Keywords

1 Introduction

During the past 20 years, enormous progress has been made in the field of optical range scanning. Among the biggest winners of this development ranks archaeology with its manifold objects and architectural structures, which both are often fragile and need to be preserved from irrecoverable destruction. In this field of work, non-contact 3D scanners can unfold their whole potential by digitizing objects fast and accurately, hence making them spatially independent and available to the public. Today’s scanning applications range from airborne laserscanning with a spatial resolution of about 10 cm and terrestrial measuring systems up to object scanners whose accuracy currently tackles the single-digit micrometer scale and will be limited in the future only by the wavelength of visible light. Although high acquisition costs impeded comprehensive usage so far, it could be proved in many projects that the new technology can not only provide many surprising insights, but shall also be employed simply for economical reasons. Daily practice has shown that accelerating the documentation process frees many resources which could then be used much better for the more scientific parts of archaeology [1, 2].

Besides the question of long-term data integrity and safety, a hitherto under-estimated problem of digital cultural heritage documentation is the amount of data that accumulates during the scanning sessions. Even though the development of computer hardware still follows Moore’s law and hard disk space is still available at very low costs, many issues of data processing and visualization have remained the same, because the resolution of scanners continuously increased as well. One of the first large-scale projects in this area has been the Digital Michelangelo Project in the late 1990s [4]. Already then it turned out that the merging and visualization of several hundred highly resolved scans is extremely challenging. The project itself even caused the investigation of new algorithms for processing and visualization of large-scale geometry data. Without doubt, high-accuracy digitization of finds and buildings has offered a number of new possibilities to archaeology, but it definitely seems appropriate to critically consider the problems coming along with this, since by far not every object needs to be scanned with the highest resolution available.

In this contribution, we like to concretely examine which parameters have an influence on the scanning effort and the amount of acquired data in order to deviate a formula with which the final memory demand can be estimated beforehand. Afterwards, we present a selection of possible fields of application for digital documentation, and we show that often a significantly lower resolution would be totally sufficient without decreasing the visual quality of the images. Finally, the calculations are illustrated by an example object in Sect. 4.4.

2 Practical Aspects of the Scanning Process

There is a broad range of applications for 3D scanning in archaeology, and the resulting requirements are highly different. In the following we will restrict ourselves to close-up range scanners, but the calculations remain valid for the bigger scales of terrestrial and airborne laserscanning as well.

At first, we like to construct some scenarios that are typical for today’s 3D documentation of finds. Therefore, we define three fictitious objects of different orders of magnitude.

  • Object 1 shall have a volume of about 1 m3, e.g. a head-high sculpture or column.

  • Object 2 shall have a volume of about 1 dm3, e.g. a medium-size ceramic vessel.

  • Object 3 shall have a volume of about 1 cm3, e.g. a coin or tooth.

Since the amount of acquired data is primarily dependent on the surface area of the object and not its volume, as a first step a conversion is necessary. Here, and in all of the following assumptions we proceed rather conservatively. More precisely, we will assume that the given objects are spheres with the denoted volume (1 m3, 1 dm3, 1 cm3), and one length unit shall be more generally referred to as 1 u.

$$ \begin{array}{ccllclc} {\text{V }} = { }\frac{1}{6}\pi {{d}^3} \hfill \\{\text{d }} = { }\root{3}\of{{\frac{{6V}}{\pi }}}(V = 1{\rm{[u]}^3}) \hfill \\d \approx 1.241\rm[u] \hfill \\A = \pi {{d}^2} \hfill \\A \approx 4,836[{\rm{u}^2}]\end{array} $$
(4.1)

Since the sphere is the body with the smallest surface-volume ratio, the denoted value is in fact a lower bound. Even on a cube with an edge length of 1 u this ratio would already be 6 and it would increase even further on more complex surfaces.

However, the crucial criterion for the amount of acquired data certainly is the lateral resolution of the measuring system, i.e. its sampling rate. Usually, the optical resolution of the sensor is fixed, and therefore the spatial resolution at the object primarily depends on the field of view used. Here, three typical configurations shall be considered as well:

  • System A shall have a sampling rate of 1 point/mm2 (e.g. Konica Minolta VI-910 with a field of view of 640 × 480 mm).

  • System B shall have a sampling rate of 25 points/mm2 (e.g. Konica Minolta VI-910 with a field of view of 128 × 96 mm).

  • System C shall have a sampling rate of 2,500 points/mm2 (e.g. Breuckmann stereoSCAN 3D-HE with a field of view of 48 × 36 mm).

Before coming to the data volume itself, at first the effort for digitizing the three given objects shall be estimated. This effort can be measured by the number of single scans necessary to cover the whole surface. To this end, it is not sufficient to simply compute the quotient of surface area and field of view, because on the one hand the object does not necessarily take the whole field of view and on the other hand a sufficiently big overlap is demanded for the robust registration of the scans. This overlapping rate should be specified to at least 50%, but a more realistic value would be 100% or even more as our own experiments and those of McPherron et al. [6] have shown (cf. Fig. 4.1). The greater the ratio of object size and field of view becomes, the more the tiling effect comes to the fore, but experience has also shown that the minimal number of scans is 10–12 independent of the object shape. Having these considerations in mind, we get the following approximated values:

Fig. 4.1
figure 1

Overlapping rates of a wooden beam (length = 111 cm) and a Bronze Age vessel (height = 12 cm), both scanned with different lenses and fields of view

Full size image

# Scans

Object 1 (4.8 m2)

Object 2 (4.8 dm2)

Object 3 (4.8 cm2)

System A (3,000 cm2)

32

> 10

> 10

System B (120 cm2)

800

> 10

> 10

System C (17 cm2)

6,000

60

> 10

The tasks A1 and C2 can still be handled and realized within one working day, but B1 and especially C1 are however questionable simply for economical reasons.

After the registration and merging of the particular scans we obtain the following point clouds. These are basically independent from the overlap factor, because during the merging process redundant information is simply discarded.

# Vertices

Object 1

Object 2

Object 3

System A

4,800,000

48,000

480

System B

120,000,000

1,200,000

12,000

System C

12,000,000,000

120,000,000

1,200,000

It can be seen that the number of vertices varies within several orders of magnitude depending on the object size and acquisition system. While the combinations B2 and C3 are already above average,Footnote 1 A1 is a high-density model even from today’s scales. All the other models are either too coarsely or too densely sampled, what is also visible from the corresponding memory demands. If we assume a memory demand of at least 44 bytes per vertexFootnote 2 for the moment, we get the following:

Memory demand

Object 1

Object 2

Object 3

System A

202.9 MB

2.03 MB

20.8 kB

System B

4.95 GB

50.7 MB

519.5 kB

System C

495.4 GB

4.95 GB

50.7 MB

Again, B2, C3, and also A1 can easily be handled by modern graphics hardware, but processing 4.95 GB of data (B1 and C2) already requires an up-to-date 64-bit system and causes serious difficulties for visualization at interactive rates. A data volume of 500 GB for scenario C1 (raw data not yet included) seems to be an utopic one even for the near future.

In summary, four parameters are to be named which influence the memory demand M during runtime: the surface area A, the optical resolution of the camera with n X  × n Y pixels, the size of the field of view A fov , and the size of the internal data structure for storing the geometry data (Φ in bytes per vertex). For the reasons already mentioned above, the overlap factor is irrelevant here. Be furthermore VBB the volume of the object’s bounding box, then by using (4.1) we get

$$ {\text{M }} \approx { }\pi { } \cdot { }\left( {\frac{{6.{{V}_{{BB}}}}}{\pi }} \right) \cdot \frac{{{{n}_x} \cdot {{n}_y}}}{{{{A}_{{fov}}}}} \cdot \Phi $$
(4.2)

which simplifies with Φ = 51 B (uncompressed normal vectors, 8-bit RGB colors) to the following estimation which has proven to be very reliable in many tests:

$$ M{ } \approx { 25}0{\text{B }} \cdot { }\root[3]\of{{VB{{B}^2}}} \cdot \frac{{{{n}_x} \cdot {{n}_y}}}{{{{A}_{{fov}}}}} $$
(4.3)

3 Determining the Optimal Resolution

Documentation of cultural heritage objects should never be an end in itself. Its main applications include the recording of the current state of preservation, damage mapping, and visualization for educational purposes. If this purpose is just popular scientific, accuracy is only of subordinate importance. But even if the original geometry shall be acquired as good as possible, in many cases a minimal feature size can be estimated and thus the scanning resolution can be limited. Basically four scenarios are conceivable:

  1. 1.

    The visualization shall be performed on a screen or via beamer. Even on current HD-ready devices the 2-megapixel border is not crossed. Consequently, no information gain is achieved above a vertex count of about 4,000,000 (assuming that front and back side are equally sampled), unless highly magnified details shall be shown.

  2. 2.

    A big poster or an oversize canvas shall be printed. This is mostly done for popular scientific or marketing purposes for which in most cases a photograph, or at least a texture-mapped 3D model with highly reduced mesh complexity are sufficient as well. Without doubt, macroscopic properties shall be highlighted and the viewing distance will in general be several meters.

  3. 3.

    An image in a findings catalogue shall be generated for scientific purposes [1, 5]. Usually a scale between 1:1 and 1:4, for bigger objects sometimes 1:10 or even more is chosen. Plastic details are clearly visible in a normal viewing distance of 30–50 cm.

  4. 4.

    An especially filigree object or a detailed view of the object surface shall be magnified true to scale in order to better depict mesoscopic properties that would not or only hardly have been visible in the 1:1 view.

Of course, this enumeration could have been proceeded towards the microscopic scale, but then a totally different kind of question would be present that with purely optical measuring systems could not be processed anyway. In this case a sample scan instead of scanning the whole surface would be much more convenient.

Which sampling rate is necessary for pictorial object documentation, i.e. scenarios 3 and 4, finally depends on two parameters: the resolution of the printing hardware and the visual acuity of the human eye. Current ink jet and laser printers achieve 300 dpi across the board. Although technically much higher resolutions would be feasible as well, these are often realized only in high-quality print media. This is mainly due to the fact that the resolving power of the human photoreceptors is restricted to approximately one arc minute even under optimal conditions. Hence, for a viewing distance of 50 cm two points can barely be distinguished if they are 0.15 mm apart (corresponding to a resolution of 170 dpi). For a distance of 3 m this value is still 0.9 mm (28 dpi).

Thus, if r is the image resolution in dpi and s is the image scale, the necessary (and sufficient) point distance in object space is d = 1/(r · s). In this case, every sample corresponds to at most one pixel. For a typical resolution of 300 dpi and a scale of 1:3 this would require for example a point distance of about 0.25 mm (acquisition system B). However, it should be mentioned, that good results can be obtained even for lower resolutions, when interpolatory shading techniques such as Gouraud or Phong shading are used.

4 Discussion and Conclusion

In this final section, the above considerations shall be discussed and illustrated on a biconical pot from the Bronze Age cemetery of Kötitz (Eastern Saxony), whose upper part is burnished and can hence be called smooth at the mesoscopic scale. Its lower part is roughened with a silt decoration (Fig. 4.2). At the break, a tripartite band of rills as well as a band of diagonal grooves can be seen. The vessel was scanned with a Breuckmann stereoSCAN 3D-HE and not digitally smoothed afterwards. Nevertheless, measuring noise is virtually invisible. The original model consists of about 6.7 million triangles which are sampled adaptively, i.e. areas of high curvature are tesselated higher than smooth ones. The median edge length of the mesh is 260 μm corresponding to a resolution of 98 dpi in the 1:1 view. This model is compared to its 15% reduction consisting of one million triangles with an average point distance of 568 μm (45 dpi).

Fig. 4.2
figure 2

Two levels of detail of the same ceramic vessel

Full size image

From Fig. 4.2 we can see two important facts. First of all, even in the wireframe model of the 1:1 view, the triangles of the high-resolution model are so small, that they are hardly visible in the at areas and even invisible within the rills and grooves. Hence, they are certainly smaller than one pixel in the 1:4 view and therefore lose their function as a 2D face. Secondly and consequently, the 1:4 shaded view of the reduced mesh is almost as accurate as the original, because missing information is 3 now compensated by the Gouraud shading technique.Footnote 3 Even the surface details, such as the rills, grooves and breaking edges are still preserved well enough.

Although the visual differences are hardly visible in the diffusely shaded view, the object tesselation can significantly influence the optical result. This becomes especially evident when a curvature-based shading is chosen, as it has recently become popular in documentation of archaeological artefacts [1, 3, 5]. If areas of high curvature are represented by fewer triangles, then the curvature is estimated on a coarser scale. Consequently, this leads to an apparent increase of the curvature magnitude, but also to an apparently broader range of the shading effect (Fig. 4.3). However, as long as the geometry reduction is not too high, this can cause a significantly better contrast in the shaded view without losing visual quality in general.

Fig. 4.3
figure 3

Influence of resolution on curvature shading

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As a conclusion, we can state that accurate documentation of archaeological artefacts undoubtedly requires high resolution 3D scanners, but this need for accuracy is often overestimated. In many cases, both time and memory could be saved if the purpose of the digitization is considered beforehand. In our opinion, 3D models with more than ten million triangles are mandatory and reasonable in only very few exceptional cases.