A Critical Review of Methods and Techniques Used for Monitoring Deformations in Wooden Panel Paintings

The manuscript presented a challenging problem, of interest for conservators and restorers all over the world. Deformation of wood substrate of the artefacts affects the entire object and it is present not only on paintings, but furniture and ceilings or other wood painted surfaces too.

I welcome the idea of such a topic, very useful for understanding the methods to measure deformations and for further approaching the correct artifacts restoration.

Over the years a lot of methods have been developed for measuring the deformation of wooden panels, but this review papers discussed many methods, revealing the main field of their use and positive and negative aspects.

For wood restorers the problem of wood deformation is very common and very difficult to entirely solve it.

The paper is a little bit long and could be in the future a chapter of a book.

But as review article, the information could be more concentrated.

Thank you for your kind observations.

Fig 2- What is the green line? Figure must be comprehensible.

The green line is the outlined representation of the painting surface. In agreement with your comment, we have edited the image and included the information in the caption as follows: “Figure 2. A) Schematic representation (modified from [32]) of the position of the three potentiometric transducers installed on the aluminum housing attached to the auxiliary frame of the “Mona Lisa”, here outlined as the wooden support (b) and the painting surface (a). B) Image providing a clearer view of the instrument.”

Fig 3 – Could be improved. Maybe is too schematically represented and difficult to understand by the reader. If you turn on 180 degree it will be better.

We have rotated the figure 180°, but it is not possible to remove the labels, as they are essential for understanding the equations used to calculate the parameters of interest. However, we have included an additional image to further clarify the tool.

Fig 5- Please indicate the main components on the image and description of the figure.

As suggested, we have added the indications of the main components to the image and modified the caption as follows: “Figure 5. Schematic representation of a general StereoDIC setup, consisting of two digital cameras positioned at a specific stereo angle to capture images of the object from different viewpoints and a processing unit that acquires and correlates the images. The representation also includes the indication of the parameters used to calculate the minimum stereo angle required for camera positioning.”

Fig 6,7,8- Please explain the components.in figures as you write in the text.

As suggested, we have modified both the images and the captions in order to make them more understandable. Here, the modified descriptions:

-        “Figure 6. Schematic representation of the photogrammetric setup (modified from [77]), where the object is photographed from multiple angles by a camera, typically covering 360°, to accurately reconstruct it in three dimensions. ”

-        “Figure 7. Schematic representation of the setup of structured light topography, consisting of a projector that shines a structural pattern onto the object and a camera that captures the resulting pattern from a different perspective.”

-        “Figure 8. Schematic representation of a triangulation laser scanning setup, where the laser beam is directed at a specific angle toward the object, and the camera captures the interaction point between the laser and the object.”

The discussions are presented according to the objectives presented in the manuscript, highlighting also the advantages and limits of using them in terms of costs and processing data.

References are relevant and numerous for the topic.

Thank you.

It would be interesting to study in the future which deformation measurement method is more suitable for painted furniture or other painted wooden objects or elements. what happens when objects are big and you can't dismantle or move them?

Yes, it would be very interesting to explore which measurement techniques could be used to study painted furniture and other painted wooden objects or elements, even when they are big and cannot be dismantled or moved.

The article entitled: "A Critical Review on Methods and Techniques for Monitoring Deformations in Wooden Panel Paintings" is very well written. Literature research provides a good basis for understanding the issue. The methodology is elaborated in sufficient detail and is appropriately supplemented with images. Moreover, the images are of high quality throughout the article.

Thank you for your kind remarks.

I would recommend editing Table 2 and 3 to make it more clear and fit on 1 page.

We have slightly resized them and placed them on entire pages, but unfortunately, it is not possible to reduce them enough to fit on one page. This is because we want to ensure readability while presenting all the information we believe will be useful to the readers.

The results are well explained, but I would rather have a better title for the chapter where they appear.

As recommended, we have updated the chapter title from “Discussion” to “Comparative analysis of deformation monitoring techniques” to better align with the aim of this chapter.

I also miss a discussion chapter where the authors would discuss the differences with the works of other authors.

As you suggested, we have included a comparison of the techniques applied to the same artwork in the discussion section.

“To conclude this analysis of the different techniques used to study deformations in wooden panel paintings, it is important to highlight that multiple techniques are often employed to examine the behavior of the same artwork. Of interest are the monitoring studies carried out by Dupre et al. and Jullien et al. on the “La Sainte Trinité couronnant la Vierge” [40,58,59] and by Froideveux on simulacra [49], where the DK is combined with an optical technique – mark-tracking in the first case and structured light topography in the second. Although the aims of their research differ, the experimental results from both techniques were found to be comparable.

However, multiple techniques are often used to provide different information on the same artwork. This is the case in the study by Pires et al. [105], where the application of photogrammetry and laser scanning enabled the generation of highly detailed orthophotos and 3D models from photographic images, as well as the quantification of mechanical deformations in two artworks. Similarly, in the case of Giorgio Vasari’s “Lapidazione di Santo Stefano” [25–27], the simultaneous use of potentiometric transducers and DKs provided valuable information. Particularly, the former technique was used to study the slippage between the crossbeams and selected points on the panels and quantify wood displacement at the cracks, while the latter captured minor local deformations and distortions in specific areas, both before and after restoration. Additionally, displacement transducers and load cells were incorporated into the same measuring apparatus by Dionisi Vici et al. [36] to assess cupping, swelling/shrinking deformations, and the forces exerted by restraints designed to prevent deformations.

Finally, the case of the Mona Lisa involves both mechanical and optical measurements. The mechanical measurements include the use of displacement transducers and load cells [32–35] to monitor the cupping and bowing of the panel, aiming to estimate the panel's mechanical properties through numerical modeling. In the optical category, laser scanning was employed to document and measure the distorted shape of the painting [101,102], while the Moiré method was used to assess the relief of the painting in various conditions, allowing the calculation of the thickness map and identification of distortions [121]. However, in this case, these three techniques were applied by different research groups, and their results have never been compared. Lastly, the use and comparison of photogrammetry and structured light topography in [106,107] enabled the evaluation and quantification of shape changes over a medium/long period or following restoration interventions.”

English is at a good level. After a minor revision, I recommend accepting the article.

Thank you.

Explain the functioning of StereoDIC setup in detail

As suggested, we have explained better the functioning of the StereoDIC setup.

“StereoDIC, also known as three-dimensional DIC (3D-DIC) was developed in the early 1990s to directly measure surface displacements, deformations, and strains at each point by tracking surface features. To analyze the deformation of an object in all three directions, StereoDIC uses a simple setup, schematically represented in Figure 5, consisting of two stereoscopic cameras positioned at a specific stereo angle to capture images from different viewpoints and a processing unit to analyze the images and compute 3D displacement and strain fields [64]. Some setups may include a video beam projector to enhance contrast and generate a well-defined pattern, improving feature tracking when the natural surface texture is insufficient. It is important to note that the minimum stereo angle at which the cameras should be positioned is determined using the following equation [65]:

where D is the maximum diameter of the lens and WD is the minimum working distance required for focusing.”

Give insights about the Figure 6, how it is incorporated into this work.

Thank you for your comment. We have provided an insight of Figure 6 in the text: “The acquisition phase is crucial as it determines the quality of the frames used to create the model. As shown in Figure 6, the photogrammetric setup involves capturing multiple images of an object from different viewpoints, typically covering 360°. This process is crucial for the accurate three-dimensional reconstruction of the object. It is important to note that a well-planned survey […]”

How does the structured light topography work? state in detail 

As you recommended, we have made changes to the section regarding how structured light topography works.

“As shown in Figure 7, the system consists of a projector that shines structured patterns onto the object to be scanned and a camera that captures the resulting pattern from another perspective. A processing unit analyzes the captured images to reconstruct the 3D surface of the object. Specifically, a controlled light pattern is projected onto the object, conforming to its surface shape: the pattern deforms where there are height variations, resulting in distortions at depressions, undulations, and extrusions. A camera, positioned at a known angle relative to the projector, captures images of the deformed pattern, which contain essential depth information encoded within the pattern distortions.

To extract depth information, specialized algorithms analyze how the projected pattern has deformed. Many codification methods exist [87,88], such as ‘binary coding’ and especially ‘Gray coding’. This divides the object into several 2ⁿ sections, where n is the number of pattern sequences or fringes. The spatial frequency of the fringes affects both the spatial resolution and the measurement accuracy of the acquired 3D image. Indeed, higher frequencies can produce finer details, while lower frequencies can generate images with a lower spatial resolution. Moreover, by adjusting the line frequency, the accuracy of the imaging system can be optimized for the specific object being analyzed. The resolutions of the projector and camera limit the spatial resolution using binary codes.

Correspondence is then established by analyzing the distortion of the captured structured images with known features projected by the projector. Indeed, once the system is calibrated and the correspondence is known, (x,y,z) coordinates can be reconstructed using triangulation. This is achieved by applying specific trigonometric formulas based on the known distance between the camera and projector, and by calculating the displacement of the projected features.

This kind of system is called “full-field” because the CCD captures the entire measurement area in a single exposure, unlike scanning systems where the light moves across the measurement area.”

How the triangulation works in laser scanning: give the reason in detail

Thanks for your comment. We have added additional information regarding how triangulation works in laser scanning.

“Triangulation scanners (Figure 8) determine the position of a point on an object’s surface using a laser light and a camera. In a single-camera setup, the emitter directs the laser beam at a specific angle toward the object, and the camera captures the point where the laser interacts with the object. This setup (emitter, camera, and intersection point) forms a triangle, from which the 3D coordinates of the point can be derived through triangulation. Indeed, by knowing the positions of the emitter and camera, as well as the angles of laser emission and detection, trigonometric formulas can be applied to calculate the depth of the spot on the surface.  The depth information, along with the scanner’s horizontal and vertical coordinates, enables the reconstruction of the 3D position of each point on the object. Moreover, the emission angle changes with predetermined angular steps, and in most cases, the object is scanned along a single line rather than a single point to speed up data acquisition.”

How are the 3D models combined?

You are highlighting a point that is not clear in the paper; we do not wish to discuss a combination of techniques but rather the use of different techniques to study the same artwork. To avoid any misunderstanding, we have changed the title from ‘Combination of different 3D modeling techniques’ to ‘Application of different 3D modeling techniques’.

Explain the significance of using Moiré method.

We have added a brief paragraph on the significance of using Moiré method:

“Although not widely used to study deformation in wooden panel paintings, the Moiré method enables high-resolution, non-contact analysis. By projecting the pattern onto the surface and analyzing the resulting Moiré fringes, it becomes possible to detect small variations, both in-plane and out-of-plane displacements, as well as surface features.”

In discussion, kindly include a figure for better clarity 

We have added a flowchart to assist conservators and scientists in selecting the most suitable technique: “Figure 9. A potential flowchart intended to guide conservators and scientists in identifying the most appropriate technique for analyzing support deformations in WPPs, considering the type of monitoring, the available technical skills and budget, and the possibility of direct contact with the artwork.”

Provide detail insights about the table 4 

We have (1) included a clearer reference in the text, (2) provided more detailed information in the caption of Table 4, and adjusted the placement of the table accordingly.

1)     “After categorizing the techniques into those that provide localized deformations and those that offer full-field information, this article aims to compare them and provide guidelines for selecting the most suitable tool for a given application. As shown in Table 4, the discussion will compare the techniques based on monitoring type, the ability to provide surface information, cost, data complexity, data processing difficulty, real-time capability, and the possibility of generating 3D models. ”

2)     “Table 4. Comparative overview of the main techniques used to study the support deformations of WPPs, highlighting their differences in monitoring type, cost, data processing complexity, real-time data capability, and the ability to generate 3D models. Specifically, in the ‘Costs’ and ‘Processing Data’ columns, the symbols represent the degree (low, medium, or high) of each characteristic, while in the other columns, a marker indicates the presence of a given ability.”