDF in accordance with a parameter-ized model, specifically the Ward model.15 This isaccomplished by acquiring images over various azi-muthal angles under a collimated white-light source.The brightness of each pixel in each image is depen-dent upon the illumination, view, and normal direc-tions, as well as the BRDF of the surface. Given thedata and the known illumination and view directions,the BRDF and normal map are iteratively estimated.The normal data resulting from photometric stereoanalysis can be integrated over small areas to obtaingood estimates of the surface height. Unfortunately,the normal map does not form a conservative surface,and small errors accumulate when integration is at-tempted over larger areas; the data are locally accu-rate but suffer larger scale inaccuracies.16,17

B. Application of Structured Light

The structured light technique implemented projects aseries of 1D sinusoidal patterns onto the object at afixed polar and various azimuthal angles. By acquiringdata at multiple azimuthal projection angles, it is pos-sible to determine surface orientations that may beunder shadow at a subset of projection angles. How-ever, there is still a limit to the steepness of surfacesthat can be measured; the limitations to structured

light measurement involving phase-to-height conver-sion algorithms are quantified by Zhang and Huang.18

At each projection angle, four patterns, each out ofphase with one another by 90°, are projected for eachof a series of iteratively doubled frequencies. Each ofthe images of different phase for a single frequencyis used to determine a phase value that is unaffectedby variations in surface reflectance. This processingis performed using the Carré technique of phase-measurement interferometry.19 The resulting imagesare compared to images of a flat white background tocalculate the phase difference and corresponding rel-ative object height.12 The resulting height data, al-though sampled at the same resolution as the normaldata, are inherently lower in resolution. This resultsin the opposite characteristics of the surface normaldata—globally accurate but of low resolution.

C. Combination of Normal and Height Data

The two preceding analysis techniques form a syner-gistic data set that contains all information necessaryto construct an accurate surface map of the object.The global, low resolution height from structuredlight analysis is combined with the locally accuratenormal data from photometric stereo via an errorminimization algorithm; this results in a high reso-lution data set that is geometrically accurate on boththe global and local scales.

3. Processing Algorithms

A. Photometric Stereo

The technique of photometric stereo is used to calcu-late both the surface normal map and the BRDF of

Fig. 2. Scanner operation.


the object. The main premise of the technique is thata surface will appear brighter when the illuminationdirection converges toward either the surface normal(for a Lambertian reflector) or the angle of specularreflection with respect to the camera (for a diffuselyspecular surface). By acquiring enough images undercontrolled illumination conditions, it is possible toboth reconstruct the BRDF of the object surface andto determine the surface normal map. In principle,three images are the minimum required for calcula-tion of the surface normal map.10 To reconstruct theBRDF, one additional image is required for each pa-rameter of the BRDF model. However, it is beneficialto acquire more images than are absolutely necessaryso that the error attributable to measurement noise isreduced. Acquiring additional images also mitigatesthe shadowing problems.

The photometric stereo algorithm implemented issimilar to that of Goldman et al.,13 but has severalkey differences. In particular, rather than allowingthe BRDF to vary for each individual pixel, we as-sume that it is constant over the object surface. Inaddition, we do not assume known material types orcharacteristics and fit the parameters of the Wardmodel15 directly (instead of adjusting the materialweights for preset Ward parameters).

The initial step of the algorithm assumes a Lam-bertian BRDF and solves for the normal map via themethod detailed by Woodham.10 The intensity valuesof the point �x, y� for a series of images acquired underuniform and collimated illumination are written as

I� � QN� n� , (1)

where Q is the reflectance of the point, N� is a matrix,which describes the directions of incident illumina-tion, and n is the surface normal at �x, y�. Althoughonly three images are required to uniquely invert Eq.(1), more are used and a least-squares approach istaken to reduce error and to account for shadowedfacets. Defining the z axis to point downward from thecamera toward the object, Eq. (1) becomes

�I1

É

IK�� Q�sin��sin��1� sin��cos��1� �cos��

É É É

sin��sin��K� sin��cos��K� �cos��

��nx

ny

nz�, (2)

where � is the polar angle and � is the azimuthalangle. The least-squares solution is

Qn� � ��N� TN� ��1N� T�I�. (3)

The normal map resulting from Eq. (3) is used asan initial guess in an iterative algorithm that firstoptimizes the parameters of the BRDF and thenupdates the normal map. A three-parameter Ward

BRDF model is used15:

��i, �r� ��L

�

�s

�cos��i�cos��r�

exp��tan2��2�4��2 , (4)

where the independent parameters are the coefficientof the Lambertian term, �L, the coefficient of the spec-ular term, �s, and the width of the specular term, �. InEq. (4), �i, �r, and � are the angles between the normaland the illumination directions, L, view direction, V,and halfway vector, h � �L V��L V�, respec-tively. Parameter optimization is performed usingthe Levenberg–Marquardt nonlinear optimization al-gorithm20 with the objective function

� � k,p

�Ik,p � f�np, Lk, �L, �s, ��2, (5)

where Ik,p represents the observed intensity of eachpixel p in each image k, and f�np, Lk, �L, �s, �� is thetheoretical intensity according to the pixel normal,illumination direction, and BRDF model.

Once the BRDF parameters have been determined,an updated normal map is calculated. Unfortunately,this is not trivial for the case of a non-LambertianBRDF; the only way to perform this operation is tominimize the objective function, �, with respect to thesurface normals.13 In other words, a search is per-formed over the upward facing hemisphere by vary-ing the normals and keeping the Ward parametersconstant. The exit criterion for this condition is achange in all three Ward parameters of less than0.1%.

As previously noted, the normal map resultingfrom this approach does not form a conservative sur-face owing to the nature of the point-by-point calcu-lations. The integration from the normal map to aheight field is path dependent and results in unreal-istic shapes when performed on a global scale. Tocounter these problems, structured light data are in-corporated into the final surface determination.

B. Structured Light

The basic premise of the structured light techniqueemployed is to measure the phase shift of a sinusoidalpattern projected onto the object versus onto a flatbackground. The resulting phase difference is propor-tional to the relative object height where the constantof proportionality is determined by applying the tech-nique to a flat object of known height.12 There arethree main problems with this approach. First, eachprojection angle results in some of the object featuresbeing shadowed. This problem is resolved by usingmultiple projection angles and statistical analysis tointelligently select an appropriate final value of thephase difference at the point �x, y�. If a final value ata given point cannot be determined within an accept-able degree of certainty, the hole is filled when thedata are combined with the normal map to constructthe final surface. Such cases might arise due to mea-


surement error on a multifaceted area imaged by asingle pixel or due to the lack of enough independentphase measurements (from different azimuthal pro-jection angles) in areas of deep grooves consistentlyunder shadow or areas of steep slope with respect tothe view direction.

The second problem with this approach is that il-lumination nonuniformities, camera noise, and vari-ations in surface reflectance and orientation make itdifficult to accurately measure phase. This is espe-cially true when viewing a textured object such asa cuneiform tablet. Various techniques of phase-measurement interferometry can be used to solvethis problem as they are not dependent upon localreflectance or illumination level. We have chosen toimplement the Carré technique, which requires thatfour images of differing phase (but the same fre-quency and amplitude) be acquired. A value of thephase, �, at each projection frequency is then calcu-lated via the relation19

� tan�1��I1 � I4 I2 � I3��3�I2 � I3� � �I1 � I4��I2 I3 � I1 � I4

�,

(6)

where the Ix represent four 1D sinusoidal patterns,each out of phase with its predecessor by a constantphase shift. The quadrants of � are determined byexamination of the signs of quantities proportional tosin� � and cos� �21:

I2 � I3 � sin� �, (7)

I2 I3 � I1 � I4 � cos� �. (8)

Although only three images are needed to uniquelysolve for the phase, the Carré technique uses four,and thereby reduces error due to measurement un-certainty. It also has the advantage of working whena linear phase shift is introduced in a converging ordiverging beam where the amount of phase shift var-ies across the beam.19 In other words, the experimentwill still work even if the projection beam is not per-fectly collimated.

The third and final problem associated with theimplemented structured light technique involves thetrade-off between the measurement error and phaseambiguity. In short, the greater the period of the sinu-soid, the greater the measurement error. However,short period sinusoids lead to an increase in phasedifference ambiguities ��n2��. An iterative approachis taken in which the frequency of the projected si-nusoids are doubled, and the resulting value of � isused to refine the original value of �. Thus the highestresolution sinusoid is used to determine the phase,and the iteratively frequency-halved sinusoids areused to resolve the �n2� ambiguities.

The shortcoming of this particular implementationof the structured light technique is that it is intrin-

sically low in resolution, both laterally and axially.The projector is lower in resolution (number of pixels)than the camera and also overfills the area viewed bythe camera. In addition, the acquired images are sub-ject to intrinsic camera noise; this contributes to un-certainty in high resolution phase values. The endresult is an oversampled and low resolution surface,in comparison to the normal map obtained using themethod of photometric stereo. However, the benefit ofthis structured light technique is its high level ofglobal accuracy, which is unattainable by the photo-metric stereo method.

C. Final Surface Determination

The photometric stereo and structured light resultsare complementary data sets that contain the infor-mation necessary to construct an accurate surfacemap of an object. The normal map resulting fromphotometric stereo analysis does not form a conser-vative surface, and integration of the data yieldsglobal shape inaccuracies. The resolution of the nor-mal data, however, is excellent. Structured lightmeasurements, on the other hand, provide globallyaccurate height information that is inherently con-sistent but low in resolution. An iterative minimiza-tion algorithm was therefore designed to combine thedata sets in such a way as to take advantage of thebenefits of each and to mitigate the drawbacks.

Two main constraints are incorporated into the al-gorithm. The first minimizes the error between theslope of the final surface and the normal map on apoint-by-point basis,22 thereby taking advantage ofthe high resolution of the normal data and avoidingproblems due to large-path integration. The secondconstraint minimizes the relative height differencebetween the final surface and a median filtered struc-tured light height map. This constraint uses theglobal accuracy of the height data while removing theeffects attributable to isolated noisy data points. Acomplete description of the algorithm follows.

The height of the object surface is updated accord-ing to the rule

hn1�x, y� � hn�x, y� �1 � ��x, y��hP�x, y� ��x, y�hSL�x, y��. (9)

In this equation, hSL is the difference between themedian filtered height, hSL, and the surface height

hSL�x, y� � hSL�x, y� � hn�x, y�, (10)

� is a weighting factor bound to the interval �0, 0.5�,

��x, y� ��hSL�x, y��2�2; hSL�x, y� � �

1�2; otherwise ; (11)

� is the lateral image resolution (product of the pixelsize and telecentric lens magnification); and hP is the


height error calculated by comparing the shape of thecurrent surface to the normal data

hP�x, y� ��

4�Sx�x � 1, y� � Sx�x 1, y�

Sy�x, y � 1� � Sy�x, y 1��, (12)

where S is the slope error

S� �x, y� � S� �x, y� � S� P�x, y�. (13)

S is the slope as calculated from the surface height,

Sx�x, y� �hn�x � 1, y� � hn�x 1, y�

2�;

Sy�x, y� �hn�x, y � 1� � hn�x, y 1�

2�, (14)

and SP is the slope measured by photometric stereoanalysis

S� P�x, y� � �nx�x, y�nz�x, y�

x �ny�x, y�nz�x, y�

y. (15)

The initial guess, h0, used in the algorithm is a 4 � 4block-integrated surface (the x- and y-slope maps arecombined and locally integrated using the Fried al-gorithm23) where the shape of each block is deter-mined by integration of the normal data. The centerheight of each block is set to the average height overthe region as measured by structured light analysis.An average height adjustment of less than ��100 isused as the exit criterion for the algorithm, with theadded restraint that at least ten iterations be per-formed.

D. Color Map

The color map of the object, C, is calculated bymultiplying the reflectance data (Q) determinedfrom photometric stereo analysis by a normalizedred-green-blue (RGB) color map of the object. Thisnormalized color map is obtained by summing andnormalizing the background corrected monochromeimages (red, green, and blue) over all azimuthalangles of data acquisition. Specifically,

C� � Q ��CR CG CB�

��CR CG CB��, where (16)

CX � �

�background corrected r, g, or b color images�.

(17)

4. Results

All data presented hereafter have been acquired us-ing a camera with square pixels 6.7 �m in size and atelecentric lens of 4� magnification, making eachdata point 26.8 �m apart laterally. The finest reso-

lutions of structured light phase images were projec-tions of each sinusoidal cycle over a lateral distance ofapproximately 0.6 mm. We present results from twospherical test objects, as well as an actual cuneiformtablet (denoted T24).

Note that lateral resolutions as low as 5 �m can berealized by replacing the imaging camera with onehaving 5 �m square pixels and the imaging lenswith one of unity �1�� magnification. However, thesechanges would also reduce the field of view of thescanner by a factor of 4 in both lateral dimensions.The imaging components used were chosen to bestoptimize this trade-off between the lateral resolutionand the scanner field of view for the purpose of scan-ning cuneiform.

Fig. 3. Z components of the surface normals of (a) a mouseballand (b) painted ball bearing resulting from photometric stereoanalysis. The solid curve represents the initial guess assuming aLambertian BRDF, the dotted curve the final normal map afterBRDF parameter optimization, and the dashed curve the theo-retical normal map assuming perfect spheres of the appropriateradii.


A. Spherical Test Objects

The absolute accuracy of the scanner (including theprocessing algorithms) was evaluated by scanningtwo spherical targets, a 22.7 mm diameter com-puter mouseball and a 12.7 mm diameter ball bear-ing painted with flat (diffusely reflecting) paint. Theformer constitutes a Lambertian spherical object,while the reflectance properties of the latter includea diffuse specular term. The data were acquiredwith the light source at a polar angle of 35.8° and 12azimuthal angles spaced at 30° increments.

Figure 3 shows the results of photometric stereoanalysis on the two spheres by comparing the z com-ponent of the surface normal of a cut through thecenter of each sphere to the theoretical values. Thecalculated normal data shown are from both the ini-tial guess assuming a Lambertian reflectance [Eq.(3)] and the final result [Eq. (5)] after optimization ofthe BRDF Ward model parameters. As can be seen inFig. 3(a), the mouseball is much closer to a Lamber-tian reflector than the painted ball bearing. However,subsequent BRDF and normal optimizations do stillmake a noticeable improvement to the normal map ofthe mouseball. The ball bearing [Fig. 3(b)] has a muchmore significant diffuse specular component to itsBRDF. As a result, the initial normal map based on aLambertian BRDF is grossly misshapen. Again, theoptimization of the objective function [Eq. (5)] revealsa much improved set of surface normals.

The resulting parameterized BRDFs of the spheresare compared to purely Lambertian BRDF profiles inFig. (4). We have chosen to calculate and show theexpected reflectance in the view direction over a cutthrough the center of a spherical target given a par-

ticular BRDF and illumination direction. This is di-rectly representative of the observed intensity on theoverhead camera with the light source at the polarangle (35.8°). As can be seen in Fig. 4, the BRDF ofthe mouseball is indistinguishable from that of aLambertian sphere with a reflectance of 0.85. Thepeak reflectance of these BRDFs occurs where thesurface normal is oriented directly toward the an-gle of incident illumination. This is not the case forthe painted ball bearing, whose BRDF contains asignificant diffuse specular term. The shape of theball-bearing BRDF is drastically different, and thepeak reflectance occurs where the surface normal isbetween the view and illumination directions, as isexpected for a specular reflector.

The height of the mouseball is shown in Fig. 5,which compares the results of structured light anal-

Fig. 4. Reflectance profiles of a cut through the center of a sphereplotted against the zenith angle of the sphere’s surface. The viewdirection is directly overhead the sphere and the incident illumi-nation at a zenith angle of 35.8°. The diamonds represent thereflectance profile given the BRDF of the mouseball, the squaresthe BRDF of the painted ball bearing, and the solid and dashedcurves Lambertian BRDFs of 0.85 and 0.22 reflectance, respec-tively. The latter Lambertian BRDF is in fact the Lambertiancomponent of the BRDF of the ball bearing.

Fig. 5. Height profile of a cut through the center of the mouseballcompared to that of a perfect sphere of like radius. The solid curveand diamonds are the final surface height and structured lightheight of the mouseball (not all points plotted to reduce clutter),respectively, while the dashed curve represents the surface of aperfect sphere.

Fig. 6. Histogram of the angular difference between the surfacenormals of the mouseball and those of a perfect sphere of like radius.


ysis and the final surface [Eq. (9)] to the theoreticalheight. We have chosen to show the results of theseanalyses on the mouseball, the larger of the twospherical targets, to better represent the global res-olution of the scanner. By setting the height of aperfect sphere equal to the height of the top of thetarget, the absolute height deviation was calculated.Over the top half of the mouseball (a distance of over11 mm in the vertical direction and 22 mm in thehorizontal direction) 98% of the height deviation re-sulting from structured light analysis was within0.2 mm with the mean and standard deviations be-ing 67 �m (absolute value) and 85 �m, respectively.These results indicate the excellent global accuracy ofthe structured light technique. The statistics of theabsolute height deviation of the final surface areslightly improved; 98% of the height deviation wasagain within 0.2 mm, but the mean and standarddeviations were lowered to 59 �m (absolute value)and 76 �m, respectively. The most significant im-

provement from the raw structured light result is thereduced noise of the final result, evidence that theminimization algorithm has used the photometricstereo normal data to reduce the noise in the heightmap. Note that even though the final height looksrough compared with a perfect sphere, the mouseballitself has a rough surface (not perfectly smooth);therefore it is quite plausible that the roughness ob-served, which is on the order of 50 �m, is represen-tative of the true surface.

Figure 6 shows a histogram of the angular differ-ence between the final surface normals (resultingfrom the minimization algorithm) of the mouseballand those of a perfect sphere. The mean and standarddeviations of the distribution are 3.3° and 4.8°, re-spectively. It is indeterminate how much of this erroris attributable to the surface roughness of the mouse-ball; however, it is evident from Figs. 5 and 6 thatboth the overall shape and high resolution surface

Fig. 7. (Color online) A small cuneiform tablet (test specimen T24) compared to the size of a U.S. quarter.

Fig. 8. Meshed surface maps of a 2.68 mm � 2.68 mm cross section of the T24 tablet showing (left) the structured light height and (right)the final surface.


orientation of the mouseball are well captured by thescanner.

B. Cuneiform Tablet (T24)

To put a perspective on the size of the T24 tablet andthe resolution of the data, Fig. 7 shows a U.S. quarternext to the T24 tablet. The tablet was scanned usingthe methods previously described. The meshed sur-face maps of a 2.68 mm � 2.68 mm cross section�100 � 100 pixels� of the front of the tablet are shownin Fig. 8; the left mesh shows the structured lightheight while the right mesh depicts the final surface.These figures substantiate the claim that the mini-mization algorithm preserves the global height infor-

mation resident in the structured light data whilediscounting the local noise.

The absolute error of this data cannot be calculatedwithout a priori knowledge of the cuneiform surface.To quantify the expected error, an independent ex-periment consisting of scanning a flat metallic blockwas performed. The standard deviation of height val-ues over a 2 mm � 2 mm area of the block were 9 and2 �m for the structured light and final surface heightmaps, respectively.

Photometric stereo analysis resulted in a BRDFsimilar to that of the mouseball—indistinguishablein shape from that of a Lambertian surface, butslightly lower in amplitude due to the reflectivity of

Fig. 9. x (top) and y components (bottom) of the normal vectors over a 2.68 mm � 2.68 mm cross section of the T24 tablet (left) asmeasured by the photometric stereo method and (right) computed from the final surface.

Fig. 10. Height profiles of the T24 tablet. Circles represent the structured light height map. A local integration of the normal data isshown with squares. The stars are the final surface (10 iterations).


Fig. 11. (a) Photograph and (b) rendering of the T24 tablet (Ref. 4) from approximately the same view direction.


the tablet. The x and y components of the photometricstereo normal vectors are shown in the upper plots inFig. 9 and compared to those calculated from the finalsurface in the lower plots in Fig. 9. Overall, the slopeinformation resulting from photometric stereo is wellpreserved in the final surface. In areas of steepslopes, however, the final surface exhibits a slightlysteeper slope than the measured normal data. This isbecause the minimization algorithm adjusts the finalsurface to more closely match the structured lightheight in these areas, thereby avoiding an excessivesmoothing of the genuine structure.

Example height profiles of tablet data are shown inFig. 10. Both the integration of the normal map andthe final surface suppress the noise of the height data.However, the integration is inaccurate with respect tothe genuine structure of the tablet in comparison withthe minimization algorithm in areas of steep slopes.This is evident in the center valley in the left plot inFig. 10. Here, a sharp groove was detected in thestructured light data but smoothed over by purenormal integration. The final surface, on the otherhand, comes within approximately 50 �m of thegroove depth as measured by structured light analysis.

Fig. 12. Rendering of the T24 tablet (Ref. 4) from approximately the same view direction as the photograph in Fig. 7. The distance fromthe top to the bottom of this rendering is approximately the diameter of a U.S. quarter.


A photograph of the tablet under ambient lightingis shown in Fig. 11(a), and a rendering from approxi-mately the same view direction and with the lightsource toward the right is shown in Fig. 11(b). Thisrendering was created by digitally stitching scans ofthe tablet front and bottom together.4 The position ofthe light source was chosen to accentuate the featuresof the tablet in order to demonstrate the utility ofhaving a 3D surface model compared with photo-graphic records. The rotations of both the surfacemodel and the light source to any orientation allow forthe best possible rendition of a given tablet feature.The rendering matches the photograph cuneiformcharacter for cuneiform character, wedge for wedge,and also maintains the gross shape of the tablet. Thisfigure pair also points out one of the distinct features ofa rendering versus a photograph. Photographs inevi-tably display a finite depth of field in which some fea-tures are sharply in focus and others are blurred. Thisis not the case for a rendering that inherently has aninfinite depth of field. Another rendering is shown inFig. 12. In this rendering, the view direction matchesthat of the photograph in Fig. 7.

In addition to photographic comparisons, cunei-form scholars were presented with the T24 tablet andthe visualization software portraying the T24 dataset. Their observations and comments indicated thatall characters were not only clearly and accuratelyrepresented, but were observable at a much finerresolution and smaller scale than conventional tech-niques allow. Other observations and remarks madeaddressed the accurate reconstruction of dents andsurface scratches smaller in scale than cuneiformcharacters, the ease and safety of visualization, thesignificant improvement over photographic digitiza-tion, and the unprecedented potential for remotestudy.24,25

5. Conclusion

We have implemented an incoherent light 3D scan-ner capable of achieving lateral resolutions rangingfrom 5 to 100 �m or more and depth resolutions ofapproximately 2 �m. Associated data-processing al-gorithms were also detailed; these included photo-metric stereo techniques that allow for the recovery ofthe surface normal map and BRDF, a phase-steppingstructured light technique, an error minimization al-gorithm used to combine high resolution normal andlow resolution height data, and an object color recon-struction scheme.

The scanner was originally designed to scan cunei-form tablets, and it is for this reason that BRDF de-termination is of significant importance; the materialsand material characteristics of cuneiform tablets varygreatly depending on the time and geographic locationof origin.24 However, the robust design of the scannerallows for application toward many objects, includingbut not limited to historical artifacts, fossils, teeth, andbones.

The data presented from spherical objects haveshown the high resolution of the scanner on bothglobal and local scales. The scans of a cuneiform tab-

let were also presented herein, as well as to scholarsin the cuneiform community, who provided compli-mentary feedback on the data quality and the tech-nology potential.24

This work has been supported by the NSF Me-dium ITR IIS-0205586. The authors thank all thosewho have collaborated on other aspects of the Dig-ital Hammurabi project, including Subodh Kumar,Dean Snyder, and Lee Watkins. The authors alsothank special Jerry Cooper (who was able to ar-range for loan of the T24 tablet from the collectionat Johns Hopkins University) and Jonathan Cohenand Budirijanto Purnomo (who provided the ren-dering software with which to view the scanned 3Ddata).4

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non-laser-based scanner for three-dimensional digitization of historical artifacts

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