Objective and Subjective Evaluation of Virtual Relighting from Reflectance Transformation Imaging Data

Abstract

Reflectance Transformation Imaging (RTI) is widely used to produce relightable models from multi-light image collections. These models are used for a variety of tasks in the Cultural Heritage field. In this work, we carry out an objective and subjective evaluation of RTI data visualization. We start from the acquisition of a series of objects with different geometry and appearance characteristics using a common dome-based configuration. We then transform the acquired data into relightable representations using different approaches: PTM, HSH, and RBF. We then perform an objective error estimation by comparing ground truth images with relighted ones in a leave-one-out framework using PSNR and SSIM error metrics. Moreover, we carry out a subjective investigation through perceptual experiments involving end users with a variety of backgrounds. Objective and subjective tests are shown to behave consistently, and significant differences are found between the various methods. While the proposed analysis has been performed on three common and state-of-the-art RTI visualization methods, our approach is general enough to be extended and applied in the future to new developed multi-light processing pipelines and rendering solutions, to assess their numerical precision and accuracy, and their perceptual visual quality.

Full text

EUROGRAPHICS Workshop on Graphics and Cultural Heritage (2018)
R. Sablatnig and M. Wimmer (Editors)
Objective and Subjective Evaluation of Virtual Relighting from
Reflectance Transformation Imaging Data
R. Pintus1, T. Dulecha2, A. Jaspe1, A. Giachetti2, I. Ciortan2, E. Gobbetti1
1CRS4, Italy
2University of Verona, Italy
Abstract
Reflectance Transformation Imaging (RTI) is widely used to produce relightable models from multi-light image collections.
These models are used for a variety of tasks in the Cultural Heritage field. In this work, we carry out an objective and sub-
jective evaluation of RTI data visualization. We start from the acquisition of a series of objects with different geometry and
appearance characteristics using a common dome-based configuration. We then transform the acquired data into relightable
representations using different approaches: PTM, HSH, and RBF. We then perform an objective error estimation by comparing
ground truth images with relighted ones in a leave-one-out framework using PSNR and SSIM error metrics. Moreover, we carry
out a subjective investigation through perceptual experiments involving end users with a variety of backgrounds. Objective and
subjective tests are shown to behave consistently, and significant differences are found between the various methods. While the
proposed analysis has been performed on three common and state-of-the-art RTI visualization methods, our approach is gen-
eral enough to be extended and applied in the future to new developed multi-light processing pipelines and rendering solutions,
to assess their numerical precision and accuracy, and their perceptual visual quality.
CCS Concepts
•Human-centered computing →Empirical studies in visualization; •Computing methodologies →Visual inspection; Image
representations;
1. Introduction
The interactive inspection of digital representations of artworks is
of fundamental importance in the daily activity of Cultural Heritage
(CH) scholars, as it can reveal geometric cues or precious informa-
tion about the materials used to create an object, supporting the
definition of conservation and preservation strategies. Moreover,
digital representations are also increasingly used to present cultural
objects to experts or to a wider public, in order to replace, augment,
or complement the inspection of real objects.
Among all methods to acquire, process and visualize virtual
replicas, Reflectance Transformation Imaging (RTI) is one of the
most popular in CH. This is due to the low acquisition hardware
cost and to the simple and fast capture and processing pipeline. In
addition, RTI is a technique that naturally supports interactive re-
lighting, a type of visualization very appropriate to inspect fine sur-
face details and resembling the classical physical inspection raking
light sources to reveal surface detail of actual objects under study.
For this reason, RTI visualization is broadly used for relighting im-
ages of a wide range of items, e.g., coins [MVSL05,KK13], rock
art [Duf10,UW13], paintings [MBW∗14], bas-relief [PCC∗10],
and many more CH items [AIK13].
In the most common RTI capture, process and visualization
pipeline, a series of images is taken under the same fixed view point
but with different lighting conditions. The acquired image stack de-
scribes for each pixel the so called appearance profile, which is a
sequence of measurements of per-point reflectance response. This
data is analyzed and visualized by fitting a model that permits to go
from the sparse measured samples to a continuous description of
the reflected light. The goal of these models is to find the optimal
trade-off between the amount of input data (sparse light sampling
vs high-density gonioreflectometer acquisition), the complexity of
reflectance model (computational effort vs model accuracy), the
amount of data compression (e.g., for remote/web-based transfer
and visualization), rendering interactivity (real-time relighting vs
off-line rendering). The final result is a set of parameters that pro-
vide a virtual relighting environment in which the user can move a
virtual light source in positions different from those sampled. The
quality of the RTI visualization depends on how expressive, real-
istic and artifact-free the rendering is while the user inspects the
artwork by moving that virtual light source.
In this work, we carry out an objective and subjective evalua-
tion of RTI data visualization. Using a series of objects with dif-
ferent geometry and appearance characteristics, we acquire them
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R. Pintus & T. Dulecha & A. Jaspe & A. Giachetti& I. Ciortan & E. Gobbetti / Evaluation of RTI-based Virtual Relighting
using a common dome-based configuration. We then transform the
acquired data into relightable representations, using different ap-
proaches. The resulting relightings, from a variety of light direc-
tions, are then evaluated using both objective and subjective tests,
aimed at comparing each technique with ground-truth images, as
well as to compare each relighting technique with respect to the
others. While we present results for selected widely used and state-
of-the-art RTI processing and visualization methods, the proposed
investigation rationale for RTI quality assessment goes beyond that
choice, and can be applied in the future as new solutions will be
available. To the best of our knowledge, this is a first attempt to
perform an objective/subjective evaluation that systematically in-
vestigates the quality of different RTI techniques, applied to the
CH field, with both error/perceptual metrics and a web-based vi-
sual test performed by different user groups, including experts and
non-expert in the visual inspection of CH objects.
2. Related work
The acquisition, processing, analysis and visualization of RTI data
is a well known and broadly studied research field. A complete re-
view of this topic is out-of-the-scope of this work, and for a re-
liable coverage of this research area we refer the reader to recent
renowned surveys [Sze10,AG15,DRS10,PPY∗16]. Here, after a
general description of the acquisition setups, we focus on the liter-
ature on multi-light data processing for visualization, which serves
as a state-of-the-art background for the proposed evaluation of re-
lighting approaches based on RTI data.
The seminal insight behind RTI [MGW01] was to replace clas-
sical multi-light processing based on Photometric Stereo [Woo80]
with a more flexible interpolation-based approach that transforms
the high amount of data in RTI image stacks into a compact
2.5D multi-layered representation directly usable by applications
(e.g., CH object inspection [Duf13]). Those layers might include
geometric-based attributes (e.g., normal maps, gradient vector field,
local curvature), or appearance based quantities (e.g., albedo maps,
per-pixel specular component) [Mac15]. For some applications,
this type of approach proved to be a good trade-off compared
to more complex 4D Bidirectional Reflectance Distribution Func-
tion (BRDF) or Bidirectional Texture Function (BTF) captures.
For this reason, the ability of this technique to easily convey
meaningful visual information of acquired objects fosters the de-
velopment of a wide variety of acquisition setups. They range
from low-cost, transportable kits [CHI17] to more complex light
domes [CHI17,SSWK13,Ham15]. Apart from the way they or-
ganize light distribution (i.e., movable or fixed) some solutions
increase the number of captured light frequencies in a multi- or
hyper-spectral setup [LG14,Leu15].
RTI processing is typically a data reduction procedure, where
each N-dimensional per-pixel data (appearance profile) is con-
verted in a parametric representation, where the number of parame-
ters is low compared to the N acquired images. Given an analytical
model, RTI processing consists in a data fitting problem. The sem-
inal work [MGW01] uses a bi-quadratic polynomial with coeffi-
cients found by linear regression. After that, a lot of different solu-
tions have been proposed in the literature, whose models include
spherical and hemispherical harmonics [MMC∗08,GKPB04],
eigen hemispherical harmonics [LLW12], bi-polynomial functions
[STMI14], discrete modal decomposition [PLGF∗15], and bivari-
ate Bernstein polynomials [IA14]. They are all prone to errors
due to the fitting of a matte model with an input data that can
contain a relevant number of outliers (e.g., produced by shad-
ows and highlights). For this reason, recent methods exploit Ro-
bust regression [RL05] to extract outlier free input data to in-
crease the reliability and repeatability in the computation of dif-
fuse model parameters [PGPG17,ZD14]. In addition, some meth-
ods obtain alsa the high frequency material behavior by fitting the
data with other types of analytical models, e.g., Radial Basis Func-
tions (RBFs). Drew et al. [DHOMH12] use RBFs to fit the differ-
ence between the original and the computed matte signals, while
Giachetti et al. [GCD∗17] use RBFs to produce relighted images
by directly processing the original raw RTI stack. The output is
used for several applications ranging from visualization [Mac15] to
material classification [WGSD09,GDR∗15,TGVG12], and feature
extraction (e.g., edge detection [BCDG13,Pan16]) and enhance-
ment [CHI17,RTF∗04,FAR07].
Previous studies have already shown the interest of RTI anal-
ysis for conservation, and several tests have been made to mea-
sure repeatability and appropriateness of RTI for conservation
tasks [Pay13]. In the application scenario of RTI-based reconstruc-
tion and rendering, some state-of-the-art contributions provide a
few comparative results. Shi et al. [SWM∗16] propose the DiLi-
GenT benchmark and detailed evaluation results that compare var-
ious Photometric Stereo approaches with a wide range of optical
properties; however, that work assesses the quality of geometric
attribute computation (i.e., normal map), leaving the visualization
aspect as a complementary unexplored aspect of multi-light pro-
cessing. The DiLiGenT benchmark has also been used to evalu-
ate PTM fitting quality [PGPG17]. Conversely, other works val-
idate specific approaches for RTI data visualization, which im-
prove the output quality of fitting techniques [GCD∗17], compres-
sion algorithms [PCS18], or enhanced non-photorealistic render-
ings [BSMG05]. However, although useful, they mostly present
sparse and limited comparative results, without a wide coverage
of relighting conditions (e.g., light direction range) and material
behavior. Moreover, none of them couples an objective set of er-
ror metrics together with a human-based visual evaluation provided
by experts in the cultural heritage field. For those reasons, in this
work we focus our attention on the virtual relighting application,
and we proposed an extensive evaluation, both objective and sub-
jective, that aims at assessing which techniques are more suitable
to process RTI raw image stacks, and to convey the proper surface
appearance visualization for computer-aided object inspection.
3. Overview
To perform the proposed objective and subjective evaluation, we
selected four objects with different types of shape and appearance
(Sec.4). We acquired their RTI image stacks with the same fixed
light dome (Sec. 4), to avoid biases due to variations in the acquisi-
tion conditions. We then process raw data with three different tech-
niques capable to produce relightable representations (Sec. 6). The
first two, i.e., classical Polynomial Texture Map (PTM) [MGW01]
and HSH relighting [MMC∗08,GKPB04], are standard approaches.
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Figure 1: Objects. Original images of the objects chosen for relighting test.
First Row: two metallic coins (Coin1,Coin2). Second Row: an ancient gold
lamina (Lamina), and an imprint of a shell (Shell).
The third one, i.e., Radial Basis Functions (RBFs) [GCD∗17] has
been recently introduced to the RTI domain, and was chosen since
it differentiates from the others in the way it computes model pa-
rameters by favoring local fitting in the light direction space rather
than a global regression. The relighted images produced by the
three computed models are compared through an objective and a
subjective approach. For the objective comparison, we compare er-
ror measurements (PSNR) and perceptual metrics (SSIM) through
a leave-one-out evaluation strategy (Sec. 7). We provide also a
subjective evaluation by submitting a visual questionnaire to two
groups of volunteers: experts and non-expert in CH visual assess-
ment (Sec. 8). The respondents evaluated the effectiveness of each
selected technique by providing preferences, as well as estimations
of the capability to reproduce ground truth images.
4. Objects
In order to evaluate the quality of the chosen relighting techniques,
we consider RTI acquisitions of four objects made of materials that
are relevant for the Cultural Heritage domain: two coins made of
one and two different metal alloys, an ancient gold lamina, and
the imprint of a shell (see Figure 1). In general, we have cho-
sen those objects because they all exhibit different micro/meso-
geometry, and different optical material behaviors (both specular
and diffuse response). The first coin (Coin1) is a quarter US dollar.
It has a diameter of 24.26mm and a thickness of 1.75mm, and it
is composed of silver, copper and nickel. The second coin (Coin2)
is a Polish coin made up of metal, Bi-Metallic Copper-nickel cen-
ter in Aluminum-bronze ring, and it has a diameter of 21.55mm
and a thickness of 1.97mm. We chose those coins because of their
high specular characteristics which allows us to examine the per-
formance of the aforementioned algorithms for the case of specular
materials. The other metallic object is a piece of a Phoenician gold
lamina, named (Lamina del Sulcis). It is a fragment of an inscrip-
tion engraved on thin gold leaf (a thin plaque or panel intended to be
affixed to some other surface), that was found in the earliest stratum
of the Sulcis tophet or infant cremation cemetery (West Sardinia).
Only 1.4cmx1.5cmx0.05cm in size, the lamina seems to have been
once attached to an iron object, which has partially damaged the
surface. The text has been dated to the 8th −7th centuries BCE on
the basis of its paleographic features [Bar65]. This makes the ob-
ject extremely important in Mediterranean archeology [Dix13]. In
addition to specular materials, we also examine RTI on matte ob-
ject, an imprint of shell on a plaster (Shell). The object has a very
cooperative material, but a difficult geometry, with long and thin
curved concave and convex parts.
5. Acquisition Setup
The RTI data has been acquired by a custom light dome with a ra-
dius of about 30cm, and with 48 LED lights placed as shown in
Figure 2: 18 are put equally spaced in the azimuth coordinates at
the elevation of 10 degrees, 12 at 30 degrees, 9 at 50 degrees, 8
at 70 degrees, and one parallel to the camera view direction. The
LEDs are neutral white lights that covers the entire visible spec-
trum. The capture device is a 36.3 Mpixels DSLR FX Camera
Nikon D810, and a 50mm AF Nikkor Lens. The acquisition system
has been calibrated with a white planar target and reflective dark
spheres, coupled with a light direction/intensity estimation proce-
dure [CPM∗16,GCD∗18].
Figure 2: Custom light dome used for the objects’ acquisition.
6. RTI Fitting
Although our evaluation framework can be applied to validate any
RTI relighting method, here we focus on three techniques, i.e., two
of the most used RTI data fitting approaches (PTM, HSH) and
one of the most recent appearance profile interpolation strategies
(RBFs). We do not cover multi-spectral processing, since the treat-
ment of multi-channel, color signals is an orthogonal problem. Af-
ter the acquisition of the raw RTI image stack, we thus pre-process
the data to transform the color space into a LRGB representation,
which is used in all the three fitting procedures. So, we consider
a single chroma value per pixel and we apply the computation to
the luminance channel. This choice also helps in reducing chro-
matic aberrations, mostly in metallic samples. We used in our com-
parison a second order PTM (6 coefficients), the de-facto standard
representation used in many practical applications, and a third or-
der HSH (16 coefficients) that is probably the most accurate global
function commonly used for relightable images. We also use a 5-
neighbors RBF as an alternative to those global fitting methods.
Polynomial Texture Maps. Polynomial Texture Maps
(PTMs) [MGW01] are the current standard in RTI applica-
tions (mostly in the CH field) where a lot of museums use
them to convey virtual, remote visualization of artworks. This
is the seminal method in this field, and it proposed a per-pixel
bi-quadratic polynomial interpolation of RTI stacks to produce
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a spatially varying reflectance Ias functions of light directions.
At each pixel, given the six parameters αicomputed from
data fitting, and a light direction ~
l, reflectance is computed as:
I~
l=α0~
l2
x+α1~
l2
y+α2~
lx
~
ly+α3~
lx+α4~
ly+α5. Due to the
easiness in data capture, the simple model, which allows for a quite
fast processing and efficient storing, and the availability of open
source tools for RTI data processing and for web-publishing the
resulting relightable images, PTM became the most widespread
RTI visualization method. For this reason, we include it in our
evaluation. For our test, we compute the six PTM parameters αiby
using the standard least square approach.
Hemispherical Harmonics. Similarly to the Fourier series, spher-
ical harmonics are a good set of basis to describe functions on
the surface of a sphere, and low order set of those basis are
typically used in modeling low frequency reflectance, e.g., ap-
plied in photometric stereo scenarios [BJK07]. In the RTI ac-
quisition setup we have a single viewpoint and only the upper
hemisphere of surface normals is visible, rather than the whole
sphere, and the spherical harmonics functions are no longer or-
thonormal. For this reason, the hemispherical basis has been intro-
duced [MMC∗08] to represent image irradiance, and they are de-
fined from the shifted associated Legendre polynomials [ERF11].
They are capable to model near and asymptotically distant illumi-
nation conditions, and the resulting relighted images from new vir-
tual light sources proved to better preserve contrast from the orig-
inal images. For our test, we compute HSH parameters by using
the standard Singular-Value Decomposition method. It has been
proved that good results are obtained with sixteen parameters αm
l
per-pixel [Mac14], which consist in four first-order, five second-
order and seven third-order terms. The per-pixel reflectance is com-
puted as: I~
l=∑n−1
l=0∑l
m=−lαm
lHm
l~
l, where Hm
lare the hemi-
spherical harmonic basis functions.
Radial Basis Functions. Since the typical RTI acquisition pro-
duces a sparse set of samples within the (lx,ly)light direction space,
Radial Basis Function (RBF) [Buh03] can be considered as an ef-
ficient way to interpolate them and produce a relighted image with
a new virtual light [GCD∗17]. Given Ninput images in the RTI
capture, RBF interpolation is achieved by computing the parame-
ters that define a sum of Nradial functions. Here we use Gaussians
centered at each light direction, with standard deviation Rcompute
from the light distribution: the more are light directions, the smaller
will be the value of R. In order to perform the fitting and find the
parameters, for each radial function the light directions the closest
five lights are considered to solve the fitting. Of course, this choice
is due to a trade-off between local, high-frequency signal preser-
vation (e.g., highlights and shadows), and proper data smoothing.
Once all the per-pixel parameters αihave been computed, the re-
flectance Iis expressed as I~
l=∑N
i=1αie
k~
l−
~
lik2
R2.
7. Objective Evaluation
The first part of the evaluation is devoted to an objective measure-
ment of differences between the expected result of a light-based
interpolation method and the actual outcome of the analyzed RTI
techniques. The standard way to compute multi-light fitting qual-
ity is the so called leave-one-out strategy. Given an RTI raw stack
of Nimages, we loop on that set, and for each image we com-
pute fitting parameters with N−1 images, by excluding the cur-
rent image from the computation. Then we use those parameters
to produce the relighted image corresponding to the excluded one.
The error metric is computed by comparing the original and re-
lighted images. We use two classical image comparison metrics,
i.e., Peak Signal to Noise Ratio (PSNR) [WTFE18a] and Structural
Similarity (SSIM) [WTFE18b], which have been recently used as
well for measuring the compression quality in RTI data visual-
ization [PCS18]. We compute those error metrics for all the three
tested techniques (PTM, HSH, RBF) and the four objects of study
(Coin1, Coin2, Lamina, Shell).
Method PSNR SSIM
Avg. Med. 1st Qr 3rd Qr. Avg. Med. 1st Qr 3rd Qr.
PTM 22.20 23.10 19.43 25.77 0.69 0.71 0.59 0.79
HSH 23.82 24.17 21.60 26.87 0.73 0.75 0.65 0.82
RBF 24.14 24.35 21.00 27.56 0.80 0.83 0.73 0.88
Table 1: Global PSNR and SSIM. Global statistics of PSNR and SSIM
computed across all the four RTI image stacks of datasets Coin1,Coin2,
Lamina, and Shell.
To analyze the statistics of PSNR and SSIM, we present a series
of error data measurements, i.e., the average, the median values,
and the 25th and the 75th percentiles. In Table 1, we present the
global error across all datasets. We can see that, on average, RBF
is consistently better than the two other techniques, especially for
the more perceptual metric SSIM. PTM is, by contrast, consistently
presenting lower results. On the whole image set, the difference be-
tween RBF and HSH is not statistically significant at the 95% con-
fidence level (even if close, p=0.07 in a paired t-test for PSNR),
while the differences between PTM and the other methods are both
highly significant (p<10−14 in a paired t-tests for PSNR).
A better interpretation of the results can be given by looking at
those statistics on a per-object basis (Table 2and 3). The first three
objects (i.e., Coin1,Coin2, and Lamina) exhibit a glossy material
behavior. We can see how the RBF interpolation better conveys
this metallic appearance. The per-image PNSR does not improve
so much because the highlight region is typically small compared
to the entire image, and due to the fact that the neighborhood based
RBF-sampling in the leave-one-out framework results in a slight
drift of the rendered highlight peaks. Conversely, under a more
perceptual metrics (i.e., SSIM), we can observe a significant in-
crease in visual performances while relighting those three metallic
objects. In particular, while a big number of images are almost dif-
fuse for the coins, in the Lamina data a large part of the per-pixel
appearance profile has highlights, and we can see here how the im-
provement is bigger by using the local-driven fitting of the RBF
approach. An interesting result arises from the matte object Shell.
Here, the HSH method proves to be a better choice in rendering new
virtual light source positions. The reason is that with a diffuse, low-
frequency optical behavior the choice of a global fitting method (as
HSH), that takes into account the entire appearance profile, is ca-
pable to reasonably model the regularity of behavior. RBF, which
weights only the contribution of a small number of close lights, is,
instead, introducing more error in the areas near shadows. Look-
ing at the statistical significance of the differences, it is possible
to understand the variability of the methods’ behavior on different
materials. For the shell, there is a significant difference between
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R. Pintus & T. Dulecha & A. Jaspe & A. Giachetti& I. Ciortan & E. Gobbetti / Evaluation of RTI-based Virtual Relighting
Method
PSNR
Coin1 Coin2 Lamina Shell
Avg. Med. 1st Qr 3rd Qr. Avg. Med. 1st Qr 3rd Qr. Avg. Med. 1st Qr 3rd Qr. Avg. Med. 1st Qr 3rd Qr.
PTM 20.96 22.37 17.14 25.56 22.43 23.71 19.85 25.60 20.27 19.67 16.03 24.26 24.53 24.78 21.77 27.50
HSH 22.92 23.01 21.37 26.1 23.67 24.00 22.07 26.11 21.26 20.99 16.63 25.44 26.60 26.68 24.41 29.51
RBF 23.74 24.83 21.99 27.22 24.35 25.01 22.37 26.96 22.45 21.01 16.88 27.90 25.48 24.23 21.61 29.82
Table 2: PSNR vs Objects PSNR statistics corresponding to PTM, HSH, and RBF relighting techniques for each of the studied objects, i.e., Coin1,Coin2,
Lamina, and Shell.
Method
SSIM
Coin1 Coin2 Lamina Shell
Avg. Med. 1st Qr 3rd Qr. Avg. Med. 1st Qr 3rd Qr. Avg. Med. 1st Qr 3rd Qr. Avg. Med. 1st Qr 3rd Qr.
PTM 0.61 0.64 0.49 0.68 0.70 0.73 0.65 0.75 0.61 0.59 0.50 0.71 0.81 0.83 0.75 0.89
HSH 0.66 0.68 0.61 0.75 0.75 0.76 0.71 0.80 0.61 0.64 0.53 0.72 0.85 0.87 0.82 0.91
RBF 0.77 0.82 0.70 0.87 0.81 0.84 0.76 0.88 0.78 0.80 0.72 0.88 0.81 0.83 0.72 0.93
Table 3: SSIM vs Objects SSIM statistics corresponding to PTM, HSH, and RBF relighting techniques for each of the studied objects, i.e., Coin1,Coin2,
Lamina, and Shell.
HSH and PTM (p<10−5in a paired t-test for PSNR) and an al-
most significant difference between HSH and RBF (p=0.02 in a
paired t-test for PSNR) and between RBF and PTM (p=0.03 in a
paired t-test for PSNR). On the other hand, for the lamina, we get
a significant improvement using RBF rather than HSH (p=0.03
in paired t-test for PSNR) or PTM (p<10−5in paired t-test for
PSNR). The difference between PTM and HSH is not statistically
significant (p=0.07). For the coins, RBF based relighting are al-
ways significantly better than HSH based (p=0.005 for Coin 1
and p=0.004 for Coin 2 in paired t-tests) and HSH based relight-
ing are always significantly better than PTM based ones (p<10−7
for Coin 1 and p<10−5for Coin 2 in paired t-tests for PSNR).
Similar trends are obtained testing SSIM differences.
In Figure 3and 4we respectively plot the PSNR and SSIM as
functions of light angle of incidence. Since we would like to un-
derstand how the fitting behaves in the presence of specular re-
flection, we put in the x-axis the Half Angle, i.e., the angle be-
tween the half vector and the surface normal. Given Lthe direc-
tion of the light, and Vthe view vector, the half vector will be
H= (L+V)/kL+Vk; since we have almost flat objects we con-
sider the average per-image normal as~n= [0,0,1]. For metallic ob-
jects we can see how the numerical error in the relighting strongly
depends on this angle, which, for a dome measuring an almost flat
object, is roughly proportional to light elevation. As soon as we get
to the specular angular region the quality of the rendering decreases
(Figure 3a,3b, and 3c). For a diffuse object (Figure 3d the PSNR
increases; in fact, in this case, we have more non-idealities for rak-
ing lights than for lights aligned with the mirror-reflection direction
(e.g., self and cast shadows). On the other hand, while the percep-
tual SSIM is statistically better for RBF than the other techniques,
its behavior seems to be independent of the half angle (Figure 4).
8. Subjective Evaluation
In order to evaluate the effectiveness of the three chosen RTI visu-
alization techniques in terms of performance, suitability for the CH
field, and the improvement of the visual quality of rendered objects,
we performed a thorough user evaluation involving quantitative and
subjective measurements, by conducting an online survey through
a web-based questionnaire carried out by a number of volunteers.
Goal. The main goal of the evaluation was to assess which RTI fit-
ting and rendering method is more adequate for the usage in the typ-
ical scenario of object inspection and daily research activity, where
many users with different skills and experiences try to interactively
explore virtually relighted artworks. Given the large number of fit-
ting and relighting methods, it is out of the scope of this work to
provide a fully comprehensive comparison of existing techniques
and outcomes. As explained in previous sections, similarly, in this
user-based evaluation we limited our comparison to the three RTI
fitting techniques presented before, i.e., PTM, HSH, and RBF.
Setup. The experimental setup considered the RTI data of the ob-
jects presented in section 4, and the fitting methods explained in
section 6. For each RTI stack we consider a subset of five represen-
tative images taken at different light source elevations, each corre-
sponding to a different parallel of lights in the dome; in this way we
can test the visual performances in the presence of shadows (i.e.,
raking lights) or highlights. For each of those original images we
compute the relighted one in the same leave-one-out sense (Sec. 7)
for the PTM, HSH, and RBF techniques. At the end of this proce-
dure we will have five quadruples (original, PTM, HSH, and RBF
image) for each dataset; in total, we will use a set of 76 images
for our visual evaluation. In Figure 5we show one quadruple from
each analyzed object.
Tasks. The experiments consist in two main sections/tasks, which
ask respondents to give preferences on the relighted images based
on their experience in daily artwork inspection, and the visual qual-
ity of CH item presentation. The first test asks respondents to se-
lect the most similar relighted images with respect to ground truth
data. We show the user a sequence of three images (Figure 6Top).
The centered one is a photo of the real artwork (ground truth im-
age). The lateral ones are two computer-generated images of the
same artwork rendered from the same point of view of the ground
truth image and relighted with the same light source intensity and
direction of the ground truth image. The user has to click/select
the lateral image whose rendering he considers the most similar
compared to the center ground-truth image. The second one is not
guided by the presence of a real photograph, and asks respondents
to provide an "unsupervised" preference between two RTI virtual
relightings (Figure 6Bottom). We show the volunteer a sequence
of two computer-generated images of the same artwork viewed by
the same point and relighted with the same light source intensity
and direction. He has to select the one whose rendering he prefers
as a meaningful visualization related to his daily CH inspection ac-
tivity and quality expectation.
Participants. 25 participants were recruited across various lead-
ing institutions involved in CH studies and applications (see Ac-
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(a) (b) (c) (d)
Figure 3: PSNR vs Half Angle PSNR statistics corresponding to PTM, HSH, and RBF relighting techniques as functions of the half angle (the angle between
the half vector and the average per-image normal): ( a)Coin1;(b)Coin2;(c)Lamina;(d)Shell.
(a) (b) (c) (d)
Figure 4: SSIM vs Half Angle PSNR statistics corresponding to PTM, HSH, and RBF relighting techniques as functions of the half angle (the angle between
the half vector and the average per-image normal): ( a)Coin1;(b)Coin2;(c)Lamina;(d)Shell.
Figure 5: Objects. Rows (top to bottom): coin1, coin2, lamina and shell.
Columns (left to right): original image, PTM, HSH, and RBF relightings.
knowledgments). They are subdivided in two groups, the experts
working in different areas related to the CH field, such as art his-
torian/curators, restorer/conservators, conservation scientists (12 in
total), and non-experts volunteers (another 13 people). Considering
Figure 6: Web-based Questionnaire. Two tests have been performed in
a web-based questionnaire. The first (top figure) is a visual comparison
guided by using a ground truth image, while the second (bottom figure)
asks an "unsupervised" preference between two virtual relighted images.
those two groups is due to the fact that RTIrendering and relighting
has been widely used not only for CH studies performed by expert
scholars, but also for cultural dissemination and virtual presenta-
tion to the more general public. All the tests are as much blind as
possible; all the respondents are unaware of the type of relighting
methods we have used to construct the relighted images, and they
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R. Pintus & T. Dulecha & A. Jaspe & A. Giachetti& I. Ciortan & E. Gobbetti / Evaluation of RTI-based Virtual Relighting
Figure 7: Global Scores. Global number of votes for PTM, HSH, and RBF techniques across all datasets. We present statistics for Test 1 and Test 2 (Left).
We also present the same global votes splitted by type of participants, i.e., CH people and others (Middle and Right).
Figure 8: Scores vs Objects. We present the scores of the three techniques
for each studied object. RBF wins for metallic samples, while HSH and
RBF are comparable for matte materials. As in Figure 7, the missing ground
truth reference in Test 2 flatten the overall scores.
Figure 9: Match Statistics. Matches between the techniques (PTM vs
HSH, PTM vs RBF, and HSH vs RBF) are displayed for Test 1 (Left) and
Test 2 (Right). Values are normalized number of victories across all objects.
have never worked on those objects before. This helps us to ob-
tain an unbiased evaluation of the RTI fitting techniques and their
results on the objects of study.
Design. We carried out the evaluation using a website developed
with HTML5 and Javascript. Users access the test by a private link.
Before starting with the two tests described before, participants are
asked to fill a small, anonymous form with four questions about
their institution, role, usual tasks and kind of objects they use to
work with. Then a few lines explain every test, where users can
click the left or right image, or none of them. Even if the whole
combination of pair images is exposed to all the users, the showing
sequence was randomized for every session, as well as the left-
right order of the comparisons. It is also allowed to go forwards
Figure 10: Lamina. An image for the subjective evaluation. Top row: orig-
inal image and PTM relighting. Bottom row: HSH and RBF relightings.
and backwards through the pairs of images, and change the elected
one in every moment. We set limitless time for the experiment, as
we want users to inspect and select their options carefully and have
the chance to correct previous elections. Instead, we set a limit of
not-null answers of 50% for every test. The average filling time
stands around 14 minutes.
Performance evaluation. The evaluation of the subjective quality
of the relightings is based on a "score" given by each subject to each
technique on each original image and for each of the two tests. This
score is simply the number of "wins" in the binary comparisons,
that can be, clearly, 0, 1, or 2. We divide this score by two to obtain
a normalized value and perform statistics over the different tests,
user profiles and objects. In a few cases, where the user did not
perform all the three binary comparisons for the same relighting,
we discarded the score from the statistics.
In the objective evaluation we have witnessed how PTM is the
technique that behaves poorly across datasets compared with the
other two; HSH improves a little, by trying to render better non-
diffuse material properties, while RBF on average wins over both
other techniques. Now, we are interested in understanding if this
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Figure 11: Lamina - Single Image Scores. Voting scores for the Lamina
image in Figure 10. While scores in Test 1 (ground truth comparison) are
similar between experts and non-experts, Test 2 produces non consistent
results between the two groups. This is probably due to the fact that experts,
without a ground truth, prefer a more readable, smoothed image (i.e., PTM),
while non-experts tend to vote to a more photorealistic one (i.e. RBF).
result has been confirmed visually and perceptually by the users.
Figure 7shows the scores of the three techniques for the first and
the second tests, averaged over the voting subjects, objects and light
directions. We can see how RBF wins in both tests. An interesting
result is that it wins more when the user judgment is guided by
the presence of the ground truth image, while PTM scores improve
in the "unsupervised" second test. This is probably due to the fact
that PTM removes many sharp hilights, a non-photorealistic ap-
proach which might be preferred in some cases, even though far
from ground truth. Checking the statistical significance of the dif-
ferences, we see that, for Test 1 pairwise Wilcoxon signed rank
tests between couple of methods provide always highly signifi-
cant differences (p<10−20 comparing PTM and HSH, p<10−56
comparing PTM and RBF, p<10−15 comparing HSH and RBF).
There is a clear ranking between the perceived quality obtained
with the different methods. Statistical tests also confirm the fact
that the quality of PTM is no longer considered so bad in Test 2.
There is still a clearly significant difference between groups, but
only pairwise differences between RBF and HSH (p<10−4in
Wilcoxon test) and between PTM and RBF (p<10−6in Wilcoxon
test) are significant, while the difference between PTM and HSH is
not (p=0.65 in Wilcoxon test). By separately analyzing votes of
experts and non-experts other interesting differences emerge. The
results of Test 1, "guided" by the displayed ground truth images,
are consistent between those two groups, while in the second test
CH people don’t make a clear choice on the best method. Even
with the presence of burned highlights, and also of some artifacts,
non-experts consider that the renderings with more highlights and
shadows are better, since they probably judge them more photoreal-
istic, even without a looking at a ground truth image (the behavior is
consistent with the Test 1). Conversely, in the Test 2, the CH people
tend to increase the preference on a smoothed PTM signal, which,
although it fails to render high-frequency material behavior, it con-
veys a cleaner (and readable) surface visualization. An example of
this statistical behavior is given in Figure 10 and Figure 11. There
we show only one image of the dataset Lamina and we present the
original photo, and the PTM, HSH, and RBF rendering. From the
statistics corresponding to just this photo and its relightings, we
can see how in the Test 1 RBF wins both for experts and non-expert
people, while in the Test 2 the votes are not consistent between the
two groups, i.e., PTM wins for experts while RBF has more votes
for non-experts. Statistical tests show that, while all the pairwise
differences between groups are highly significant for Test 1 (for
experts we get p<10−8comparing PTM and HSH, p<10−25
comparing PTM and RBF, p<10−5comparing HSH and RBF in
Wilcoxon signed rank tests, for non experts p<10−13 comparing
PTM and HSH, p<10−32 comparing PTM and RBF, p<10−9
comparing HSH and RBF ), but this is no longer true for Test 2.
For both experts and non-experts, the difference between PTM and
HSH is not statistically significant (p=0.23 for experts, p=0.07
for non-expert). For the experts the differences between HSH and
RBF and PTM and RBF are significant only at the 95% confidence
level (p=0.013 and p=0.032 in Wilcoxon tests). For non ex-
perts we have, instead, highly significant differences (p<10−2
and p=<10−6in Wilcoxon tests). Figure 8presents the same
results for each single object. They confirm two trends: in Test 1
the RBF wins over the other techniques, while in Test 2 the differ-
ences between preferences are flattened. In the matte object Shell
HSH and RBF are equally voted; this is not surprising, since a lo-
cal fitting method such as RBF is expected to behave better with
high-frequency signals (e.g., highlights). The different trends are
confirmed by statistical analysis: considering Test 1, we have that,
for the matte object (shell), the pairwise comparison does not show
significant differences between HSH and RBF (p−value =0.06
in Wilcoxon test) while HSH/PTM and RBF/PTM differences are
highly significant (p<10−4and p<10−7, respectively). For the
highly specular object (lamina), instead, there is no statistically sig-
nificant difference between PTM and HSH (p−value =0.93 in
Wilcoxon test), while the differences between RBF and the other
methods are highly significant (p<10−6comparing PTM and
RBF, p<10−4comparing HSH and RBF ). For the intermediate
behavior (coins), the differences between all the groups are highly
significant. RBF is always clearly the better technique. In Test 2,
for the shell we get the same results of Test 1: p-values are quite
low in comparisons between HSH/PTM (<10−10) and RBF/PTM
(<10−11), but there is no statistically significant difference be-
tween HSH and RBF (p=0.80 in Wilcoxon test). The outcomes
of Test 2 are, however, different for the Lamina, where the ranking
of the methods is different with respect to Test 1 and differences
are always statistically significant: PTM wins more than the other
methods and the p-values are statistically significant ( p<10−8
in comparison with HSH and p<10−5in comparison with RBF),
and there is also a statistically significant preference of RBF over
HSH (p<10−4). The reason is probably due to the failure of the
HSH relighting for high level of specularity and the better visibil-
ity of details in non-specular relighting obtained with PTM. For
the coins, we have that the methods seems equivalent on Coin 1,
where there are no statistically significant differences between the
methods, this may be due to the fact that without references some
users prefer "matte" rendering and others a specular one. On Coin
2, however, we have statistically significant preferences for RBF
relighting both with respect to PTM (p<10−5in Wilcoxon test)
and HSH (p<10−4). In Figure 9Left, we show how, in Test 1,
the HSH wins over the PTM, the RBF wins more against the PTM,
and how RBF exhibits a better quality compared to HSH. Similarly,
single matches in the Test 2 (Figure 9Right) confirm the trend that
in the "unsupervised" test the scores are flattened; nevertheless, the
RBF proved to be again the best technique.
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R. Pintus & T. Dulecha & A. Jaspe & A. Giachetti& I. Ciortan & E. Gobbetti / Evaluation of RTI-based Virtual Relighting
9. Discussion
Analyzing the quality of relightings from RTI stacks is interesting
as their analysis is commonly used for objects’ inspection in CH.
So far, issues related to the quality of the renderings have not been
addressed in the literature. Our comparisons of different methods
on different materials give useful insights. RTI is extremely popu-
lar in CH object inspection due to its ease of capture and capabil-
ity to quickly produce relightable images. However, the relatively
sparse sampling of the light direction field and the simplicity of the
fitting/interpolation approaches may lead to errors with complex
objects and appearance properties. On matte surfaces, as the Shell,
synthetic images are closer to the reference ones, and the technique
used is less critical. Greater errors appear with raking lights as the
projected shadows are not reproduced accurately. On challenging
specular surfaces (coins, lamina), the quality is lower as expected.
PSNR clearly decreases with elevation, while SSIM is not simi-
larly changed. This may be caused by large-scale luminance shifts
between original and relighted images, compensated by the percep-
tive adjustments of the SSIM metric. While the RBF interpolation
seems to provide the best similarity with respect to original images
both in objective and subjective tests (and 3rd order HSH is clearly
superior to second order PTM), CH experts been asked to compare
relighted images without reference do not show clear preferences
(Figure 7and 10), showing that non-photorealistic depictions might
be accepted if judged more readable. These results lead to the iden-
tification of two competing research directions. First of all, it looks
interesting to devise specialized task-specific relighting techniques,
which do not strive to photorealistically reproduce the original ob-
ject, but limit themselves to reproduce the set of interesting features
for a particular task (e.g., matte behavior for surface readability,
discontinuities for crack detection). Since fitted representations are
shown to be significantly lossy, these depictions should be extracted
from raw data, rather than as enhancements of fitted models. On
the other hand, to provide a photorealistic rendering, while still re-
quiring only a relatively sparse set of input images, it might prove
interesting to introduce some level of domain-specific knowledge
in the light interpolation process, while still avoiding to solve the
complex problem of full geometry and appearance reconstruction.
Due to the presence of many BRDF datasets and benchmarks, and
the possibility of producing a huge quantity of controlled relight-
ings of different materials and geometries, an emerging research
path is to exploit learning approaches to extract information from
very sparse input samples [DAD∗18].
Our preliminary analysis has clearly also some limitations. First,
it is based on static images. Interactive variation of the light direc-
tion allows a better understanding of surface and material details,
especially if the interpolation methods can capture well highlights
and shadows. So, CH experts could probably appreciate even more
HSH or RBF interpolation in the case of interactive relighting of
non-matte objects. Testing the quality of interactive relighting is,
however much more difficult, due to the necessity of designing spe-
cific tasks. We plan to perform this investigation in future work.
Second, it is based on high-quality relighting made with floating
point coefficients and without compression. Interactive relighting
is often performed, in practice, by using data structures storing ap-
proximate values (often converted in 8 bit depth) and using com-
pressed images. On-line relighting with RBF has been proposed us-
ing PCA compression of the image stack further reducing accuracy.
Of course, it could be interesting to evaluate the effects of compres-
sion on the results. Another issue to be considered is related to the
metrics used for quantitative comparison, that are generic and av-
eraged on the whole image. It may be interesting to develop specif-
ically designed to capture the ability to preserve a specific feature
of interest for the CH analysis.
10. Conclusions
We have presented an evaluation framework to test three RTI-based
rendering and relighting techniques, i.e., PTM, HSH, RBF. We used
the data acquired with a fixed light dome, and we present both
an objective and subjective evaluation scenario. The first tests the
quality of reconstructed images through different error metrics (i.e.,
PSNR and SSIM) and by using a leave-one-out strategy. The sub-
jective test has involved both experts and non-experts volunteers
for a visual test of the quality of virtually relighted images. Al-
though our work is a preliminary attempt to define a standard way
to judge the perceived quality of RTI-based visualization, we al-
ready found that the objective and user-guided outcomes behave
consistently. A lot of interesting work should be done to further
investigate these results. So far, both tests proved that local inter-
polation methods (RBF) are more convenient than more standard
techniques (PTM/HSH) to render high-frequency details.
Acknowledgments. This work was partially supported by the Scan4Reco project (EU H2020 grant
665091), the DSURF (PRIN 2015) project funded by the Italian Ministry of University and Research,
and Sardinian Regional Authorities under projects VIGEC and Vis&VideoLab. We are grateful to
all the end users that participated in our survey. We thank the National Archaelogical Museum of
Cagliari for their collaboration in the capture and analysis of Lamina del Sulcis.
References
[AG15] ACKERMANN J., GOES ELE M.: A survey of photometric stereo
techniques. Foundations and Trends in Computer Graphics and Vision
9, 3-4 (2015), 149–254. 2
[AIK13] ARTAL -ISBRAND P., KLAUSMEYER P.: Evaluation of the re-
lief line and the contour line on greek red-figure vases using reflectance
transformation imaging and three-dimensional laser scanning confocal
microscopy. Studies in Conservation 58, 4 (2013), 338–359. 1
[Bar65] BAR REC A F.: Nuove iscrizioni fenicie da Sulcis. Oriens An-
tiquus 4, 1 (1965), 1–5. 3
[BCDG13] BRO GNARA C., CORSINI M., DELLEPIANE M., GIA -
CHETTI A.: Edge detection on polynomial texture maps. In Proc. ICIAP
(2013), pp. 482–491. 2
[BJK07] BAS RI R., JACOB S D., KEMELM ACHE R I.: Photometric stereo
with general, unknown lighting. International Journal of Computer Vi-
sion 72, 3 (2007), 239–257. 4
[BSMG05] BART ESAG HI A., SAPIRO G., MALZBENDER T., GEL B D.:
Three-dimensional shape rendering from multiple images. Graphical
Models 67, 4 (2005), 332–346. 2
[Buh03] BUHMANN M. D .: Radial basis functions: theory and imple-
mentations, vol. 12. Cambridge university press, 2003. 4
[CHI17] CHI: Cultural heritage imaging, 2017. [Online; accessed 25-
June-2018]. URL: http://culturalheritageimaging.org.
2
[CPM∗16] CIORTAN I. M., PINTUS R ., MARCHIORO G., DAFF ARA C.,
GIAC HET TI A., GOBBETTI E.: A practical reflectance transformation
imaging pipeline for surface characterization in cultural heritage. In
Proc. GCH (2016). 3
[DAD∗18] DESCHAINTRE V., AIT TALA M., DURAND F., DRET TAKI S
c
2018 The Author(s)
Eurographics Proceedings c
2018 The Eurographics Association.

R. Pintus & T. Dulecha & A. Jaspe & A. Giachetti& I. Ciortan & E. Gobbetti / Evaluation of RTI-based Virtual Relighting
G., BOUSSEAU A.: Single-image svbrdf capture with a rendering-aware
deep network. ACM TOG 37, 128 (2018), 15. 9
[DHOMH12] DREW M. S., HE L-ORY., MALZBENDER T., HAJARI
N.: Robust estimation of surface properties and interpolation of
shadow/specularity components. Image and Vision Computing 30, 4-5
(2012), 317–331. 2
[Dix13] DIXON H. M.: Phoenician Mortuary Practice in the Iron Age
I-III (ca. 1200-ca. 300 BCE). PhD thesis, U. Michigan, 2013. 3
[DRS10] DORSEY J., RUSHMEIER H., SILLION F.: Digital modeling of
material appearance. Elsevier, 2010. 2
[Duf10] DUFFY S.: Polynomial texture mapping at Roughting Linn rock
art site. In Proc. ISPRS Commission V Mid-Term Symposium: Close
Range Image Measurement Techniques (2010), pp. 213–217. 1
[Duf13] DUFFY S. M.: Multi-light imaging for heritage applications.
English Heritage, 2013. 2
[ERF11] ELHABIAN S. Y., RARA H., FARAG A. A.: Towards accurate
and efficient representation of image irradiance of convex-Lambertian
objects under unknown near lighting. In Proc. ICCV (2011), pp. 1732–
1737. 4
[FAR07] FATTAL R., AGR AWALA M., RUSINKIEWICZ S.: Multiscale
shape and detail enhancement from multi-light image collections. ACM
TOG 26, 3 (2007), 51. 2
[GCD∗17] GIACHE TTI A., CI ORTAN I., DAFF ARA C ., PINTUS R.,
GOBBETTI E.: Multispectral RTI analysis of heterogeneous artworks.
In Proc. GCH (2017). 2,3,4
[GCD∗18] GIACHE TTI A., CI ORTAN I., DAFF ARA C ., MARCHIORO
G., PINTUS R., GOBBETTI E.: A novel framework for highlight re-
flectance transformation imaging. Computer Vision and Image Under-
standing 168 (2018), 118–131. 3
[GDR∗15] GIACHE TTI A., DAFFARA C., REGHELIN C., GOBBETTI E.,
PINTUS R.: Light calibration and quality assessment methods for re-
flectance transformation imaging applied to artworks’ analysis. In Optics
for Arts, Architecture, and Archaeology V (2015), vol. 9527, p. 95270B.
2
[GKPB04] GAUTRON P., KRIVANEK J., PATTANAIK S. N., BOUA-
TOU CH K.: A novel hemispherical basis for accurate and efficient ren-
dering. Rendering Techniques 2004 (2004), 321–330. 2
[Ham15] HAMEEUW H.: Mesopotamian clay cones in the ancient near
east collections of the royal museums of art and history. Bulletin van de
Koninklijke Musea voor Kunst en Geschiedenis 84 (2015), 5–48. 2
[IA14] IKEHATA S., A IZAWA K.: Photometric stereo using constrained
bivariate regression for general isotropic surfaces. In Proceedings of the
IEEE Conference on Computer Vision and Pattern Recognition (2014),
pp. 2179–2186. 2
[KK13] KOTO ULA E., KYRANOUDI M.: Study of ancient greek and
roman coins using reflectance transformation imaging. E-conservation
magazine 25 (2013), 74–88. 1
[Leu15] LEUVEN K.: Multispectral microdome, 2015.
[Online; accessed 25-June-2018]. URL: https://
portablelightdome.wordpress.com/2015/04/29/
rich-presents- the-new- multispectral-microdome/.
2
[LG14] LIU C., GUJ.: Discriminative illumination: Per-pixel classifi-
cation of raw materials based on optimal projections of spectral BRDF.
IEEE TPAMI 36, 1 (2014), 86–98. 2
[LLW12] LAM P.-M., LEUNG C.-S., WONG T.-T.: Noise-resistant
hemispherical basis for image-based relighting. IET image processing
6, 1 (2012), 72–86. 2
[Mac14] MAC DONALD L. W.: Colour and directionality in surface re-
flectance. In Proc. AISB (2014). 4
[Mac15] MAC DONALD L. W.: Realistic visualisation of cultural heritage
objects. PhD thesis, UCL, 2015. 2
[MBW∗14] MANFREDI M., BEARMAN G., WILLIAMSON G., KRO -
NKRIGHT D., DOEHNE E., JACOB S M., MARE NGO E .: A new quantita-
tive method for the non-invasive documentation of morphological dam-
age in paintings using RTI surface normals. Sensors 14, 7 (2014), 12271–
12284. 1
[MGW01] MALZBENDER T., GELB D., WO LTERS H.: Polynomial tex-
ture maps. In Proc. ACM SIGGRAPH (2001), pp. 519–528. 2,3
[MMC∗08] MUDGE M., MALZBENDER T., CHALMERS A., S COPIGNO
R., DAVIS J., WANG O., GUNAWARDAN E P., ASH LEY M., DO ERR M.,
PROE NCA A.: Image-based empirical information acquisition, scientific
reliability, and long-term digital preservation for the natural sciences and
cultural heritage. In Eurographics (Tutorials) (2008). 2,4
[MVSL05] MUDGE M., VOU TAZ J.-P., SCH ROER C., LU M M.: Reflec-
tion transformation imaging and virtual representations of coins from the
hospice of the Grand St. Bernard. In VAST (2005), vol. 6, pp. 29–40. 1
[Pan16] PAN R.: Detection of edges from polynomial texture maps. 3D
Research 7, 1 (2016), 3. 2
[Pay13] PAYNE E. M.: Imaging techniques in conservation. Journal of
conservation and museum studies 10, 2 (2013). 2
[PCC∗10] PALM A G., CORSINI M., CIGNONI P., SCOPIGNO R.,
MUDGE M.: Dynamic shading enhancement for reflectance transfor-
mation imaging. ACM JOCCH 3, 2 (2010), 6. 1
[PCS18] PONCHIO F., CORSINI M., SCOPIGNO R.: A compact repre-
sentation of relightable images for theweb. In Proc. ACM Web3D (2018),
ACM Press, p. 10. 2,4
[PGPG17] PINTUS R., GIACHE TTI A., PI NTO RE G. , GOBBETTI E.:
Guided robust matte-model fitting for accelerating multi-light reflectance
processing techniques. In Proc. BMVC (2017). 2
[PLGF∗15] PITARD G., LEGOÏC G., FAVREL IÈR E H., SAMPER S.,
DESAGE S.-F., PILLE T M.: Discrete modal decomposition for surface
appearance modelling and rendering. In Optical Measurement Systems
for Industrial Inspection IX (2015), vol. 9525, p. 952523. 2
[PPY∗16] PINTUS R., PAL K., YANG Y., WEYRICH T., GOBBETTI E.,
RUSHMEIER H.: A survey of geometric analysis in cultural heritage. In
Computer Graphics Forum (2016), vol. 35, pp. 4–31. 2
[RL05] ROU SSE EUW P. J., LEROY A. M.: Robust regression and outlier
detection, vol. 589. John wiley & sons, 2005. 2
[RTF∗04] RASKAR R., TAN K.-H., FERI S R., YUJ., TURK M.: Non-
photorealistic camera: depth edge detection and stylized rendering using
multi-flash imaging. In ACM TOG (2004), vol. 23, pp. 679–688. 2
[SSWK13] SCHWARTZ C., SA RLE TTE R., WEINMANN M., KL EIN R .:
Dome ii: A parallelized btf acquisition system. In Material Appearance
Modeling (2013), pp. 25–31. 2
[STMI14] SHI B., TAN P., MATSUS HITA Y., IK EUC HI K.: Bi-
polynomial modeling of low-frequency reflectances. IEEE TPAMI 36,
6 (2014), 1078–1091. 2
[SWM∗16] SHI B., WUZ., MOZ., DUAN D. , YEUNG S.-K., TAN P.:
A benchmark dataset and evaluation for non-lambertian and uncalibrated
photometric stereo. In Proc. ICCV (2016), pp. 3707–3716. 2
[Sze10] SZELISKI R.: Computer vision: algorithms and applications.
Springer Science & Business Media, 2010. 2
[TGVG12] TINGDAHL D., GODAU C., VAN GOOL L.: Base materials
for photometric stereo. In Proc. ECCV (2012), pp. 350–359. 2
[UW13] URIBE M. D.-G., WHEATLE Y D. W.: Rock art an digital tech-
nologies: the application of reflectance transformation imaging (RTI) and
3D laser scanning to the study of late bronze age iberian stelae. Menga:
Revista de prehistoria de Andalucía, 4 (2013), 187–203. 1
[WGSD09] WANG O. , GUNAWARDAN E P., SCH ER S., DAVIS J.: Ma-
terial classification using brdf slices. In Proc. CVPR (2009), pp. 2805–
2811. 2
[Woo80] WOODHAM R. J.: Photometric method for determining sur-
face orientation from multiple images. Optical engineering 19, 1 (1980),
191139. 2
[WTFE18a] WIKIPEDIA, THE FREE ENCYCLOPEDIA: Peak signal-to-
noise ratio, 2018. [Online; accessed 25-June-2018]. URL: https:
//en.wikipedia.org/wiki/Peak_signal-to- noise_
ratio.4
[WTFE18b] WIKIPEDIA, THE FREE ENCYCLOPEDIA: Structural simi-
larity, 2018. [Online; accessed 25-June-2018]. URL: https://en.
wikipedia.org/wiki/Structural_similarity.4
[ZD14] ZHANG M., DR EW M. S.: Efficient robust image interpolation
and surface properties using polynomial texture mapping. EURASIP
Journal on Image and Video Processing 2014, 1 (2014), 25. 2
c
2018 The Author(s)
Eurographics Proceedings c
2018 The Eurographics Association.