A high-precision photogrammetric recording system for small artifacts

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Original article

A high-precision photogrammetric recording system for small artifacts Philip Sapirstein Department of Art History/Center for Digital Research in the Humanities, University of Nebraska-Lincoln, 120 Richards Hall, P.O. Box 880114, 68588-0114 Lincoln, NE, USA

a r t i c l e

i n f o

Article history: Received 26 March 2017 Accepted 19 October 2017 Available online xxx Keywords: 3D recording Photogrammetry Accuracy Best practices Digital heritage Small artifacts Museums

a b s t r a c t Archaeologists, preservationists, and many other researchers have increasingly turned to photogrammetry as an alternative to optical 3D-scanning hardware. The technology is sufficiently new that researchers have only begun to establish the protocols and standards. This article presents a simple yet rigorously controlled method for 3D modeling small artifacts ca. 5–10 cm across. The specimen is rotated on a turntable to facilitate photography, and artificial lighting creates an even illumination throughout the resulting models. A masking technique allows a full 360◦ view of the object to be restored simultaneously, eliminating the need for aligning and merging partial scans or other post-processing. Repeatability tests of the resulting models indicate high precisions and accuracies that exceed those reported previously for photogrammetric modeling in the literature. The method can match the accuracy typically attained by commercial optical scanning systems. © 2017 Elsevier Masson SAS. All rights reserved.

1. Introduction Archaeologists and preservationists have recognized the great potential for 3D recording by means of highly automated varieties of photogrammetric software. An alternative to optical scanning hardware, photogrammetric recording is becoming increasingly common in projects modeling artifacts, excavations, and heritage sites [1–7]. In addition to the inherent value of creating highquality digital surrogates for the preservation and dissemination of antiquity, 3D models have found numerous applications in archaeological and historical research [8]. One area has been the enhancement and illustration of scanned objects, which on one level may supplant the time-consuming and potentially inaccurate process of drawing by hand [2,9], and on another can enhance faint traces of weathered inscriptions [10,11]. Another application involves the automated classification based on 3D shape or profile, especially for comparison among potsherds or intact vases [12–14]. Reassembling fragmentary objects is another common archaeological problem that may be partially automated through analysis of 3D scans [15–17]. Despite the growing popularity of photogrammetry, researchers have expressed skepticism about its reliability [18,19]. Depending on the cameras and strategies for implementation, the

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quality of photogrammetric recording can vary widely in comparison to optical scanning hardware, whose design and operational parameters necessitate more standardized procedures. Thus, it remains unclear when this promising low-cost alternative is able to create 3D content meeting the levels of accuracy and efficiency required by a particular research application. This paper focuses on the challenges posed to photogrammetry when recording small museum objects. It proposes new protocols for a seamless 360◦ modeling of artifacts about 5 cm across, effective for a range of materials frequently encountered in archaeological collections. It assesses the accuracy of the system, concluding that it may outperform uncontrolled approaches by up to an order of magnitude, and arguing that archaeologists and preservationists who have examined the accuracy of their photogrammetric models have sometimes employed ineffective methods that underestimate real performance. In fact, when implemented with coded targets, photogrammetry can be as reliable for measurement as much costlier commercial hardware.

2. Context of the research The investigation began with the digital study of the temple of Hera at Olympia, Greece, a seminal monument in use over 1300 years as a Greek shrine, a Roman repository for sculpture, and

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finally an early Christian wine cellar [20,21]. Under construction by the first decade of the sixth century BCE, the Heraion was one of the most ambitious and innovative building projects attempted in the archaic Greek world, possessing a stone peristyle and many other characteristics that would soon become defining attributes of the Doric architectural style. In the Olympia museum, about 200 architectural terracottas that may be associated with the temple represent not only the best-preserved example of the archaic Laconian roofing system, but also belong to several distinctive series, including imitations made in Roman times to repair the aging archaic roof [22,23]. The ongoing research at Olympia prompted the design of a new photogrammetric recording system for the tiles. The long-term objective is restoring the temple as far as possible and publishing the digital records and 3D scans online in a virtual museum of the monument [17]. The whole of the architecture and associated fragments at the site had already been fully recorded by photogrammetry. While the many small terracotta fragments that survive from the superstructure of the Heraion should also be included in the corpus, their digitization poses a different set of problems. The Heraion tiles were originally very large, scaled suitably for a monumental temple, but the surviving fragments have been reduced to 5–20 cm across their maximum dimension and are just 1.5–4.0 cm thick. Their thin, plate-like shapes are challenging to model in 3D because the narrow edges provide little information by which to align opposite faces (Fig. 1). The tile fragments can only be understood by careful geometric analysis and reconstruction. Archaic Laconian tiles are almost perfectly circular in section, and the tiles decorating the perimeter of the roof are actually wheelmade [23]. Manually determining the original stance, diameter, and cross-sections from the irregularly broken fragments is difficult and prone to high errors, whereas 3D scans can be more reliably measured with algorithms already in common use for potsherds [12,14] (Fig. 1a). Once the overall geometry of a fragment is estimated, highresolution imagery is valuable for assessing surface markings. Formerly painted brightly, today the surfaces of most tiles preserve only faint traces of light decoration over the dark background paint (Fig. 1b). Marks left by the manufacturing process require especially fine imagery. Two of the many such examples are compassed lines marking divisions in the painted decoration that were later erased, and wheel-marks on the outer and back surfaces (Fig. 1c–d). In conventional photographs, these narrow incisions and ridges tend to be obscured by paint and post-depositional accretions. Even in areas where they are legible, close-up photographs divorce the texture from the context — the specific location on the original specimen — which is more effectively captured within a full 3D recording. Toward the various goals of preservation, geometric reconstruction, and surface analysis, the 3D models should capture geometry accurately down to at least 0.1 mm. Higher resolutions would be preferable for recording the faded paint and manufacturing marks, or other attributes such as the clay fabric. Moreover, the whole 360◦ of the object should be captured, not incomplete views. Because of the limited time frame available for handling specimens at Olympia, it also is paramount that the 3D models are generated quickly and at a predictable level of accuracy, allowing quality to be monitored during the fieldwork. The previous use of photogrammetry for site recording at Olympia, and the unparalleled high quality of the textures generated by this method, both make it an appealing approach to recording the tiles. However, at the outset it was not clear whether the technique could efficiently meet the recording objectives at Olympia.

3. Photogrammetry in recent heritage research As a general concept, photogrammetry is almost as old as the camera itself, whereas software-based techniques classified as “close-range” photogrammetry (CPG) have been available since the 1970s [24]. In CPG, the relative orientations of scanned or digital photographs are estimated through targets visible from several points of view. The targets might be machine-recognizable encoded 2D patterns physically present in the scene, or else points manually marked by the user in the software. Although valued for its high precision, CPG is far too slow to generate enough 3D surface data to approach the densities of points acquired by optical scanning hardware. In the 2000s, new methods known collectively as Structure from Motion (SfM) automated scene reconstruction by replacing the targets of CPG with feature points detected and matched through Scale-Invariant Feature Transform (SIFT) [25–27]. Next, during Multi-View Stereo (MVS), the software interpolates surface points at a higher resolution. Although Image-Based Modeling has been a popular description of this new approach, it is referred to as Automated photogrammetry (APG) here to emphasize that the software builds upon the core principles of CPG. 3.1. Challenges for photogrammetric recording of small objects At small scales, especially for artifacts less than 20 cm across, APG confronts the optical limitations of a digital single-lens reflex (dSLR) camera [28,29]. The primary obstacle to image clarity is the depth of field (DOF), which narrows as a progressively smaller subject is projected onto a sensor of fixed dimensions. Multi-focused image stacking has been demonstrated as an effective countermeasure to restricted DOF with very small subjects less than 2 cm across [30,31]. However, image stacking greatly increases the number of photographs and adds new software to the processing pipeline. It has been tested with only partial views of the subject rather than a full 360◦ recording desirable at Olympia and many other archaeological and heritage applications. Reducing the aperture widens the DOF. At high apertures the whole image is blurred by diffraction (Appendix B.2), making it difficult to acquire images at high resolution of objects smaller than 2 cm across. For objects 2–15 cm across, an aperture setting above f/11 can be adequate to mitigate DOF restrictions without multifocal imagery. However, higher apertures also restrict so much light that artificial illumination is desirable and, regardless of the particular setting, the exposures will almost certainly be long enough to require that the camera be stabilized on a tripod to prevent motion blur. Because repositioning the tripod between every shot can be time-consuming, an expedient solution adopted by, among others, Nicolae et al. [29], Porter et al. [5], and Magnini et al. [32] is to rotate the object in a full circle on a turntable, allowing the photographer to take a rapid succession of shots at a fixed distance from the subject, and only adjusting the camera height between these “rings.” In these studies, autofocus was active to accommodate changes in distance as the object rotates relative to the stationary camera. The turntable introduces new problems. SfM assumes that the scene does not change throughout a batch of photographs. When the background is visible in the photographs behind the turntable, the software will tend to restore (correctly) the scene with every camera in one position relative to the static background, entirely omitting the rotating object. The user must intervene to prevent this normal operation. Black paper and cloth help mask out the background, leaving only the object and turntable for consideration by the APG software [5], so SfM restores the desired (albeit incorrect) scene as if the camera had rotated around the artifact. By

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Fig. 1. Architectural terracottas 1L34, 1L43, and 11L4 from Olympia. Identifying the stance and (a) cross-sectional profile is essential to restore the original geometry. Traces of faded decorative (b) light-on-dark painting and (c) incisions require high resolution 2D imaging of at least 10 samples per mm. Partially effaced (c) planning incisions and (d) wheel marks on tile 11L4 are most clearly revealed by the uncolored 3D mesh generated at an equally high sampling resolution.

masking out a potentially large background, however, the image area available to SfM for calibration is reduced, potentially degrading the parameters for lens projection.

Another obstacle is obtaining a full 360◦ recording when the turntable obscures lower views of the object, whose bottom might be hidden by its mounting (Fig. 1: 1L34). At least two workarounds

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have been proposed, the first balancing the object on a wire and taking all the photographs in one batch [32], and the second capturing separate top and bottom views that are later fused [5,32]. Neither approach is entirely effective. The first will be unsuitable for many varieties of delicate artifacts, obscures the surfaces in contact with the wire, and all but rules out the use of a tripod – severely degrading image clarity and the control over DOF. The second method raises a problem common to optical 3D-scanning hardware, where multiple viewpoints are needed to capture every side of an object [8]. During post-processing, partial scans are aligned, usually by an iterative-closest-point (ICP) algorithm, and fused in a unified mesh [33]. Besides the considerable amount of user time required for secondary processing, the latter APG method offers no straightforward manner to transfer the texture layers from the partial scans to the merged model – whose high texture resolution would otherwise represent a major advantage of APG over scanning hardware. 3.2. Accuracy assessment of APG at small scales Investigations into the accuracy of photogrammetric systems have compared software-reported lengths to ground truth measurements taken by some other means. Such errors can be most conveniently expressed as a dimensionless 1:k ratio, where k is the maximum dimension across the subject divided by absolute error [34]. Although time-consuming, CPG is known for its exceptionally high accuracy, capable of measuring coded targets at precisions up to 1 part in 500,000 with a large-format metric camera, and at least 1:100,000 with a dSLR. In contrast, recent tests of the new APG methods have reported much lower precisions of 1:500 to 1:1500 – or 100 times the error of CPG using similar equipment [18,35,36]. No inherent flaw in APG lessens its accuracy relative to CPG. The high error in recent archaeological and heritage recording is attributable to low-quality optics, a lack of attention to stable calibration, and the omission of machine-readable coded targets [7,36]. In fact, when coded targets are included, SfM alignments in APG have been shown to reach CPG precisions of 1:100,000 [36–38]. Moreover, the very low precisions in the 1:1000 range are not necessarily due to poorly calibrated camera networks, but also to the widespread use of measurement by laser distances (usually a Total Station) or rulers as the ground truth against which the photogrammetric measurements are assessed. Because the distance errors for these tools can easily exceed those attainable by photogrammetry, the APG accuracies were not effectively tested [36]. Reports on APG with objects less than 1m across have reported comparatively high accuracies, in part due to the use of more reliable reference models. Two studies of subjects ca. 50–100 cm across found a good correspondence between the APG surfaces and references created by structured-light scanners, the discrepancies having a Root Mean Squared (RMS) of just 0.2–0.3 mm [39,40]. Fewer tests have been tried with very small objects, though Koutsoudis et al. [41] modeled a 20 cm-tall Early Cycladic figurine with APG and an optical scanner, finding correspondences within 0.1 mm. A comparison of APG and scanned models of five crania had similar results [42]. Several researchers have addressed a problem with many small objects — surfaces lacking sufficient patterning to be effectively modeled by APG software — by projecting contrasting patterns [26,28,29,43] or developer spray on the subject [5]. From the reported errors, the 3D surfaces created by APG would appear to be within about 1:1000–1:5000 of models generated by an optical scanner. Most of the preceding tests involved fairly large objects, more than 20 cm across, where DOF restrictions and lighting are manageable. The recording procedures vary, or are not fully reported, and in most cases the object was not overturned to capture all of its sides [28,40]. The turntable-based systems discussed in the

previous section were developed for recording stone tools down to about 5–10 cm long, but the testing is inadequate to assess accuracy. Porter et al. [5] compare their photogrammetric models to those created with low-quality optical scanning systems but present no quantitative assessment. Using the same photographic method, Magnini et al. [32] compare distances on the models to measurements taken manually with digital calipers. Discrepancies among the landmarks are generally low — in the range of 1:300 to 1:1000 — but may well indicate the error of the calipers and its users more than that of the APG models. 3.3. Repeatability testing at small scales In order to assess accuracy methodically, recent APG implementations of small artifacts have compared point and distance measurements to some variety of “ground truth” data. Yet acquiring suitable models from which to assess the APG performance is no simple task [26,28]. Optical scanners have been the norm for testing small objects. The systems common in the cultural heritage sector have sampling intervals of 50–200 ␮m and precisions down to 5–25 ␮m for depth [28,31,44]. Actual performance may be lower than that claimed by the manufacturers. Error in models created by the inexpensive NextEngine scanner has a standard deviation of 40–100 ␮m [45]. The Brueckmann StereoScan, with a resolution down to 12 ␮m, was used effectively for reference data to which to compare APG models of ca. 25 cm-long crania [42]. However, tests of the Brueckmann against X-ray microtomography (microCT) models of teeth revealed a standard deviation of 20–30 ␮m, and significantly higher levels of noise caused by translucent surfaces are obvious in the Brueckmann imagery [46]. Performance may also be degraded by reflective or dark surfaces [47]. Moreover, scans produced by optical hardware must be assembled from multiple stations, typically at least a dozen partial scans, whose relative alignment by ICP introduces some error [44,47]. Dental scanners and MicroCT might improve the resolution and precision [30] but are not well suited for roof tiles or most other archaeological specimens. Assuming for the sake of argument that a photogrammetric system is precise to at least 1:3000, we might logically conclude that the model of a subject 10 cm across would be sensitive within less than 35 ␮m, or a 3 cm object within 10 ␮m. However, if the precisions of ca. 1:50,000–100,000 demonstrable in large scenes could be scaled down, a 5 cm artifact could theoretically be measured at intervals as fine as 1 ␮m. In other words, there is no guarantee an optical scanner will outperform photogrammetry, and in fact the standard errors measured for optical scanners [44,47] could be more than an order of magnitude greater than the best-case scenario for APG. When no method of higher accuracy is available for generating control data, metric performance can be estimated by the repeatability of several models produced using one technique [36,48]. A series of separately photographed and processed models of the same subject reveals the internal consistency. This approach is advantageous because it is simple to apply and makes no prior assumptions about the reliability of the reference data. A disadvantage is that systematic skews or omissions cannot be quantified, although a user may perceive badly distorted or missing elements and describe them qualitatively. Overall, because APG generates massive quantities of measurements, repeatability tests provide a good sense of the consistency of the models generated in separate photography sessions. 3.4. Objectives for the study The models produced by a particular APG implementation cannot be assumed to meet a standard precision and resolution

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without an explicit presentation of the hardware, digitization methods, and at least some testing data. At present, the majority of tests have employed reference measurements whose relatively high systematic error might have blurred the real performance of APG. Furthermore, the conditions, equipment, and protocols used for testing vary substantially. Neither do any small-scale APG approaches adequately address the problem of calibration, which in APG and CPG scenarios alike is most effectively accomplished by integrating coded targets [7,36]. By relying on self-calibration of auto-focused imagery where the parameters of the lens might vary significantly from photograph to photograph, the small-scale systems published to date may not achieve high internal consistencies. Errors in the range of 1:1000 or better might be deemed acceptable for the purposes of many recording projects involving cultural heritage, but we have yet to establish the real performance of APG recording at small scales. At Olympia, the minimum performance before selecting APG as the primary recording method was determined by a collection of 75 tiles selected for 3D recording, while the remaining less-informative fragments were simply photographed and sketched in preparation for simpler forms of cataloguing. Comprising at least several of the better preserved examples of each type, fragments captured in 3D were most frequently between 10–15 cm across and as small as 5 × 5x2 cm (Fig. 1). The standard ca. 2.0 cm thickness meant that every object needed to be imaged at relatively high resolutions. To reach a minimum desired resolution of 50 ␮m or finer, the APG would need to be precise to at least 1:2000, and ideally 1:4000 [7]. An additional question is whether APG is expedient under the circumstances at the Olympia museum. If optical scanning hardware were much faster per object, the higher equipment price

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might be offset by longer hours spent creating photogrammetric models. Because the terracottas are in storerooms off limits to scholars without written permission, any research imposes additional demands on the museum staff. These factors together with the remote location of the site, to which imaging equipment generally must be brought, militate against experimenting with different recording methods. Rather than improvising an APG system with limited tools and under time pressure at Olympia, the protocols described here were developed elsewhere. 4. A high-precision system for small-object recording In preparation for APG recording projects, a series of models were created in a more accessible archaeological collection at the University of Nebraska State Museum (UNSM), where different equipment and protocols could be subjected to repeatability tests. The protocols worked well not just with terracotta, but with a variety of objects representative of most archaeological specimens. Twenty-five specimens in the UNSM ranging from ca. 5 cm to 50 cm across were modeled. Because the DOF restrictions were not greatly problematic for artifacts greater than 15 cm across, only the three smallest objects were selected for accuracy testing (Table 1). Each presented different challenges for AGP modeling. The burnished surface of the pot is mildly reflective, and its interior could only be viewed only from above its mouth (Fig. 2a). The solidcast bronze deer has many slender projections, in particular on its antlers, although the mottled green patina is advantageous for MVS (Fig. 2b). A rodent skull from the paleontology collection (Fig. 2c) was the most difficult to record. The surface is reflective (Suppl. Fig. A2), its concave spaces are difficult to capture, and several

Table 1 Objects modeled by APG.

Pot Deer Skull

UNSM Inv.

Dims./Area (cm/cm2 )

Material

Reflectivity

Shape

961.5.1949 A23017 1606-62

8.3 × 8.1 × 7.9/358 6.6 × 8.0 × 2.3/35.8 5.2 × 3.3 × 2.5/47.2

Ceramic Bronze Bone

Mild (burnished) Very low Moderate (varnish)

Hollow interior Tubular, narrow Complex, holes

Fig. 2. The photography system using a tripod, (a) turntable, and illuminated by (b) a ring-flash mounted on the lens. The (c) dark background assisted the software when initially masking out background areas. Both scale bars and target field are incorporated in the scene (Appendix A.1). The illumination from the sides of the object can reduce shadowing, but only if the object is matte.

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Fig. 3. Top (a) and (b) bottom views with the camera artificially restored by SfM as if it had orbited the object. After masking, the two stations can be merged into (c) a complete 360◦ recording.

holes lead into inaccessible interior cavities. The teeth are not only reflective but also slightly translucent, which can be problematic for optical scanning hardware. 4.1. Modified protocols for achieving an optimal calibration Significant departures from the protocols published elsewhere [5,32,42] are the use of fixed camera settings during photography, the integration of coded targets and scale bars, and the methods for unifying the top and bottom views within the APG software (also see Appendices A and B). A turntable system is standard when photographing small objects. Because the new approach is designed for stable calibration, it is important that the lens settings, including focus, be fixed throughout photography. The camera may be held at the same distance from larger subjects without difficulty, but, because DOF is severely restricted with close-ups, a small object must be carefully centered on a turntable to preserve the focal length in each ring of photographs (Fig. 3). Static lighting from the camera position means that the specimen is illuminated from different angles as it revolves (Fig. 3a). Changing illumination can degrade SfM/MVS performance by altering the appearance of features used by SIFT to match adjacent photographs. However, if the lighting is always directed from the camera, every captured surface will be nearly unshadowed. A ringflash mounted on the lens is effective for small subjects, eliminating modulations in shading except in deep concavities not reached by the flash (Appendix A.3). Because SfM relies on variations in the value of the surface, this approach works best for artifacts with high frequency texturing and is ineffective with completely featureless surfaces – which are rare for archaeological specimens. The camera is metered and focused manually once per batch of photographs (Appendix A.2–A.3). Several turntable rotations with the camera at different elevations result in 90–130 images. Extra photographs are taken of complex areas of the specimen, especially concavities, when deemed necessary. In order to capture all views, the specimen is flipped over and the process repeated, for a total of 180 to 270 images. Larger or spherical subjects might not require as many photographs, but as a rule there should be at least 35 images per side, and 70 total, or else SfM will not reliably reconstruct the camera positions.

4.2. Coded targets and unified orientations Machine-readable targets and scale bars are seen in Figs. 1–3. APG generally benefits from the inclusion of targets, whose centers the software can automatically locate at sub-pixel precision [36] (Appendix A.1). First, the targets allow camera orientations and calibrations to be refined beyond the estimates obtained by SfM alone. Second, the targets accelerate SfM. They provide a priori information about the relative positions of the camera and ensure the software will prioritize features moving on the turntable rather than the static background. The acceleration to the calculation estimating the camera network is particularly advantageous when digitizing large numbers of objects, since SfM should be run during the fieldwork to identify any errors in the photography that must be remedied. Third, targets help the user detect and correct any images that have been aligned incorrectly by SfM. Following the stages detailed in Appendix B, the two batches of “top” and “bottom” views, each restored to resemble a hemispherical array of cameras, are separately aligned, pre-processed, and masked (Fig. 4a and b). After every photograph has been masked to precisely the silhouette of the object, a final SfM processing stage aligns the two sides to each other, resulting in a full 360◦ coverage of the evenly illuminated specimen, rendered as a watertight mesh (Fig. 4c). The cameras share a single calibration profile refined by the SfM features and targets. Although the final images are masked to only the surfaces of the object, the targets previously detected outside the object improve the calibration. 5. Test results at the UNSM The following tests compare multiple 3D models created by the proposed recording system. First, the range of specimens selected in Table 1 reveal how APG is affected by material, topology, and size of the subject. Second, different camera systems were employed to allow a direct comparison of the effects of DOF and other optical parameters during an otherwise similar recording session. Third, the contribution of coded targets to the resulting models is assessed by their inclusion or suppression during processing. Generally, a bigger camera sensor should outperform a smaller due to improved clarity and projection stability, but in close-up photography the increased blurring on the bigger sensor relative

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Fig. 4. Orthographic projections of the specimens reproduced at 1:1 scale from the final APG models.

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8 Table 2 Cameras with their abbreviations tested in the study.

FX DX RX

Camera model

Sensor: size (mm), pixels, pixel size (␮m)

Nikon D800e Nikon D7100 Sony DSC-RX100

35.9 × 24.0 23.5 × 15.6 13.2 × 88.0

to that of the smaller may be problematic [30]. Accordingly, three camera systems abbreviated as FX, DX, and RX were tested (see Table 2; Appendix A.2). Two dSLR systems, the DX and FX, were compared using the same Nikkor 60 mm f/2.8D capable of focusing down to a 1:1 reproduction ratio. The fixed focal-length (“prime”) lens was selected because of its superior clarity and internal stability compared to zoom lenses. The RX is a popular model that had recently been tested by Porter et al. [5]. At less than 1/7th the area of the FX sensor, its sensor is prone to significant levels of noise. The all-purpose zoom lens could only focus up close at its widest setting, equivalent to 28 mm on the FX camera. Because less of the specimen could be captured in each image (Suppl. Fig. A2), additional photographs were needed: 235–270 per specimen vs. 180–210 for the dSLR cameras. Two completely independent batches of photographs were taken of the specimens with each camera system, for a total of six models of each object. From the 18 separate photography sessions, a total of 42 models were rendered using different software settings. To take advantage of the consistent lens settings throughout the job, the models were rendered with the full set of coded targets and a fixed calibration. A second set for each FX and DX set was rendered with no targets except for six points and scale bars to fix the scale of the scene (three each for the “top” and “bottom” views). For the RX camera, a similar set of tests were conducted, but due to its instability a third APG set was generated including the targets but allowing calibrations to vary per image.1 There are two principal values reported below. First, “precision” — the threshold of uncertainty below which measurement is probably unreliable — is assessed by the discrepancy of APG-generated points from control data. Precision is the value most frequently reported in the previous literature on APG accuracy. Because the mean or Root Mean Square (RMS) of the errors are sensitive to outliers, the median absolute discrepancy is preferred here. Second, “accuracy” is represented by the 2-␴ (95.45%) confidence level of the absolute error. Repeatability tests are straightforward to implement with linear distance measurements (Section 5.1), whereas the 3D meshes have been compared to a reference model whose points were averaged from four independently generated models (Appendix C.3). Systematic errors are considered in terms of scale (Section 5.2), resolution and depth (Section 5.3), and surface derivatives (Section 5.4). 5.1. Photogrammetric calibration and distance First are the target-to-target distances estimated by the APG software relative to scale bars, whose lengths had been previously calibrated within ca. 20 ␮m (see Appendix A.1). The dSLR camera sets including targets diverged from the given measurements with an RMS of 10 ␮m, about what one would expect from the precision at which the scale bars had been measured. However, the APG estimates also converged at new values that coincided significantly better with one another than with the distances provided to the software. The RMS of the dSLR estimates from these new “consen-

1 The calibration for the DX and FX cameras was also allowed to vary in additional tests that have been excluded because no significant changes were observed in the resulting models.

Lens

7360 × 4912 6000 × 4000 5472 × 3648

4.9 3.9 2.4

60 mm f/2.8–60 same 10–37 mm, f/1.8–4.9

Table 3 Absolute distances (␮m) from consensus scale bar lengths from the values reported by SfM. Camera

Sets

Both dSLRs FX DX FX DX FX DX RX

Targets No targets Pot (∼ 20 cm)a Deer (14–18 cm) Skull (9–13 cm) Targets No targets

n

Median

RMS

2-␴

144 72 24

1.7 7.2 3.1 3.5 1.7 1.0 2.1 0.9 11 48

2.9 45 3.8 4.4 2.1 1.4 2.9 1.3 18 124

6.3 125 7.2 8.6 4.0 2.9 6.5 2.7 41 281

24 24 158 34

a For the three specimens, the number in parentheses is the view width during photography. See Appendix Table A.1 for further information. Only measurements taken using targets are reported. The other comparisons are for all the specimens.

sus” values is just 2.9 ␮m, and the median discrepancy was also improved by a factor of four, from 6.5 to 1.7 ␮m. These refined consensus measurements are treated as the ground truth in the calculations in Table 3, which supports several important conclusions. First, using targets, APG length measurements are repeatable with a median less than ±2 microns for scenes 9–20 cm across, equivalent to a precision around 1:100,000, while the 2–␴ accuracy is close to 1:30,000. The best performance is with the medium-sized deer, whose accuracy is about 50% better than for the others relative to its scale. Such results are promising. A precision close to 1:100,000 had been demonstrated with the FX camera at a 50 m site [36], and, despite the DOF restrictions, the target-based survey appears to scale down to miniature photography without a detectable loss. Second, the scale bars and a target field lead to substantial accuracy improvements (Table 3). Even without targets, most measurements are within 0.1 mm of the reality, but, compared to scenes with targets, the target-less precision is reduced by a factor of four, while the RMS and 2-␴ repeatability errors are greater by almost a factor of 20 – a scale accuracy below 1:2000. Even though the scenes without targets retain six targets and scale bars, they are insufficient to set the scale accurately.2 Third, at small scales, optical limitations on the FX camera remove the advantages to be expected from its larger sensor area. The FX camera only outperforms the DX on the pot, while the DX was the optimal system for the smaller deer and skull. The smaller sensor is increasingly advantageous for tiny objects because of the comparatively broad DOF (Appendix A.2). Still, the smallest RX sensor delivered the poorest performance (Table 3). The amalgamated RX data with targets show that error is consistently six times greater than for the dSLR cameras. When targets are omitted, the dSLRs lose some of their advantage but still outperform the RX. Fourth, the software-reported RMS for the targets in the scene is shown to be a useful proxy for the actual accuracy. When there are many targets present, the software reports an RMS measured in units of pixels on the camera sensor. The median value is typically

2 Setting the target-less scale-bar lengths to the refined consensus measurements did not improve performance.

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P. Sapirstein / Journal of Cultural Heritage xxx (2017) xxx–xxx Table 4 Absolute discrepancies (␮m) of the mesh vertices from the reference after rescaling by the specified absolute percentage. Camera

Sets

Rescaling/%

Median

2-␴

Max

Both dSLRs FX DX FX DX FX DX RX

Targets (n = 9) No targets (n = 9) Pot (∼ 20 cm) Deer (14–18 cm) Skull (9–13 cm) Targets (n = 12) No targets (n = 6)

0.010 0.023 0.016 0.011 0.010 0.015 0.022 < 0.001 0.049 0.484

4.6 5.7 5.7 5.1 3.8 4.1 7.2 5.6 20 20

22 32 24 22 19 17 34 30 79 79

568 625 568 642 408 197 756 685 521 733

For cases with more than one observation, the median or the larger of two values is reported. Like in Table 3, the width of view is given in parentheses for the individual specimens, whose errors are assessed only for scenes with targets. The other rows are averaged values for every specimen.

0.16–0.23 for the dSLR cameras in this study, and about twice that for the RX camera. Accuracy (A) can be estimated by the view width (v) and the pixel width on the sensor (p): A∼ = v·RMS⁄p For the pot modelled with the DX camera — with a software report of 0.17 pixel RMS error, a 19 cm view width, and a sensor 6000 pixels across — the formula suggests a real-world RMS (for A) of 5.4 ␮m – very close to the observed value of 4.4 ␮m in Table 3. When applied to the other objects in this study, the estimate of A is consistently between the actual RMS and the 2-␴ accuracy. The overestimation of the actual value may be attributed to the out-offocus targets whose centers cannot be restored accurately and thus raise the apparent RMS reported by the software. In a target-based APG recording, the real accuracy may be estimated from just the software-reported error. During the recording at Olympia, the quality of the orientations could be monitored after the relatively fast calculation of SfM. Any scene with the error expected for the camera system would render predictably in later stages of MVS, and higher errors prompted a return to the object for additional photography. The computationally intensive rendering of the final surfaces by MVS could then be performed reliably after the fieldwork concluded, using more powerful computers available at the university. 5.2. Scaling The foregoing section treats only the measurement performance for the coded target centers. What of the 3D surfaces restored by MVS, which matches whole pixels and thus is unlikely to reach such a high precision? First, in light of the relatively large errors in Table 3, it is unlikely that the models omitting targets have been correctly scaled. All models generated by both methods were rescaled by a uniform factor relative to a reference scan used for every model, eliminating previous discrepancies (see Appendix C.2; Fig. C.2). Even if the absolute scale of the reference is only approximately known, the models will be consistently scaled relative to one another. As shown in Table 4, the rescaling is lesser when targets are included. The change is more than halved for the dSLRs, and, without targets, the surfaces generated with the RX imagery have at least ten times the scaling error. The improvements are strongest for the largest object, the pot. With the dSLRs, rescaling is lessened by only 25% for the deer, and by less than 10% for the tiny skull, whereas the improvements are minimal for the RX camera. Even the target-based dSLR models have a systematic scaling error in the vicinity of 0.01%, indicating that the meshes generated by MVS cannot be precise above 1:10,000. In this study, the scale bar

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was set flat on the turntable beneath the specimen and thus primarily visible in photographs taken from overhead. Because the target centers themselves have been located more precisely than the SIFTgenerated tie points, additional targets and scale bars placed at different orientations around the object would likely improve the absolute scaling, if the research objectives were to demand even higher precision. 5.3. Surface consistency The camera sensors’ horizontal resolutions of 5500–7500 pixels are likely to limit the precision of MVS. The real-world x/y resolution of the imagery, or Ground-Sampling Distance (GSD) is 15–30 ␮m in this study (Appendix A.2/Table A.1). However, the APG software was run at 1/2-pixel sampling, so depth maps are generated at reduced resolutions. Together with diffraction blurring the effective GSD is closer to 50 ␮m (Appendix B.2). While measurements of target centers might be precise within a few microns, APG is unlikely to restore any surface geometry much finer than this GSD, equivalent to roughly 1:2000 at the scale of the specimens. However, much like an optical scanning system, due to the comparatively high precision at which the camera positions are estimated (on the order of 2 ␮m), finer depth measurement is theoretically attainable. An algorithm developed for this study reorients the models to a reference mesh and measures the distance from every vertex to the closest triangle of the reference (Appendix C.1). As shown in Table 4, the surfaces of the rescaled models are significantly more repeatable than might be assumed from the GSD. For the target-based dSLR models, the median absolute surface discrepancies are just 3.8–5.7 ␮m, and 95% of the points are within 20 ␮m of the reference. When targets are omitted from even the rescaled model, these values are degraded by ca. 20–40%.3 The FX camera is slightly outperformed by the DX for every specimen, most likely due to DOF limitations (Appendix A.2). Both systems produce surface meshes precise within 1:30,000–40,000 and accurate to 1:7000–1:10,000 for the pot and the deer. After scale corrections, it appears that the models’ surfaces are located with 95% confidence at the resolution of the sensor, and at a precision down to ¼ of a pixel. However, these figures are roughly halved for the smaller and more reflective skull, where the measurement system has evidently been degraded by optical limitations. The error for the RX models is about four times greater. These results are excellent, but the maxima in Table 4 reveal a few very large discrepancies in the restored meshes. These blunders, where errors reach 200–800 ␮m, are concentrated in small regions where the APG software failed to reconstruct the actual surface. While the presence of blunders undermines the reliability of APG generally, a closer look suggests they are predictable defects in surfaces that hinder successful imaging: occlusions and reflections (Fig. 5). For the pot (Fig. 5a), the 2-␴ errors are less than 25 ␮m, yet maximum discrepancies are about 20 times greater. The largest blunders are limited to interior, concave surfaces, which can only be viewed from above and are largely hidden from view. The only mistakes on the exterior are rare, at tiny pock-marks whose depth is inconsistently restored. The performance for the deer is generally excellent except at a small cavity near the neck. However, Fig. 5b shows a half-mm blunder in the FX models at the tip of an antler, where a featureless white inclusion hinders SfM/MVS reconstruction. Moreover, because the deer was supported on a prop during

3 There is no improvement for the RX camera after the rescaling is taken into account, probably because the lens is unstable so that the individual calibrations were not much refined by the presence of targets in overhead images.

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Fig. 5. Blunders in the models of the pot, deer, and skull (a–c). Red indicates areas with discrepancies greater than the 3-␴ level. For the pot, the interior (left) is contrasted with the exterior (right) of the model.

photography of the “bottom” views, the lower edges of the antlers were not completely imaged. This blunder is not present in the DX models and might have been addressed through additional photographs with the FX camera or a better prop. The skull (Fig. 5c) was the most problematic due to its reflective surface and deep concave regions, especially on its underside, which have been inconsistently modeled. The blunders might have been reduced by more photographs of these features, or by projecting a randomized pattern on the surface to enhance the contrast [28], [29]. Regardless, the sides of these cavities are almost totally hidden and will never be as reliably recorded as the exposed surfaces. Even if a structured-light scanner

might perform better, such areas are difficult to capture using any 3D recording method.

5.4. Resolution While the results suggest that surface depths can be restored precisely, what of the mesh derived from imagery with a GSD of ca. 50 ␮m? A related question is how accurately the surfaces smoothed by the GSD reflect the true orientations and curvature of the specimen. Appendix C.4 describes quantitative tests that corroborate the following conclusions.

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Fig. 6. Close-up on a 1.5 cm region of the deer, showing the mean curvature per vertex for the (a) FX and (b) DX models; in (c) the two uncolored meshes are overlaid to show their correspondence. The arrow indicates a patch of accretions which are similarly reconstructed in the scans, but artificially smoothed compared to what can be seen in the (d) higher-resolution photograph.

Fig. 7. Close-up on a 1 cm region of the pot, showing (a) the triangulation with most edges 0.15–0.20 mm long; (b) the textured model averaging pixels from every projected photograph; and (c) one of the original photographs. While some of the resolution of the original photograph is lost in the averaged texture, almost all shadows and reflections have been eliminated.

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Fig. 6 shows the mean curvature estimate from two different dSLR models of the deer. The correspondence in strong positive (blue) and negative (yellow) curvature is strong. However, there is also a considerable amount of smoothing compared to the reality indicated by the photograph (Fig. 6d). The sub-mm stone accretions on the surface are not fully modeled. The height at which they protrude from the bronze is reproduced, as is their outer curvature, yet MVS is unable to capture the full curvature of these nodules, which turn back toward the bronze surface to form a concavity, not the smooth transition modeled by APG. The true surface is much rougher in comparison to the smoothed 3D meshes. Such blurring is also clear in Fig. 7, where the ca. 170 ␮m spacing of the mesh (7a) loses the finer perturbations apparent in the original photograph (7c). Because the spacing of the vertices varies with the local curvature of the surface, the meshes are dense enough to record surface geometry below 100 ␮m, but even features up to 200–500 ␮m (equivalent to a width of several pixels on the camera sensor) might be distorted. The tendency of MVS to smooth out undercut surfaces like those in Figs. 6–7 means that the rougher the original surface, the less accurate the reconstructed normals and curvatures will be. The user will inevitably discover fine details in the photographic texture that are difficult to discern from the mesh.

6. Conclusions The photogrammetric protocol tested here significantly outperforms others published to date. The system is highly transportable and its results predictable from values reported within the APG software. Photography typically lasts 10 minutes per object, and seldom more than 30 minutes (Appendix A.4). Stabilizing the object on the turntable, focusing the camera, and maintaining a consistent focus across different camera elevations occupy the most time, meaning that objects of similar sizes and shapes can be captured more rapidly in sequence. The operator might spend 15 to 45 minutes in the software setting up the processing, and machine computational times vary with computer hardware and level of extracted detail (Appendix B.3, Table B.1). Over the course of a workday, an experienced operator can photograph and calculate the final orientations for 10 or more models. At Olympia, the 75 objects were imaged over the course of four days, with less than 20 hours devoted to photography, and about twice this time was required for processing and checking the quality of the scene determined by SfM while still at the site. To date, more than 300 models have been completed using these methods at a similar pace, including other digitization projects. The failure rate is less than 2% and attributable to problems in the original photographs – blurring, omission of required vantages points, and the like. As long as the researcher completes the SfM processing of the photographs on site, such issues can be identified and addressed immediately. The computationally intensive final stages of production can be postponed until after the museum work. The system benefits from several key elements. First, integrating machine-readable coded targets refines measurement performance, most emphatically through its scaling of the model within 1:10,000. By refining the camera calibration, targets also can reduce the discrepancies among the vertices restored by MVS by up to 30% or more. A prime lens at one focus setting throughout the photography is required in order to take full advantage of the targets. Setting up lights on the lens enhances performance by eliminating directional illumination. For example, the texture applied to the model in Fig. 7b has been averaged from multiple images and has almost none of the shadows and reflections in the original photographs (Fig. 7c). Moreover, every camera orientation is linked through SfM into a single 360◦ recording during processing.

Table 5 Overview of the relative performance of AGP for the dSLR cameras. Type

Approach

Median

2-␴

Scale bar distances

Targets No targets Targets No targets Targets No targets

1:100,000 1:25,000 1:35,000 1:30,000 1:10,000 1:5000

1:30,000 1:1500 1:8000 1:5000

– – – – –

1:3000 1:1500 1:500–1:800 < 1:500 1:150–1:1000

Depth reconstruction (correctly scaled surface) Overall model scaling Resolution Effective GSD Textures Triangulation Surface derivatives Blunders (regions lacking imagery/contrast)

This would be difficult or even impossible to enact had there been inconsistent directional shading in the “top” and “bottom” photography sets. In this fashion, APG has a significant advantage over optical scanning hardware, which requires the combination of multiple vantage points during post-processing in order to capture a specimen fully. Although the FX camera prevails with larger specimens, the DX camera system was best for the smallest objects examined here. The RX models are several times worse than might be expected from the camera’s crisp imagery and wide DOF. Its failure can largely be attributed to the low quality and unstable lens. Even with a fixed lens, the dSLRs could perform very poorly without targets controlling error, their scaling errors increasing by as much as a factor of 20 when targets were omitted (Table 3). Overall, the tests indicate that a large or expensive camera is not so important for high-precision recording, but rather a return to recommendations for CPG: a stable lens, a carefully designed photographic environment with coded targets and scale bars, and setting the software to take advantage of these factors to refine the calibration of the scene. Table 5 recaps the approximate precisions and accuracies, which meet and on some levels exceed the requirements for the Olympia project. The results are on par with the optical scanners discussed in Section 3.3. Even if APG is slightly outperformed by a particular scanner, the advantage is small, and the DX camera system is but a fraction the cost. The inexpensive photogrammetric approach is likely to produce data that are sufficiently robust and metrically reliable to meet the requirements of most archaeological and cultural heritage research, and in an amount of time not greatly exceeding that of another 3D recording method. The analytical potential for reliable 3D models in archaeological and cultural heritage research is immense, and the demonstrably higher accuracies achieved through controls like those advocated here should promote the use of APG for creating 3D content in more contexts. Because photogrammetric models are visually appealing, especially due to the texture layer on the models that exceeds the quality of any optical hardware system, they have a high potential to serve as digital surrogates for the presentation and analysis of museum artifacts. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.culher.2017.10.011. References [1] M. Douglass, S. Lin, M. Chodoronek, The application of 3D photogrammetry for in-field documentation of archaeological features, Adv. Archaeol. Pract. 3 (2) (2015) 136–152, http://dx.doi.org/10.7183/2326-3768.3.2.136. [2] M. Magnani, Three-dimensional alternatives to lithic illustration, Adv. Archeol. Pract. 2 (4) (2014) 285–297, http://dx.doi.org/10.7183/2326-3768.2.4.285.

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Please cite this article in press as: P. Sapirstein, A high-precision photogrammetric recording system for small artifacts, Journal of Cultural Heritage (2017), https://doi.org/10.1016/j.culher.2017.10.011