Decay Detection in an Ancient Column with Combined Close-Range Photogrammetry (CRP) and Ultrasonic Tomography

: This study presents the integrated application of a few non-destructive techniques, i.e., Close Range Photogrammetry (CRP), and low frequency (24 kHz) ultrasonic tomography complemented by petrographical analysis. The aim here is to assess the conservation state of a Carrara marble column in the Basilica of San Saturnino, which is part of a V-VI century Palaeo Christian complex in the city of Cagliari (Italy). The high resolution 3D modelling of the studied artifact was computed starting from the integration of proximal sensing techniques, such as CRP based on the Structure from Motion (SfM) technique, which provided information on the geometrical anomalies and reﬂectivity of the investigated marble column surface. The inner parts of the studied body were inspected successfully in a non-invasive way by computing the velocity pattern of the ultrasonic signal through the investigated materials, using 3D ultrasonic tomography. The latter was optimally designed based on the 3D CRP analysis and the locations of the source and receiver points were detected as accurately as possible. The integrated application of in situ CRP and ultrasonic techniques provided a full 3D high resolution model of the investigated artifact, which made it possible to evaluate the material characteristics and its degradation state, affecting mainly the shallower parts of the column. The 3D visualisation improves the efﬁciency, accuracy, and completeness of the interpretative process of data of a different nature in quite easily understood displays, as well as the communication between different technicians.


Introduction
The diagnosis of the conservation state of monumental structures, from the constraints to the spatial distribution of their physical properties on shallow and inner building materials, represents one of the key objectives in the application of non-invasive techniques.
In the field of cultural heritage, the complex task of the diagnostics of the state of conservation of ancient monuments is a topic that involves many subjects, such as public and private institutions, civil protections, etc. Moreover, the economic aspect is to be taken into account, since the monitoring and intervention for the maintenance of monumental structures often require the outlay of important financial resources [1,2]. Non-destructive tests can be used to obtain the necessary qualitative and quantitative parameters needed to plan the recovery and preservation of a monumental structure.

Macroscopic Features
The column under study is located in a closed environment (inside the Basilica of San Saturnino) with no constant air recirculation and high values of relative humidity, that caused severe superficial alteration phenomena in the column. In these environmental conditions, the building material which is of a carbonate nature, suffered the effects of calcite solubilization and intercrystalline decohesion, that led to more serious problems, The high resolution 3D modelling of the studied artifact was computed starting from the integration of proximal sensing techniques, such as CRP based on Structure from Motion (SfM), which gave information on the geometrical anomalies and reflectivity of the surface of the investigated marble column. The inner parts of the studied body were successfully inspected in a non-invasive way by computing the velocity pattern of the ultrasonic signal through the investigated materials, using 3D ultrasonic tomography. This technique gives information on the elastic properties of the material related with petrophysical and mechanical properties and a number of factors, such as the presence of fractures, voids, and flaws. Extracting information on these factors, from the elastic wave velocity using 3D tomography, provides a non-invasive approach to analysing the property changes of the inner material of the ancient column.
The integrated application of in situ CRP and ultrasonic techniques provides a full 3D high resolution model of the investigated artifact. This model, which is enhanced by the knowledge of the petrographic characteristics of the materials, affords reliable information on the state of conservation of the materials used in the construction process. The noninvasive integrated approach is helpful in deciding whether any repair is needed, how to choose the optimal repair techniques, and in prioritising interventions for the restoration and future preservation [5,8,30].

Macroscopic Features
The column under study is located in a closed environment (inside the Basilica of San Saturnino) with no constant air recirculation and high values of relative humidity, that caused severe superficial alteration phenomena in the column. In these environmental conditions, the building material which is of a carbonate nature, suffered the effects of calcite solubilization and intercrystalline decohesion, that led to more serious problems, such as an increase in porosity, exfoliation, and pulverisation. The product of pulverization is characterised by a highly hygroscopic marble dust that accumulates in the protruding parts of the column base ( Figure 2). Since this dust is rich in moisture, if not routinely removed, it could trigger phenomena of alteration and dissolution that could seriously damage even the base of the structure itself, which is not yet compromised at present. However, other sectors of the column such as the upper and central part of the shaft have suffered the greatest damage due to exfoliation and pulverization. The loss of material in these critical sectors caused a localised reduction in volume, implying dangerous conditions, such as a possible worsening of the mechanical characteristics of the marble [37].
such as an increase in porosity, exfoliation, and pulverisation. The product of pulverization is characterised by a highly hygroscopic marble dust that accumulates in the protruding parts of the column base ( Figure 2). Since this dust is rich in moisture, if not routinely removed, it could trigger phenomena of alteration and dissolution that could seriously damage even the base of the structure itself, which is not yet compromised at present. However, other sectors of the column such as the upper and central part of the shaft have suffered the greatest damage due to exfoliation and pulverization. The loss of material in these critical sectors caused a localised reduction in volume, implying dangerous conditions, such as a possible worsening of the mechanical characteristics of the marble [37].

Optical Microscopy Analysis
Optical Microscopy (OM) was used for the analysis of the compositional, textural, and some petrophysical characteristics, such as the porosity of the studied building material. Optical microscopy was performed with a Carl Zeiss Axioplan microscope (Carl Zeiss, Oberkochen, Germany).
Thin sections were obtained from some fragments of material detached from the shallow part of the column shaft. It was decided to study this material mainly in order to not carry out further destructive tests on the column, as well as to evaluate the influence of degradation on texture and composition at a microscopic level.
From the OM observations, the building material was identified as marble with a granoblastic texture ( Figure 3). The calcite crystals have an average size of about 200 µm with minimum and maximum dimensions of 60 and 600 µm, respectively. The crystals, generally characterised by straight boundaries, are interconnected by a triple junction with an angle of approximately 120° (Figure 3a). Based on the dimensional and geometric characteristics of the calcite crystals, this type of marble could be geographically attributed to the marble basin of the Apuan Alps in Italy [38].
In the studied marble, the crystals are mutually well welded ( Figure 3b). However, in several sectors, there is no direct contact and they can be separated by open fractures of a width of 500 µm on average (Figure 3c). The fractures represent the main type of porosity (about 2%), subsequent to the superficial degradation phenomena, such as dis-

Optical Microscopy Analysis
Optical Microscopy (OM) was used for the analysis of the compositional, textural, and some petrophysical characteristics, such as the porosity of the studied building material. Optical microscopy was performed with a Carl Zeiss Axioplan microscope (Carl Zeiss, Oberkochen, Germany).
Thin sections were obtained from some fragments of material detached from the shallow part of the column shaft. It was decided to study this material mainly in order to not carry out further destructive tests on the column, as well as to evaluate the influence of degradation on texture and composition at a microscopic level.
From the OM observations, the building material was identified as marble with a granoblastic texture ( Figure 3). The calcite crystals have an average size of about 200 µm with minimum and maximum dimensions of 60 and 600 µm, respectively. The crystals, generally characterised by straight boundaries, are interconnected by a triple junction with an angle of approximately 120 • (Figure 3a). Based on the dimensional and geometric characteristics of the calcite crystals, this type of marble could be geographically attributed to the marble basin of the Apuan Alps in Italy [38].
In the studied marble, the crystals are mutually well welded ( Figure 3b). However, in several sectors, there is no direct contact and they can be separated by open fractures of a width of 500 µm on average (Figure 3c). The fractures represent the main type of porosity (about 2%), subsequent to the superficial degradation phenomena, such as dissolution and exfoliation, which can also be observed at the macroscopic level. The fractures became sectors of accumulation of altered material and dirt (Figure 3c,d), whose nature must be assessed in further analysis. By infiltrating into the intercrystalline spaces, these materials further intensified both the alteration processes and the general degradation of the stone material. solution and exfoliation, which can also be observed at the macroscopic level. The fractures became sectors of accumulation of altered material and dirt (Figure 3c,d), whose nature must be assessed in further analysis. By infiltrating into the intercrystalline spaces, these materials further intensified both the alteration processes and the general degradation of the stone material.

Close Range Photogrammetry
CRP is a proximal sensing methodology, which uses accurate imaging techniques to analyse the three-dimensional shape of a wide range of manufactured and natural objects. CRP is based on Structure from Motion algorithms and software facilities.
Structure from Motion (SfM) is a Remote Sensing (RS) methodology that uses multiple arrays of high quality 2D digital photographs to 3D-model the surface of a studied object, by creating a dense point cloud texturised with natural colours. Moreover, the X, Y, Z coordinates are associated with each point of this cloud in an intrinsic reference frame, defined by the user that can be successively refined using geo-referenced Ground Control Points (CGPs). Multiple 2D digital images must be acquired using photo-cameras evenly spaced all around the observed objects from different perspectives and processed with SfM-based facilities. In practice, the structure of the studied object is 3D-modelled by means of the camera movement [14,39].
Initially, the software automatically identifies the most prominent features (keypoints) that can be immediately recognised in multiple photographs by means of algorithms. These algorithms can provide Robust Feature Detection and Matching (RFDM), such as the Scale-Invariant Feature Transform (SIFT) [40]. In a second stage, the images that were previously quality-checked (carefully selected) by the operator are aligned very

Close Range Photogrammetry
CRP is a proximal sensing methodology, which uses accurate imaging techniques to analyse the three-dimensional shape of a wide range of manufactured and natural objects. CRP is based on Structure from Motion algorithms and software facilities.
Structure from Motion (SfM) is a Remote Sensing (RS) methodology that uses multiple arrays of high quality 2D digital photographs to 3D-model the surface of a studied object, by creating a dense point cloud texturised with natural colours. Moreover, the X, Y, Z coordinates are associated with each point of this cloud in an intrinsic reference frame, defined by the user that can be successively refined using geo-referenced Ground Control Points (CGPs). Multiple 2D digital images must be acquired using photo-cameras evenly spaced all around the observed objects from different perspectives and processed with SfM-based facilities. In practice, the structure of the studied object is 3D-modelled by means of the camera movement [14,39].
Initially, the software automatically identifies the most prominent features (key-points) that can be immediately recognised in multiple photographs by means of algorithms. These algorithms can provide Robust Feature Detection and Matching (RFDM), such as the Scale-Invariant Feature Transform (SIFT) [40]. In a second stage, the images that were previously quality-checked (carefully selected) by the operator are aligned very precisely using bundle adjustment algorithms as well [41] and a sparce point cloud is generated. In the third step, this cloud is used as input in the computation of the final unstructured unified dense point cloud representing the high resolution 3D-model of the studied body, by means of Multi Video Stereo view (MVS) styled algorithms [3,4,6,9,25].

The Photogrammetric Survey
To compute the HR 3D-model of an ancient marble column in the Basilica of San Saturnino in the town of Cagliari, we used a Nikon D-5300 24.2 MP CMOS digital camera mounted on a tripod equipped with a bubble level ( Figure 4a). After an in situ successful feasibility inspection, we acquired 102 digital photos evenly spaced all around the studied artifact and from different perspectives (Figure 4b). The higher the number and optical resolutions of the acquired photos, the higher the precision of the resulting final model, which can have a resolution higher than 1 mm or more. In order to obtain the optimal degree of image superposition (60% to 80%) required to optimize the image processing, the station points (poses) were settled according to the following conditions: (1) At fixed distances (1 m to 3 m) from the column ( Figure 4c); (2) the space (baselines) between them was maintained as small as possible (less than 1 m); (3) the images were acquired as far as possible at homogeneous exposure conditions; and (4) reference markers (calibrated bars) were introduced in the scene (Figure 4d).
precisely using bundle adjustment algorithms as well [41] and a sparce point cloud is generated. In the third step, this cloud is used as input in the computation of the final unstructured unified dense point cloud representing the high resolution 3D-model of the studied body, by means of Multi Video Stereo view (MVS) styled algorithms [3,4,6,9,25].

The Photogrammetric Survey
To compute the HR 3D-model of an ancient marble column in the Basilica of San Saturnino in the town of Cagliari, we used a Nikon D-5300 24.2 MP CMOS digital camera mounted on a tripod equipped with a bubble level ( Figure 4a). After an in situ successful feasibility inspection, we acquired 102 digital photos evenly spaced all around the studied artifact and from different perspectives (Figure 4b). The higher the number and optical resolutions of the acquired photos, the higher the precision of the resulting final model, which can have a resolution higher than 1 mm or more. In order to obtain the optimal degree of image superposition (60% to 80%) required to optimize the image processing, the station points (poses) were settled according to the following conditions: (1) At fixed distances (1 m to 3 m) from the column ( Figure 4c); (2) the space (baselines) between them was maintained as small as possible (less than 1 m); (3) the images were acquired as far as possible at homogeneous exposure conditions; and (4) reference markers (calibrated bars) were introduced in the scene (Figure 4d).

Data Processing
The Agisoft-Metashape v1.6.3 (Agisoft LLC, St. Petersburg, Russia) software was used to pre-process in the best way the 102 images acquired in situ during the August 2020 photogrammetric campaign. The software was operated on two multicore/multithreads processor PCs equipped with GPUs with Compute Unified Device Architectures Images are selected and aligned in a very precise way using the bundle adjustment algorithms implemented in the software, as well. Moreover, key-points are located and a Images are selected and aligned in a very precise way using the bundle adjustment algorithms implemented in the software, as well. Moreover, key-points are located and a sparce point cloud is generated. Then, a dense unified unstructured point cloud texturized with natural colours in a red, green, blue (RGB) colour scale is obtained in the last step of SfM data elaboration. Finally, the resulting dense cloud of about 6 million points is format converted in the E57 LIDAR data exchange format, which is compatible with the input of cloud processing packages.
Point clouds are manually edited, filtered, and meshed using the Poisson surface reconstruction algorithm implemented in the software Reconstructor ® to fill little gaps and to generate an HR meshed 3D model of the marble column of a 1x1 mm scale to be used as a reference model.
In order to perform an optimal comparison of CRP results with the patterns of ultrasonic velocity detected by the application of the 3D tomography, in the final step of CRP data processing we detected: (1) The residuals of the 3D model of the Carrara marble ancient column with respect to a meshed fitted cylinder adopted as reference (i.e., geometrical surface anomalies of the studied artifact); (2) the pattern of the reflectivity parameter representing the amplitude of the backscattered light after reflection on the targeted column surface, which gave interesting analogies with the geometrical anomalies. Figure 5 represents the flow chart of the CRP data processing described above.
sparce point cloud is generated. Then, a dense unified unstructured point cloud texturized with natural colours in a red, green, blue (RGB) colour scale is obtained in the last step of SfM data elaboration. Finally, the resulting dense cloud of about 6 million points is format converted in the E57 LIDAR data exchange format, which is compatible with the input of cloud processing packages. At this stage of the CRP data processing, we used the algorithm implemented in the cloud processing software JRC-3D Reconstructor ® v4.1.2 (Gexcel, Brescia, Italy) [42] and Cloud Compare v2. 11.3 (Copyright © 200011.3 (Copyright © ,200111.3 (Copyright © ,2002 Free Software Foundation, Inc., Boston, MA, USA) [43] to provide the surface geometrical anomalies and reflectivity patterns of the studied column.
Point clouds are manually edited, filtered, and meshed using the Poisson surface reconstruction algorithm implemented in the software Reconstructor ® to fill little gaps and to generate an HR meshed 3D model of the marble column of a 1x1 mm scale to be used as a reference model.
In order to perform an optimal comparison of CRP results with the patterns of ultrasonic velocity detected by the application of the 3D tomography, in the final step of CRP data processing we detected: (1) The residuals of the 3D model of the Carrara marble ancient column with respect to a meshed fitted cylinder adopted as reference (i.e., geometrical surface anomalies of the studied artifact); (2) the pattern of the reflectivity parameter representing the amplitude of the backscattered light after reflection on the targeted column surface, which gave interesting analogies with the geometrical anomalies. Figure 5 represents the flow chart of the CRP data processing described above.

Ultrasonic Measurements
Based on the 3D models with the previous technique (CRP and SfM photogrammetry), a 3D ultrasonic tomography was planned by designing a dense 3D survey to ensure a very good spatial coverage of the investigated column shaft. The 3D CRP model was indispensable to precisely locate the source and receiver stations for the 3D ultrasonic tomography, measure their mutual distance accurately, and detect their coordinates in the selected reference system (Cartesian system).
The ultrasonic experimental investigation on the column was aimed at determining the size and location of internal potential defects. In fact, after its propagation through the material, the ultrasonic signal is the result of the scattering and the delay in the transit times, which is caused by the presence of cracks, pores, and degradation zones that can change the internal structure of the stone material.
A Portable Ultrasonic Non-Destructive Digital Indicating Tester (Pundit Lab Plus) device by Proceq (Schwerzenbach, Switzerland) with 24 kHz central frequency piezoelectric transducers, that can act as either a receiver or transmitter, was used to measure the

Ultrasonic Measurements
Based on the 3D models with the previous technique (CRP and SfM photogrammetry), a 3D ultrasonic tomography was planned by designing a dense 3D survey to ensure a very good spatial coverage of the investigated column shaft. The 3D CRP model was indispensable to precisely locate the source and receiver stations for the 3D ultrasonic tomography, measure their mutual distance accurately, and detect their coordinates in the selected reference system (Cartesian system).
The ultrasonic experimental investigation on the column was aimed at determining the size and location of internal potential defects. In fact, after its propagation through the material, the ultrasonic signal is the result of the scattering and the delay in the transit times, which is caused by the presence of cracks, pores, and degradation zones that can change the internal structure of the stone material.
A Portable Ultrasonic Non-Destructive Digital Indicating Tester (Pundit Lab Plus) device by Proceq (Schwerzenbach, Switzerland) with 24 kHz central frequency piezoelectric transducers, that can act as either a receiver or transmitter, was used to measure the travel time propagation of the longitudinal ultrasonic signal along many source-receiver paths. Moreover, each station was alternatively used as a transmitter and a receiver.
In this study, only the first arrival for each source-receiver path was taken into account, as this can be confidently associated with the longitudinal wave (P wave). The transit time of the propagation of the longitudinal ultrasonic wave from the transmitter to the receiver was measured in a direct transmission mode [44,45]. The source and receiver positions lie along the perimeter of the investigated column shaft ( Figure 6) in order to obtain a good ray coverage of the investigated volume. Every station point was spaced 15 cm along parallel vertical profiles in a way as to surround the investigated column shaft entirely and homogeneously, as well as to cross the investigated volume in many directions. Considering that the surface of the marble column is rough and irregular, special care was taken in choosing the best coupling agent between the transducer and material. As a coupling agent, silicone snug sheets were used. From previous experimental ultrasonic applications [3,4,6,9,25], it was found that this kind of coupling agent is particularly suitable for use in porous media, such as natural materials. It optimises the transmissibility of the ultrasonic signal, filling the irregularities at the interface while avoiding soiling the material and interfering with it.
travel time propagation of the longitudinal ultrasonic signal along many source-receiver paths. Moreover, each station was alternatively used as a transmitter and a receiver.
In this study, only the first arrival for each source-receiver path was taken into account, as this can be confidently associated with the longitudinal wave (P wave). The transit time of the propagation of the longitudinal ultrasonic wave from the transmitter to the receiver was measured in a direct transmission mode [44,45]. The source and receiver positions lie along the perimeter of the investigated column shaft ( Figure 6) in order to obtain a good ray coverage of the investigated volume. Every station point was spaced 15 cm along parallel vertical profiles in a way as to surround the investigated column shaft entirely and homogeneously, as well as to cross the investigated volume in many directions. Considering that the surface of the marble column is rough and irregular, special care was taken in choosing the best coupling agent between the transducer and material. As a coupling agent, silicone snug sheets were used. From previous experimental ultrasonic applications [3,4,6,9,25], it was found that this kind of coupling agent is particularly suitable for use in porous media, such as natural materials. It optimises the transmissibility of the ultrasonic signal, filling the irregularities at the interface while avoiding soiling the material and interfering with it. The output signals were recorded by a portable digital oscilloscope (Fluke 96B) interfaced with a laptop to acquire and digitalise the ultrasonic waveforms for further analysis and processing.
The ultrasonic travel time along the source-receiver path was measured with an accuracy of 0.1 µs and a minimum of six measurements were assessed for each path. The transit times were measured by locating the first arrival times of the received longitudinal signals analyzing the waveforms recorded and displayed by the digital oscilloscope. In a complex situation as the studied one, the automated arrival picking techniques could not consistently detect first arrivals. Therefore, we carefully hand-picked the first arrivals of the longitudinal waves for the tomographic analysis. In fact, first-arrival picking plays an important role in the tomographic data processing and directly influences the quality of the results. Accordingly, the initial phase of the data processing was to carry out a quality The output signals were recorded by a portable digital oscilloscope (Fluke 96B) interfaced with a laptop to acquire and digitalise the ultrasonic waveforms for further analysis and processing.
The ultrasonic travel time along the source-receiver path was measured with an accuracy of 0.1 µs and a minimum of six measurements were assessed for each path. The transit times were measured by locating the first arrival times of the received longitudinal signals analyzing the waveforms recorded and displayed by the digital oscilloscope. In a complex situation as the studied one, the automated arrival picking techniques could not consistently detect first arrivals. Therefore, we carefully hand-picked the first arrivals of the longitudinal waves for the tomographic analysis. In fact, first-arrival picking plays an important role in the tomographic data processing and directly influences the quality of the results. Accordingly, the initial phase of the data processing was to carry out a quality control of the ultrasonic waveforms acquired by the digital oscilloscope. Later, a filtering to improve the Signal-to-Noise ratio (S/N) without modifying the intrinsic characteristics of the ultrasonic signal was carried out where necessary. The longitudinal wave velocity propagation between the source and receiver transducer pair can be directly estimated by considering the source-receiver distance divided by the travel time. This velocity is the result of effects of the material conditions along the ray path. The 3D Ultrasonic Tomography A tomographic inversion, starting from the position of transmitters and receivers on a 3D Cartesian grid and the transit times between the source-receiver pair, was processed by considering curved rays and applying the well-known Simultaneous Iterative Reconstruction Technique (SIRT) [46][47][48] to produce the 3D velocity distribution model in the investigated volume. The ultrasonic measurements were 1936 from 88 point stations alternatively used as transmitter and receiver, but only 1860 of these were processed by the inversion technique. In fact, when checking the ultrasonic waveforms, only first arrivals with shapes that looked undistorted were taken into consideration. The investigated volume was discretized into elements (voxels). The size of the voxels was determined by the number of source-receiver paths. Thanks to the iterative procedure, it was possible to calculate the velocity of the longitudinal ultrasonic signal within each voxel. The iterative reconstruction technique involves a series of successive approximations to correct an arbitrary initial parameter distribution (starting velocity model). In order to obtain a realistic starting velocity model as input for the SIRT to invert travel-time data and produce a reliable 3D representation of the ultrasonic longitudinal wave velocity distribution inside the column, a methodology based on the cross-correlation function proposed by Fais and Casula (2010) [49] was applied. Omitting the detailed mathematical aspects of the inversion algorithm, the main steps involved in the inversion process are briefly the following: Forward computation of the model travel times for each source/receiver pair; computation of the theoretical travel times using the ray-tracing method; comparison of the theoretical and experimental travel times; and calculation of the residuals and application of velocity corrections due to time discrepancy to the 3D volume of the voxels within the model. The iterative sequence is repeated until the necessary accuracy is obtained. In this study, the entire processing sequence was repeated for 18 iterations. This amount of iterations was found appropriate to obtain the best representation of the 3D distribution of the longitudinal velocity within the investigated volume and a good compromise between the resolving power and the reliability of the velocity model.
The 3D rendering of the longitudinal velocity distribution inside the investigated volume was plotted by the software Voxler v.4.3.771 from Golden Software, which enables an efficient and accurate three-dimensional representation. With this kind of display, the ultrasonic velocity distribution data can be viewed as a volume. By scrolling through the data volume and rotating in any direction, one can get an easy feel of the elastic characteristics of the materials inside the column. Furthermore, to facilitate the interpretation of the 3D tomography model inside the data volume, it was sliced to create cross sections along its longitudinal development. In this way, the slices were created by slicing the 3D volume horizontally and deciding their position in an interactive manner. To understand how the low velocity zones associated with degraded zones are distributed within the investigated volume, it was effective to display the slices sequentially through the longitudinal axis of the volume. In this way, one can obtain a much better understanding of the spatial development of the altered and/or damaged zones inside the column.

Results and Discussion
The integrated use of different non-invasive techniques, such as CRP digital photogrammetry and 3D ultrasonic tomography, corroborated by the analysis of the petrographic characteristics of the investigated materials is of paramount importance in assessing the state of conservation of the shallow and deep zones of the marble making up the investigated structure. Knowledge of the stone material conditions and its decay processes, as well as the mechanisms governing them depend on the intrinsic properties of the investigated material, such as mineral composition, texture, nature, and distribution of porosity, as well as their interrelationship with the environmental exposure [50].

Close Range Photogrammetry
As previously described in the section on methodologies, starting from a dense point cloud texturised with natural colours represented with an RGB scale and computed using CRP and SfM methodologies (Agisoft-Metashape ® package), we applied the algorithms for the cloud post-processing implemented in the JRC-3D Reconstructor ® package to compute the geometrical anomalies and reflectivity patterns of the studied ancient Carrara marble column. The results of these computations are represented in Figure 7a,c,d, together with the longitudinal velocity patterns obtained with low frequency ultrasonic tomography. coincidence is probably due to the presence of marble dust on the column, which is obviously less detectable by reflectivity. This is an indication for suggesting the continuous use of the two imaging maps, which together better define the state of the surfaces.

Ultrasonic Tomography
The results of the 3D ultrasonic tomography give images of the distribution of the longitudinal velocities in the investigated volume. These are shown from different viewpoints in Figure 7b to facilitate their comparison with the CRP results (Figure 7a,d).
The results of the tomographic analysis show that the ultrasonic longitudinal velocity ranges between 1000 and 3000 m/s, denoting differences in the elastic characteristics of the marble building material. These differences are mainly due to the dissolution process of the marble that modifies the pore structure and can change the pore distribution. Microweathering and some forms of marble deterioration that can be recognized through thin section analysis cause a lowering of the elastic characteristics of the material, and thus a decrease in longitudinal velocity values. A great variability in the longitudinal velocity distribution is especially evident in the surface of the marble column, as can be seen from the tomographic volume at different viewpoints (Figure 7b). Sectors characterised by a higher velocity (2500-3000 m/s) alternate with others with lower velocity (1000-1500 m/s). The latter correspond to surface alteration layers, where deterioration products formed The first result of the CRP method is the aggregated unified filtered point cloud, texturised with the natural colours derived from the photogrammetric campaign representing the detailed Carrara marble column under study, with a resolution of 1 mm or better. This cloud is meshed and reconstructed with the aid of Poisson reconstruction algorithms implemented in the JRC-3D Reconstructor package to fill little holes and to detect an HR reference model that can also be used as metrical reference in future surveys, while preserving the memory of the studied artifact. The derived reflectivity obtained with natural light radiometry gives information on the altered parts of the column surface that can be compared with the other diagnostic tools applied here, in parallel. Taking into account the general definition of reflectivity as the amount of incident energy reflected by the surface of the analysed targets, the higher the reflectivity the higher the roughness of the studied surface. However, the reflectivity also depends on the colours of the studied objects and on the inclination angle of the incident radiation. For this reason, the reflectivity pattern must be complemented with other diagnostic investigations, such as the geometrical anomalies of the material and the velocity patterns given by the ultrasonic methods.
With regards to the geometric anomalies, these are computed with the inspection procedure applied to the HR 3D model of the Carrara marble column under study as residuals, with respect to a cylindrical geometry fitted to the HR 3D model, meshed, and adopted as reference. The results of the inspection procedure applied to the HR model of the column are represented in Figure 7d, where they are compared with the results of the other diagnostic techniques applied In particular, in Figure 7, the ancient column is represented from four different points of view to give a better appreciation of the results. In the colour scale of the reflectivity pattern, ranging in the interval from 0 to 1, the smaller values are represented in Figure 7a with blue and green colour tones. Conversely, higher values are represented with red tones. The higher values of reflectivity highlight the most affected areas of the column.
In the geometrical anomalies scale, the residuals are scattered in the range +/− 0.025 m, where the positive anomalies are represented in red and the negative ones in blue. By comparing the reflectivity with the geometrical anomalies in the images obtained from different points of view (Figure 7a,d), a swelling is evident in the lower sectors of the column, as well as a superficial degradation of the marble material which appears pulverized. In each figure of the four points of view, positive geometrical anomalies (red tones) are found in the lower part of the column. Moreover, the areas with high reflectivity values mostly coincide with those where the geometrical anomalies are negative. The lack of coincidence is probably due to the presence of marble dust on the column, which is obviously less detectable by reflectivity. This is an indication for suggesting the continuous use of the two imaging maps, which together better define the state of the surfaces.

Ultrasonic Tomography
The results of the 3D ultrasonic tomography give images of the distribution of the longitudinal velocities in the investigated volume. These are shown from different viewpoints in Figure 7b to facilitate their comparison with the CRP results (Figure 7a,d).
The results of the tomographic analysis show that the ultrasonic longitudinal velocity ranges between 1000 and 3000 m/s, denoting differences in the elastic characteristics of the marble building material. These differences are mainly due to the dissolution process of the marble that modifies the pore structure and can change the pore distribution. Microweathering and some forms of marble deterioration that can be recognized through thin section analysis cause a lowering of the elastic characteristics of the material, and thus a decrease in longitudinal velocity values. A great variability in the longitudinal velocity distribution is especially evident in the surface of the marble column, as can be seen from the tomographic volume at different viewpoints (Figure 7b). Sectors characterised by a higher velocity (2500-3000 m/s) alternate with others with lower velocity (1000-1500 m/s). The latter correspond to surface alteration layers, where deterioration products formed along the surfaces or in crevices created by material detachment. The alteration product visible in the low velocity sectors could be due to the decay of calcite caused by the microclimate inside the Basilica, which is characterised by strong humidity. It should be pointed out that the low velocity sectors are almost in correspondence with the high reflectivity sectors (Figure 7a), where the roughness caused by the degradation of the shallow materials is greater. The 3D tomographic and CRP models are representations of different geophysical properties of the same shallow material. Each of these models have different levels of detail and significance, but are connected to each other. Furthermore, the above geophysical properties are linked in a complex way to many rock properties, such as mineralogical composition, texture, density, porosity, and permeability [3,4,23,26]. These properties characterise the physical and mechanical conditions of the marble.
To facilitate the diagnostic process inside the column and check the development of the zones characterised by low velocity, while also detecting their geometry and size, a number of tomographic slices corresponding to horizontal sections along the longitudinal development of the investigated structure are represented in Figure 8. The location and orientation of the horizontal slices extracted from the ultrasonic tomography data volume were decided interactively for a clearer visualisation of the internal distribution of the elastic characteristics of the investigated column, while also taking into account the results from a visual inspection ( Figure 2) and the 3D CRP models (Figure 7a,c,d). From the visualisation of the tomographic slices, we could better understand the three-dimensional development of the low velocity zones (cyan-green coloured in Figure 8b) associated with the marble degradation. In particular, it can easily be observed that the elastic characteristics of the marble worsen, from the inner part of the column shaft towards its surface. In fact, the lower ultrasonic velocities values (1000-1500 m/s), typical of a degraded marble, generally correspond to the first 5 cm of the shallow material. This thickness tends to increase in the lower part of the analysed volume of the column (see, for instance, the first two slices from the bottom in Figures 8 and 9), indicating a greater diffusion of the degradation and microfracturing in this part, where positive geometrical anomalies have also been detected. However, apart from this localized sector of the shaft, the stone deterioration is mostly superficial due to the textural characteristics of the investigated Carrara marble. In fact, the lack of intercrystalline porosity and the strong bonds between crystals (Figure 9c,d) hinder degradation in the inner parts of the structure. The surface parts of the column, directly exposed to the humid environment of the basilica, are affected by phenomena of dissolution and exfoliation correlated with the development of new fractures, that allowed for a consequent accumulation of moisture and dirt also recognised by optical microscopy observations. By favouring the degradation of the marble (Figure 9e,f), this condition causes the elastic characteristics of the shallow material to worsen.

Conclusions
In this study, a Carrara marble column was investigated with a multidisciplinary non-destructive methodology to evaluate its state of conservation, both on the surface and on the internal parts.
The 3D visualisation obtained with photogrammetric and geophysical techniques improves the efficiency, accuracy, and completeness of the diagnostic process on the conservation state of the building materials. By combining the results of the CRP and ultrasonic tomography supported by optical microscopy, an improvement was obtained in the information content on the conditions of the building material in a complex situation. The CRP methodology represents an important tool in the interpretation and quantitative evaluation of the shallow degradation. Furthermore, high resolution 3D models computed with the CRP methodology can be performed at different times, providing a complete and timely view of the external parts of the investigated column. Moreover, it can be useful for a proper documentation and preservation of the historical architectural element. The high reflectivity values, generally close to 1, were detected in correspondence with the sectors characterised by high surface roughness and low longitudinal velocity. The latter denotes poor elastic characteristics of the shallow material, clearly showing the precariousness of the condition of the column surface. It is clearly shown that the studied column is characterised by severe forms of surface degradation, such as exfoliation and

Conclusions
In this study, a Carrara marble column was investigated with a multidisciplinary non-destructive methodology to evaluate its state of conservation, both on the surface and on the internal parts.
The 3D visualisation obtained with photogrammetric and geophysical techniques improves the efficiency, accuracy, and completeness of the diagnostic process on the conservation state of the building materials. By combining the results of the CRP and ultrasonic tomography supported by optical microscopy, an improvement was obtained in the information content on the conditions of the building material in a complex situation. The CRP methodology represents an important tool in the interpretation and quantitative evaluation of the shallow degradation. Furthermore, high resolution 3D models computed with the CRP methodology can be performed at different times, providing a complete and timely view of the external parts of the investigated column. Moreover, it can be useful for a proper documentation and preservation of the historical architectural element. The high reflectivity values, generally close to 1, were detected in correspondence with the sectors characterised by high surface roughness and low longitudinal velocity. The latter denotes poor elastic characteristics of the shallow material, clearly showing the precariousness of the condition of the column surface. It is clearly shown that the studied column is characterised by severe forms of surface degradation, such as exfoliation and pulverisation, caused by the effects of solubilisation of calcite and intercrystalline decohesion, which worsen the elastic characteristics of the material. The high precision of the position and spatial distribution of the geometrical surface anomalies detected by CRP represent an efficient dataset for the best design and acquisition of the 3D ultrasonic tomography. Positive surface geometrical anomalies have been detected in the lower part of the column, where from an analysis of the tomographic slices a decrease in the longitudinal wave velocity is highlighted, both in the shallow and the inner part of the marble. The combination of the results of both independent techniques (CRP and ultrasonic tomography) points to an increase in degradation and microfracturing with consequent swelling in this part of the column shaft. Microweathering and microfracturing were also recognized by the optical microscopy analysis.
From the ultrasonic tomography slices, it could be seen that in the middle and upper part of the column shaft, the degradation of the shallow material did not spread inside the column, where the marble is generally characterised by better elastic characteristics (Vp around 3000 m/s) and therefore, less unaltered. The integration of the different datasets proves more efficient if supported by the knowledge of the petrographic characteristics of the investigated material, especially mineral composition, texture, and porosity. These characteristics affect both the longitudinal wave velocity distribution inside the column and the roughness and morphology of the shallow materials, that affect the geometrical anomalies and the reflectivity detected by the CRP analysis.
In this study, the approach used is supported and validated by the relationships between the different geophysical observations and the petrographic characteristics of the investigated stone material. Useful results that improve the diagnostic process can be obtained by combining different non-invasive techniques into an effective workflow for a complete integration of the independent datasets.
Furthermore, the integrated approach used in this study can give an effective contribution to monument conservation, providing useful knowledge to project the best restoration and to monitor its efficiency in time.
Author Contributions: S.F. and G.C. conceived the integrated non-invasive diagnostic methodology; F.C. contributed to the visual inspection and analysis of the materials; S.F. and F.C. planned and carried out the ultrasonic data acquisition; S.F. processed and interpreted the ultrasonic data with the cooperation of F.C. and performed the integrated ultrasonic and petrographic analysis with F.C. and P.L.; G.C. and M.G.B. carried out the CRP survey and processed and interpreted the CRP data; A.S. provided the support related to the historical and architectural knowledge of the investigated element. All the authors analysed and discussed the results, contributed to the manuscript drafting and revision. All authors have read and agreed to the published version of the manuscript.