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PAINTING SURVEY BY 3D OPTICAL SCANNING 1
STUDIES IN CONSERVATION 49 (2004) PAGES 1–12
Received September 2002
1
Painting Survey by 3D Optical Scanning
THE CASE OF ADORATION OF THE MAGI BY
LEONARDO DA VINCI
G. Guidi, C. Atzeni, M. Seracini and S. Lazzari
INTRODUCTION
The study of paintings belonging to our cultural heritage
and the diagnosis of their conservation condition
represent an extremely difficult task. This is due to the
fragility of the objects which require non-contact
inspection techniques.
Possible approaches for non-contact analysis range
from infrared spectroscopy [1–3], which substitutes
physical sampling to obtain chemical composition of the
painting layer in many cases [4, 5], to diagnostic
imaging. In the latter case, in addition to the con-
ventional photographic representation with visible light,
exploration with different wavelengths is quite standard
[6]. Infrared reflectography [7–9] allows the surface
underneath the paint layer to be inspected, revealing the
preparatory drawing and the artist’s pentimenti; ultraviolet
photography [10] highlights restoration work and
successive pictorial additions to the original artwork; X-
radiography [11] provides information regarding its
internal structure.
All these imaging techniques, however, share the
common feature of examining the painting as a planar
image ignoring any information regarding its depth.
Even though the essentially two-dimensional nature of
paintings largely justifies this approach, a large number
of cases exist where the character of the deviation of the
painting from plane, mainly caused by deformation of
the support, is an essential piece of information for
conservation. In particular this is the case when wood is
used as the support, as in many paintings of the Italian
Renaissance, where aging, humidity, temperature
fluctuations, internal stress and vibration from traffic can
give rise to curving, warping and cracking of the wood
with consequent damage to the image.
In these cases, providing a map of the deformations
and their measurement can provide crucial information.
Early detection of deformation and monitoring of its
evolution can allow timely intervention before
irreversible damage takes place.
Until recently, the evaluation of support de-
formation has been carried out by visual inspection or
by raking light photography in order to highlight
qualitatively the presence of hollows and cracks on the
Optical scanning has been applied to generate a complete 3D model of the famous Adoration of the Magi by Leonardo da
Vinci (Uffizi Gallery, Florence). Front and rear surfaces and the sides of the great painting on 10 vertical planks of wood were
scanned with a lateral resolution around 0.3 mm, so as to obtain a high quality three-dimensional digital representation. The
main goal was to highlight and measure a map of deviations from planarity due to the curving and warping of the wood, leading
to the possibility of planning an intervention in order to prevent further deterioration. Some parts of the painting, exhibiting
visible local defects, were acquired with 90 µm of resolution. Application of 3D optical scanning has been proved to be of unique
value for documenting spatial deformation suffered by panel paintings and can represent a reference tool for periodic monitoring of
their state of conservation.
2 G.GUIDI, C. ATZENI, M. SERACINI AND S. LAZZARI
STUDIES IN CONSERVATION 49 (2004) PAGES 1–12
painting surface. The use of recently developed three-
dimensional scanning technology, so far applied to
sculptures [12–15], can provide a detailed map and a
quantitative measurement of the painting deterioration.
3D scanners have been previously used in painting
surveys to measure the extent and depth of cracks and
swelling of the colour layer along selected cross-
sections [16, 17] or to investigate the effects of
humidity changes on models of cradled panel paintings
[18]. To our knowledge, however, a complete three-
dimensional measurement of an original painting has
never been performed. Such a full three-dimensional
investigation was required as part of a diagnostic
campaign ordered to verify the conservation status of a
celebrated masterpiece by Leonardo da Vinci, the
Adoration of the Magi (Uffizi Gallery, Florence). The
unfinished painting, commissioned from Leonardo in
1481, was carried out on a support made from 10
planks of wood, reinforced by three crossbars, and
measures about 2.40 × 2.40 m. Rough handling
damaged the panel painting before the Uffizi acquired
it in 1670. Today the Adoration appears visibly
deteriorated and diagnostic tests were carried out in
order to document its current shape and to determine
the necessity of possible restoration work.
TECHNICAL BACKGROUND
The 3D acquisition of a surface is an activity originally
developed for problems far from the conservation of
paintings, for example, the precise measurements
needed for mechanical parts. Several techniques have
been developed for this purpose. The simplest are
generally based on contact between a probing element,
such as a metallic tip, and the object to be measured.
For example, this principle is employed by calipers.
These devices consist of a fixed arm, touching one end
of the object to be measured, and a moving arm
connected to a graduated rod sliding over the fixed
part. Once the moving arm is put against the opposite
end of the object to be measured, the accurate value of
the distance between the two points can be read on the
graduated rod. In this way the measurement is
performed in one direction only (i.e., the direction
along which the sliding part of the caliper moves).
Maintaining the same principle but increasing the
mechanical complexity, more powerful systems have
been developed. Modern coordinate measurement
machines (CMMs), represent one such example. Here
measurement is performed simultaneously along the
three spatial directions x, y and z, converted into digital
form and transferred to a computer as a set of three
coordinate values. By touching a number of points over
an object, its surface can be accurately measured in the
three-dimensional space.
From the same field of industrial application, some
alternative methods have been conceived for those
materials that are not able to support the pressure of a
contact element. In this case the exploring tip is
substituted by a ray of light and the related equipment is
commonly known as a non-contact measuring device.
The working principle is sketched in Figure 1 where a
simplified two-dimensional scenario is shown. The light
source, for example a laser beam, generates a light spot
over the surface under investigation, while an optical
sensor is held apart from the light source, thus acquiring
an image of the spot. By taking into account the
displacement d of the spot with respect to the image
centre and the focal length f of the lens in front of the
sensor, the
β
angle in Figure 1a can be estimated
through the relationship:
(1)
If the system has been previously calibrated in order to
know the distance between light source and sensor
(baseline b), and the orientation of the light source
(angle
α
), the coordinates of the illuminated point P on
the xz plane can be easily estimated through simple
trigonometric formulas:
(2a)
(2b)
When this principle is extended to the three-dimensional
space a slightly more complicated configuration is
implemented and a set of three coordinates (x
P
, y
P
, z
P
)
can be evaluated for each illuminated point.
Actual illumination strategies may vary; the most
frequently used are based on a light stripe generated by a
laser which is moved along the whole surface to be
surveyed [19, 20], generating a rectangular set of 3D
coordinates for each scanning. These are usually known
as ‘point clouds’ or ‘range maps’. An efficient alternative
is obtained by using white light projectors that generate
f
d
=
β
tan
α
β
tan
tan
1
+
=
b
x
P
β
α
tantan +
=
b
z
P
PAINTING SURVEY BY 3D OPTICAL SCANNING 3
STUDIES IN CONSERVATION 49 (2004) PAGES 1–12
several light stripes simultaneously (fringe patterns), thus
allowing an increase in the acquisition speed [21, 22].
Such devices are often known as 3D laser scanners,
referring to their original laser implementation, while a
more broadly accepted term is ‘range camera’.
The displacement between the 3D points measured by
the range camera and their true coordinates is modelled
through a set of three random variables, representing the
deviation along the spatial axes x, y, z, characterized by
their standard deviations (σ
x
, σ
y
and σ
z
). Due to the
geometric set-up of the system the most important error
contribution is given by σ
z
weighting 4–5 times more
than the deviations along x and y. It depends on some of
the typical opto-geometrical parameters shown in Figure
1b, decreasing as the baseline enlarges and increasing as
the stand-off grows [23].
Although with the non-contact approach the
measurement uncertainty grows with respect to the
contact based techniques, from some tenths of a micron
to a few microns, it exhibits some advantages such as the
invaluable capability of measuring objects which should
not be touched. A typical example is represented by
ancient works of art. This is why the application of these
techniques of acquisition and modelling of artworks has
been proposed in recent years with very interesting
results [12–15].
MATERIALS AND METHODS
The range camera employed (designed and man-
ufactured by Optonet Srl, Brescia, Italy) is based on
optical triangulation with fringe pattern projection. The
pattern projection scheme is described in the Appendix.
Depending on the type of surface to be imaged, the
field-of-view and accuracy of the 3D camera can be
reconfigured. This process allows the operator to adapt
the range camera to the accuracy requirements of
different types of artworks.
This capability involves a trade-off between res-
olution and model size. As in any 3D acquisition
project, the complete model is obtained by integrating
several range maps, each one representing a partial view
of the whole object. Since a single range map taken at
high resolution covers a limited surface, the number of
images to be merged together in order to generate a
complete three-dimensional model of the artwork has to
be increased as the resolution grows.
Another element to be taken into account is re-
presented by measurement uncertainty that, as specified
in the previous section, depends on the squared distance
between the camera and the object; high precision is
achieved by suitably limiting this distance, and thus the
framed area.
In the acquisition of the Adoration of the Magi different
opto-geometrical set-ups were employed for different
portions of the painting depending on their importance.
For the front it was decided to use a lateral (x-y)
resolution of 0.27 mm. Since the CCD mounted in our
range camera is 576 × 768 pixels, the consequent field-
of-view is 160 × 205 mm. The standard deviation values
at calibration were: σ
x
= 13 µm, σ
y
= 9 µm, σ
z
= 37 µm.
With this frame dimension the whole painting was
assembled with 23 rows, each formed by 17 or 18 range
maps, depending on the actual camera positioning along
each row.
FigureFigure
FigureFigure
Figure
11
11
1 Range camera: (a) schematic representation of the triangulation approach for 3D acquisition; (b) typical parameters.
(b)(a)
4 G.GUIDI, C. ATZENI, M. SERACINI AND S. LAZZARI
STUDIES IN CONSERVATION 49 (2004) PAGES 1–12
A portion of the front, highlighted in Figure 2, was
considered particularly critical due to some areas where
paint layers were detached from the wooden support,
and it was decided to digitize it at a higher resolution in
order to measure defects restricted to precise areas.
Finally the opto-geometrical set-up chosen for the
reverse gave a field-of-view slightly larger than the one
adopted for the front, since the main purpose was to
evaluate the overall structure rather than small defects.
The complete list of parameters is summarized in Table 1.
With the larger fields-of-view the camera was placed on
a tripod and moved manually by about 15 cm per step in
order to have enough overlap between adjacent range
maps. In Figure 3 the acquisition set-up for this particular
phase is shown. On the right-hand side it is possible to
see the range camera mounted on a tripod and located in
front of the painting. On the left side the pattern
projected over the painting during the acquisition phase,
and the pre-calculated signs for laterally moving the tripod
at fixed steps on the floor, can be seen.
For the central detail the framed area was too small
and the manual tripod movement was too rough to be
used. Therefore, taking advantage of the quasi-planar
geometry of the surfaces to be scanned, the range camera
was mounted on a mechanical rail approximately parallel
to the painting and moved with a 50 µm position
uncertainty (i.e., in most cases the mechanical translation
deviates from the theoretical position from –50 to
+50 µm). An additional advantage of the situation was
that the time required to digitize each horizontal row
was dramatically reduced. Since the range maps were
aligned off line with a software algorithm it was not
necessary to have the rail exactly parallel to the painting
surface. However, this condition was ensured in order
to avoid the painting surface exiting from the measure-
ment volume in any position along the rail. This was
checked by measuring the rail–painting distances at the
two rail ends with a laser distance-meter (Disto by Leica
Geosystems). As an additional safeguard, after each
acquisition step the operator checked for possible
missing data.
The great number of partial views taken all around
the object were integrated through a complex alignment
procedure in order to represent the whole surface.
Although the alignment and merging stages were
performed through a reliable commercial package
(Polyworks
TM
from Innovmetric Software Inc., Canada),
the model generation from the raw range maps was a
complex job. The main difficulty was related to the way
FigureFigure
FigureFigure
Figure
22
22
2 The Adoration of the Magi. The area within the rectangle
was also captured at higher resolution.
TT
TT
T
ableable
ableable
able
11
11
1 Acquisition parameters for the 3D survey of the Adoration of the Magi
Front – whole surface Front – central detail Reverse
∆x, ∆y (mm) 0.27 0.09 0.35
∆z (mm) 0.38 0.1 0.57
σ
x
(µm) 13 13 28
σ
y
(µm) 9 4 14
σ
z
(µm) 37 18 47
Field-of-view (mm × mm) 160 × 205 52 × 71 205 × 269
Total area (mm × mm) 2400 × 2400 580 × 770 2400 × 2400
Assembly (rows × columns) 23 × 17/18 14 × 15 18 × 12/13
Total images 393 210 222
Overlap % Horiz. 32 28 29
Vert. 35 21 35
PAINTING SURVEY BY 3D OPTICAL SCANNING 5
STUDIES IN CONSERVATION 49 (2004) PAGES 1–12
that the alignment algorithms work in order to find a
relative orientation of two adjacent range maps. In order
to refer all the acquisitions to the same reference system,
adjacent range maps were roto-translated by means of
specific software procedures that find a best match
between overlapping points (the overlapping levels
between adjacent range maps for the different painting
sections are reported in the last line of Table 1). Such
procedures, referred to in the literature as iterative
closest point (ICP) algorithms [24–26], use a cost
function, for example consisting of the mean square
deviation between groups of homologous points that
have to be minimized. When the overlapping surfaces
are not precisely superimposed the cost function gives a
high value (large deviation). Contrarily, if one of the
two surfaces is moved in order to fit to the other, this
function gives a much smaller number. The purpose of
an ICP algorithm is to change iteratively the mutual
orientation of two superimposed surfaces in order to find
the minimum deviation between them. The function
value decreases steeply to an easily recognizable absolute
minimum in the case of surfaces with evident 3D
features such as bumps or extrusions. It becomes less
peaked, with many local minima, when the surfaces to
be aligned are interrupted by 3D details, as on the flat
surface of the front of the painting. In the latter case the
minimization became much slower; in other words, the
flatter the surface, the longer the alignment procedure.
For this reason the alignment of the front of the painting
required as long as six weeks of CPU time on a double
processor computer equipped with two Pentium III
processors at 1 GHz and 2 Gbyte of RAM. This step
could have been speeded up by using the fusion of
different sensors for posing some key range maps in a
global reference system, rather than using only the
software alignment, as already tested in the modelling of
the Magdalen by Donatello [15, 27].
The huge memory was needed because of the large
amount of data to be managed simultaneously. As
specified in the last line of Table 1, the reverse, for
example, was represented with 222 range maps. The
total memory needed for the data set was therefore
1.37 Gbyte and the PC RAM was sized accordingly.
Once the 3D model is completed it can be visualized
in many ways. Computer graphics techniques allow its
presentation in an almost real fashion, calculating the
amount of light and shade that would be produced by a
hypothetical light source located at a well-defined point.
This process is often known as ‘synthetic shading’.
Shadows can be recalculated for a light located in any
particular point, as for example in lateral displacement. In
this way 3D features are visually enhanced.
RESULTS
The models generated by the three scans were used to
make an accurate dimensional measurement of the
artwork. The representation of the model with its own
texture (Figure 4a) allows us to recognize clearly the
masterpiece by Leonardo; when the same model is
represented without texture (Figure 4b), the shape of the
underlying wooden structure is highlighted.
This aspect is even more evident in the inspection of
the reverse of the model which, when represented with
texture (Figure 5a), hides most of the critical warping of
the wooden planks. Through a synthetic shading
obtained by using an angled light source (Figure 5b),
some interesting details emerge, like the depression on
the right-hand side of the picture, between the two
central bars.
In order to perform a more quantitative analysis, once
the models were generated they were used to evaluate the
painting deformations with respect to a planar reference.
This reference was created by identifying the best-fitting
plane of point clouds associated with each side of the 3D
model. The painting deformations, represented by the
distances of the model points with respect to the reference
plane, were thus displayed using colour coding, as
normally done in geographical maps to represent
mountains of different heights.
In Figure 6 an example of such representation is
shown. Figure 6a refers to the front of the painting and
FigureFigure
FigureFigure
Figure
33
33
3 Range map acquisition. The pattern projected over the
surface is captured by the videocamera and processed in real-time by
a PC. Pre-calculated marks for quickly moving the tripod in fixed steps
are visible on the floor.
6 G.GUIDI, C. ATZENI, M. SERACINI AND S. LAZZARI
STUDIES IN CONSERVATION 49 (2004) PAGES 1–12
6b to the reverse. The pink area on the left of Figure 6b
identifies the deep depression shown qualitatively by
Figure 5b (18 mm from the reference plane of the
reverse). This pink area corresponds to the light green
spot on the right of Figure 6a. On the upper and lower
right corners of the same Figure an abrupt colour variation
is also evident, corresponding to the analogous variation
shown in Figure 6b on the left corners. This clearly
highlights a steep deviation of the wood surface from
planar behaviour; taking into account that for the reverse
the maximum positive value is +15 mm and the
minimum is –18 mm, an overall deviation from planarity
of 33 mm due to wood warping has been measured. The
same measurement made on the painted side gave an
overall deviation of 31 mm.
This suggestive representation can be properly
integrated by a set of profiles obtained by virtually
cutting the displacement map with horizontal planes
normal to the best-fitting plane as shown in Figure 7.
For a set of three profiles taken horizontally on topical
sections of the reverse side model, a complete quan-
titative representation of the condition of the wood
surface is obtained. The sections where the profiles are
evaluated are indicated with three lines on Figure 7a,
representing the projection of the ‘cutting’ planes over
the best-fitting plane. All the related displacement
profiles highlight the warping of each plank, due to the
combination of external bending forces and the natural
wood swelling in response to humidity and temperature
fluctuations [18]. In the upper and lower profiles
(Figures 7b and 7d) it is evident how the first plank
presents a profile mainly above the zero level. In Figure
7c, related to the central line, the same painting section
shows a behaviour definitely below zero with a peak
near to the –20 mm level. This peak represents a
quantitative measurement of the depression shown by
the pink colour spot shown in Figure 6b.
A possible alternative way to highlight wood
deformations is to amplify the z value (deviation) with
respect to the other coordinates. In Figure 8, for
example, a distorted version of the painted side model is
shown, obtained by amplifying z 10 times with respect
to x and y. In this way even small deformations are
enhanced, and the large depression on the left plank,
shown for the reverse, becomes dramatically evident as
an extrusion on the right side of the painting.
However, by analyzing such an image and the
previous ones, it could appear as if the painting was
made from five planks of wood, while its wooden
support was actually assembled from 10 individual
planks, as is revealed by the radiography (X-ray) of
the whole painting. A comparison between 3D and
X-ray images, shown in Figure 9, reveals how the
two can be used in a complementary fashion. Figure
9a represents a portion of the painted surface, Figure
9b shows the corresponding X-ray image and 9c, the
deviation map from the reference plane of the same
area. The former is a detail of Figure 6a and maintains
the same colour coding of displacements. Similarly to
Figure 7, a yellow line has been drawn on all these
FigureFigure
FigureFigure
Figure
44
44
4 3D model of the front of the painting: (a) with texture; (b) without texture and synthetically shaded with angled light.
(a)
(b)
PAINTING SURVEY BY 3D OPTICAL SCANNING 7
STUDIES IN CONSERVATION 49 (2004) PAGES 1–12
three images as a common reference indicating the
height where the displacement profile of Figure 9d
was extracted from the deviation map. Looking at the
X-ray in Figure 9b, some metallic parts of the
crossbar holders and the related nails are clearly visible
on the lower side. The borders of each plank are also
evident: the white vertical signs indicate glued boards
firmly joined to each other, while the dark ones
highlight the detached wooden parts. The inter-
section between the yellow line and such vertical
signs is indicated with letters: A for the unconnected
points and B for those still joined. The lateral borders
of the image area are unconnected as well, but not
signalled by letters. Bending of joined parts leads to
positive deformations (toward the viewer) on the
central part of each set of connected planks, indicated
by the large green areas in Figure 9c. The joining
points are characterized by negative values, represented
in Figure 9c with levels of blue. This analysis is
quantified thanks to the profile of Figure 9d, where
the points A
1
and A
2
lead to a marked displacement of
–6 and –8 mm respectively while the points still
joined (B
1
, B
2
and B
4
) give only a slight bending of
the profile behaviour. Only the point B
3
reveals an
intermediate behaviour, being less firmly connected
than B
1
, B
2
and B
4
.
Figure 10 shows some results obtained from the
high resolution model. Due to the wood twisting
evidenced by the previous figures, the paint layer has
been submitted to tension or compression depending
on its location within the painted area. For the
fragment shown in Figure 10a, corresponding to the
FigureFigure
FigureFigure
Figure
55
55
5 3D model of the back of the painting: (a) with texture; (b) without texture and synthetically shaded with angled light.
(a)
(b)
FigureFigure
FigureFigure
Figure
66
66
6 Image of deviations from the best-fit plane where the z
values are coded with colors: (a) front; (b) back. On the right side of
this image a deep depression (-23 mm) is evident.
(a)
(b)
8 G.GUIDI, C. ATZENI, M. SERACINI AND S. LAZZARI
STUDIES IN CONSERVATION 49 (2004) PAGES 1–12
Madonna’s head, the above-mentioned compression
generated ruffles in the paint layer as highlighted by
Figure 10b representing the same surface without
texture but with synthetic shading. In the same way as
was done over the larger model, a profile has been
generated along the horizontal line shown in Figure
10a. As shown by the arrows, it intercepts three defects
of the painting, indicated as points A, B and C. These
defects can be dimensionally characterized by
measuring the profile peaks shown in Figure 10c.
Although close to the lower limits of this technique
(measurement uncertainty is ±18 µm as specified in
Table 1), in this way it is possible to evaluate a devia-
tion as small as 50 µm, namely the height of peak A.
CONCLUSIONS
Modern, non-contact, three-dimensional scanning
techniques can be advantageous in the documentation
and monitoring of works of art. Even an intrinsically
two-dimensional structure such as a painting can be
usefully analysed through its 3D model when aging leads
to deformations in the support.
3D documentation might be a useful routine, but it is
almost indispensable as a preliminary step before
conservation and restoration. In a panel painting the
quantitative measurement of absolute deviation from
planarity can indicate stress in the support due to
blocked planks that involve tension discharge into non-
blocked parts.
The possibility of comparing 3D measurements
taken at different times during the year might also
allow evaluation of the varying deformation of wood
due to changes in environmental parameters such as
humidity and temperature. This is a crucial point for
deciding what kind of intervention to conduct on the
painting support. For example the insertion of wooden
fixtures could be decided on if the amount of de-
(a)
FigureFigure
FigureFigure
Figure
77
77
7 Deviation profiles extracted from the model on some topical
horizontal sections: (a) map of the section levels; (b) profile at
y = 2200 mm; (c) profile at y = 1200 mm; (d) profile at y = 200 mm.
(b)
(c)
(d)
FigureFigure
FigureFigure
Figure
88
88
8 3D model of the front surface with the z dimension
amplified 10 times. In this way even small deformations are enhanced,
and the large hump on the right wooden plank is dramatically evident.
PAINTING SURVEY BY 3D OPTICAL SCANNING 9
STUDIES IN CONSERVATION 49 (2004) PAGES 1–12
formation, accurately measured through 3D modelling,
were to remain below a certain threshold.
Once the conservation and restoration of a painting
support are completed, the three-dimensional survey can
finally give useful information about appropriateness and
performance of a particular intervention, allowing the
monitoring of possible new deformations induced by the
blockage of specific parts, and potential dangers for the
paint layers.
Inspection of the superficial deformation of the
Adoration of the Magi by Leonardo da Vinci described in
this paper has underlined the important aspects of the
diagnostic analysis carried out on this work. The main
purpose was to document the painting through a
representation of the movement of the linear support
from an ideal planar reference, by way of a colour map
and with sections, so that art critics and conservation
experts can determine the need for conservation or for
consolidation of the panels. Furthermore this first set of
three-dimensional data on the work of art will provide a
reference point for periodic monitoring of the work in
future, in order to verify if it has indeed suffered micro-
and/or macroscopic damage, thus making it possible to
intervene appropriately and in time before irreparable
damage occurs.
The possibility of accurately characterizing and
documenting small ruptures in the paint layer on high-
resolution 3D images is an additional advantage of this
methodology.
APPENDIX: TECHNICAL DETAILS OF THE 3D
ACQUISITION METHOD
The range camera used for this project employs the
projection of special patterns over the area of interest.
The images of the patterns deformed by the surface to
Figure 9Figure 9
Figure 9Figure 9
Figure 9 Integration of complementary data coming from X-ray and
3D shown over a portion of the whole painting: (a) visible light
image; (b) radiography; (c) deformation map; (d) deformation profile
corresponding to the horizontal yellow line shown in all images. The
radiography clearly shows the unconnected planks giving the minima
A1 and A2 in the deformation profile.
Figure 10Figure 10
Figure 10Figure 10
Figure 10 Central detail at high resolution: (a) model with texture; (b)
without texture and synthetically shaded with angled light; (c) profile
along the line drawn in (a). Three corresponding painting layer peaks,
a fraction of a millimetre high, are shown.
(a)
(b)
(c)
(d)
(c)
(a)
(b)
10 G.GUIDI, C. ATZENI, M. SERACINI AND S. LAZZARI
STUDIES IN CONSERVATION 49 (2004) PAGES 1–12
be measured are acquired by a videocamera and digitized
through a frame grabber.
The patterns represent a set of vertical stripes,
alternately black and white, usually called fringe patterns.
Each black–white interface can be considered as a blade
of light (or light plane) similar to those produced by a
triangulation based laser-scanner.
Our system combines two complementary pattern
projection strategies: the gray code method and the
phase shift method.
Gray code method (GCM)
In order to project the maximum number of light planes
that the projector can handle over the surface, the
pattern should be the finest possible (i.e., the one formed
by the maximum number of vertical lines).
By acquiring it through a camera that not necessarily
frames all the projected lines, it would be easy to detect
generic stripes, but problematic to identify each single
light plane within those generated.
Therefore a proper sequence of patterns is created
rather than a single pattern. The sequence is made by n
patterns starting from the simplest, made with an area
half black and half white, followed by one made by a
black-white-black-white sequence, and so on pro-
gressively, splitting each stripe into two black and white
areas up to the maximum level of light planes. In our
system n = 7, leading to a maximum number of light
planes equal to 2
7
= 128.
If any image acquired is thresholded in order to
discriminate black and white areas, the composition of
the seven images gives a 7-bit gray code for each pixel,
ranging from 0000000 (pixel black in all the images) to
1111111 (pixel white in all images).
The spatial coordinates are generated projecting
the same pattern sequence in two different situations,
first with a reference plane, then with the object.
Two gray codes matrices are therefore originated and
corresponding gray codes are sought in each matrix
for calculating the displacement of each light plane
due to the object. From such displacement the 3D
coordinates are evaluated through triangulation, as
schematically explained in the ‘Technical back-
ground’ section.
Phase shift method (PSM)
With the phase shift method a fine pattern of vertical
stripes with smooth intensity variation (defocused) is
used, rather than a pattern with steep black–white
transitions. Therefore no reference to specific light
planes is done.
This sinusoidal pattern is first projected over a
reference plane, then it is projected again over the
investigated surface. The presence of such a surface
involves a phase deviation of the pattern that is
proportional to the surface displacement with respect to
the reference. Hence this method evaluates phase
changes on any image pixel and from these calculates the
corresponding displacements in 3D.
By translating iteratively the pattern of a period
fraction along the horizontal direction, all of the
sinusoidal period can be covered. In our system the
whole period is divided into four steps.
Precision and accuracy of this measurement approach
are better than GCM, but a major limitation occurs: the
phase of a signal is periodic and a phase change of ϕ
might involve a real change of ϕ plus an integer number
of cycles. Although software procedures have been
conceived for reconstructing the real phase behaviour
(‘phase unwrapping’), an abrupt displacement variation
can easily involve a failure of the unwrapping algorithm
leading to a wrong 3D estimate. Such phase ambiguity
makes this approach suitable for measurement of
displacements small enough to produce phase changes
smaller than one cycle.
GCM + PSM
In the system used, the evaluation of 3D coordinates is
obtained first by projecting a sequence of gray coded
light patterns over the inspected surface in order to
evaluate its approximate coordinates, and then on phase
shifting the finest pattern for a refinement of each 3D
point estimation, according to a method described in the
literature [21, 22].
In this way the capability of measuring big distance
variations on the surface, typical of the gray code
method, is combined with the good precision and
resolution of the phase shift method that is here
employed with no unwrapping thanks to the integration
with GCM. This also makes the method very com-
putationally robust.
ACKNOWLEDGEMENTS
The authors wish to recognize the contribution of
Stefano Ciofi and Valentina Damato, former PhD
students, during the three-dimensional acquisition of the
Adoration of the Magi at the Uffizi Gallery. Ciro Castelli,
Mauro Parri and Andrea Santacesarea from the wood
PAINTING SURVEY BY 3D OPTICAL SCANNING 11
STUDIES IN CONSERVATION 49 (2004) PAGES 1–12
restoration team at the Opificio delle Pietre Dure in
Florence have also to be acknowledged for some
extremely useful discussion about application suggestions
on 3D techniques. A final thanks is due to Angelo J.
Beraldin and John Taylor from the National Research
Council Canada for their continuous support on
theoretical and technical aspects of 3D modelling in the
cultural heritage field.
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AUTHORS
GABRIELE GUIDI received his MS degree in electronic
engineering in 1988 from the University of Florence,
and PhD in bioengineering in 1992 from the University
of Bologna, Italy. Then he joined the University of
Florence where he is now Senior Researcher. Address:
12 G.GUIDI, C. ATZENI, M. SERACINI AND S. LAZZARI
STUDIES IN CONSERVATION 49 (2004) PAGES 1–12
Dipartimento Elettronica e Telecomunicazioni, Università
degli Studi di Firenze, Via S. Marta 3, 50139 Firenze,
Italy. Email: g.guidi@ieee.org
C
ARLO ATZENI has been full professor of micro-
electronics at the University of Florence since 1980,
after 15 years at the Electromagnetic Research Institute
of the Italian National Research Council. Address: as for
Guidi.
M
AURIZIO SERACINI received his BA in applied mech-
anics and engineering sciences at Revelle College,
University of California, San Diego, and Laurea in
electronic engineering, University of Padua, Italy. In
1977 he founded Editech, the first private company in
Italy to provide diagnostic services in art and architecture.
Currently, as an adjunct professor, he teaches art and
architecture diagnostics at the Universities of Florence,
Venice and Calabria. Address: Editech S.r.l., Firenze, Italy.
S
ARA LAZZARI received her MS degree in electronic
engineering (electronics for automation) at the University
of Brescia, Italy, in 1996, and in 2000 a PhD in electronic
instrumentation from the same university. Since 1999 she
has been president of Optonet, an Italian company
involved in the development, production and selling of
optical systems. Address: Optonet S.r.l., Brescia, Italy.
Résumé — On a effectué un balayage optique de l’Adoration des mages de Léonard de Vinci (Musée des Offices, Florence), de
façon à obtenir un modèle complet en 3D. La face, le dos et les côtés de ce célèbre tableau peint sur 10 planches ont été balayés
avec une résolution d’environ 0,3 mm, de façon à obtenir une représentation tridimensionnelle numérisée de haute qualité.
L’objectif principal était de mettre en évidence et de mesurer les déviations de planéité dues à la courbure et au gauchissement du
bois, de façon à pouvoir planifier une intervention ultérieure visant prévenir toute détérioration additionnelle. Quelques parties de
la peinture, montrant des défauts ponctuels visibles, ont été numérisées avec une résolution de 90 µm. La mise en œuvre du
balayage optique en 3D s’est révélée être un moyen exceptionnel de documentation spatiale des déformations subies par les
panneaux peints et peut constituer un outil de référence pour un contrôle périodique de leur état de conservation.
Zusammenfassung — Durch Optisches Scanning wurde ein dreidimensionales Modell der berühmten “Anbetung der Könige!”
von Leonardo d Vinci (Uffizien, Florenz) erstellt. Oberfläche, Rückseite und Seiten des großartigen, aus 10 vertikalen brettern
bestehenden Holztafel wurden mit einer Auflösung von ca. 0,3 mm aufgenommen, so dass ein sehr qualitätsvolles
dreidimensionales Digitalbild erhalten werden konnte. Der Hauptgrund für die Untersuchung war die Erstellung einer
dreidimensionalen Karte der Verwölbungen des Holzes, um die Möglichkeit einer Planierung der Tafel abzuschätzen, die zur
Vermeidung weiterer Schäden notwendig werden könnte. Einige Stellen in Bereichen sichtbarer Schäden wurden mit einer
Auflösung von 90 µm aufgenommen. Es konnte gezeigt werden, dass 3D Optisches Scanning ein einzigartiges Werkzeug ist,
um Verwölbungen an Tafelgemälden zu dokumentieren und um Veränderungen des Zustands des Gemäldes durch periodische
Untersuchungen zu beobachten.
Resumen — Se ha aplicado escaneado óptico con el fin de generar un modelo completo en 3D de la famosa Adoración de los
Magos de Leonardo da Vinci (Galería de los Uffici, Florencia). Las superficies frontal y trasera, así como los lados de la gran obra
(formada de diez planchas de madera verticales) se escanearon con una resolución lateral de cerca de 0,3 mm, obteniéndose así una
representación digital tridimensional de gran calidad. La intención principal fue obtener un mapa preciso mediante mediciones y
resaltados de las variaciones de planimetría de la superficie, variaciones éstas causadas por las curvaciones y alabeos de la madera,
estableciendo la posibilidad de crear un plan de posible intervención con el fin de prevenir futuros deterioros. Algunas zonas del
cuadro, que muestran defectos locales, se capturaron con una resolución de 90 µm. La aplicación de escaneado óptico de 3D se ha
mostrado de excepcional valor para documentar deformaciones espaciales sufridas por las pinturas sobre tabla, puede además
representar una herramienta de referencia para la monitorización periódica de su estado de conservación.