Use of Image Correlation to Measure Macroscopic Strains by Hygric Swelling in Sandstone Rocks

Round 1

Reviewer 1 Report

The work addressed a based on 2D-DIC, method to measure the deformation of a sandstone rock which is submerged in water due to hygric swelling. The issue is interesting although the method used is very simple in terms of DIC. Furthermore, there are flaws and methodological aspects which must be clarified and/or modified.

1. Please, indicate the main features of the CMOS camera (at least sensor size, resolution and frames per second). The same for the optical features of the lens.
2. Authors indicate “which means that the image is not affected by field curvature or distortion” It is not fully true. It is really affected but in a low degree.
3. How was the DIC method calibrated?
4. Why only the green channel is analyzed? Please note that the DIC using color sensors in some cases can be really a controversial issue. it is possible to use it, and sometimes with quite high quality based on the information from the three channels. Many studies address it, but dispensing with two channels may yield incomplete results, and this deserves at least a justification or precedents that have been successful in similar cases.
5. Authors indicate “the sample was dried in an oven at 50 °C for 1 h” How was these parameters established? Is there any standard which established it?
6. Authors indicate “This procedure was repeated for the different ROI sizes, ranging from 5×5 px to 200×200 px” What is the position of the different ROIs? Is the center of the regions the same regardless of size?
7. The lighting conditions of the experiment and the camera configuration (focal length, obturation, etc.) is not indicated in the paper. Please indicate them.
8. In Fig. 11, “sample 2” is missing.
9. It would be convenient to include the deformation map of at least one specimen.
10. Since the study raised is very simple (2D DIC, only one camera, measures on one surface, etc.) it is convenient to indicate futures works in the conclusions section.

Author Response

The work addressed a based on 2D-DIC, method to measure the deformation of a sandstone rock which is submerged in water due to hygric swelling. The issue is interesting although the method used is very simple in terms of DIC. Furthermore, there are flaws and methodological aspects which must be clarified and/or modified.

We acknowledge the reviewer the encouraging words. We also acknowledge the suggestions. We have done our best to address all of them.

  1-  Please, indicate the main features of the CMOS camera (at least sensor size, resolution and frames per second). The same for the optical features of the lens.

In lines 115 to 127 we have specified some more data from the camera and the lens. The frame rate is mentioned in lines 141 and 142. Of course, there are more specifications that can be added but we consider that they do not add relevant information to the reader. In any case, the exact model of the camera and the lens is specified, so any reader can replicate the experiment.

2-  Authors indicate “which means that the image is not affected by field curvature or distortion” It is not fully true. It is really affected but in a low degree.

We agree with the reviewer and we have rewritten the sentence accordingly (lines 123-125). The image telecentric lens is very few affected by field curvature or distortion, but according to previous pre-calibrations on optical benches and USAF test, this distortion in negligible compared with other experimental errors.

3-  How was the DIC method calibrated?

Since we were using a pre-tested telecentric lens and distortion was expected to be negligible, we did not perform any specific geometrical calibration of the image.

The DIC method used in this paper has been already used and calibrated in previous papers. In reference 12 you can find a complete description of the method applied on 5 sequences of the DIC challenge database, together with the full Matlab program.

Regarding the experimental setup, since the movement is unknown, we could not pre-test the sample, so we decided to make a theoretical calibration of the calculation method (Section 2.2) and an experimental calibration with a dry sample (lines 228-270). With this method, two different errors appear. The most evident one is a general drift, that may be due to thermal dilations of the sensor. The second one consists of some oscillations that may come from Gaussian noise in the image. An explanation about these instabilities has been added in lines 236-242.

Unfortunately, because of the thermal drift, our proposal is not reliable for measuring absolute deformations but, to the best of our knowledge, it may be useful to address strains in the rock, since displacement subtraction cancels that drift. We are convinced that the method can be applied with a normal objective (with geometrical correction of distortion) and using some free image processing software as ImageJ for analysing the images. This purpose has been added to the Conclusions.

4-  Why only the green channel is analyzed? Please note that the DIC using color sensors in some cases can be really a controversial issue. it is possible to use it, and sometimes with quite high quality based on the information from the three channels. Many studies address it, but dispensing with two channels may yield incomplete results, and this deserves at least a justification or precedents that have been successful in similar cases.

We agree with the reviewer about the convenience of using colour channels. Usually, when dealing with real objects, using several colour channels can provide additional information about the phenomenon. However, this information is often strongly correlated and a decomposition in independent components is advisable prior to further analysis.

In our particular case,  the samples of the rock are greyish, as can be seen in the text. We have replaced Figure 2 in grey scale by a new Figure 1 so that the colour of the sample can be appreciated. Therefore, we checked that any channel produced similar results, although results from the green channel were cleaner and thus, we selected this channel for the analysis and discarded the other. This justification has been added to the text in lines 117-120.

Conversion from RGB to Gray channel was also tested and no relevant differences were found. Therefore, we decided to take the simplest option and note that in the text, meaning that this is a particular case but should not the general procedure.

  5-  Authors indicate “the sample was dried in an oven at 50 °C for 1 h” How was these parameters established? Is there any standard which established it?

According to tests performed by D. Benavente (who is acknowledged at the end of the manuscript) higher temperature would induce physicochemical change of the rock and eventually its disaggregation.

  6-  Authors indicate “This procedure was repeated for the different ROI sizes, ranging from 5×5 px to 200×200 px” What is the position of the different ROIs? Is the center of the regions the same regardless of size?

The test performed in order to decide the optimal ROI size is explained in the text, although the position of figures 4 and 5 was swapped and induced to error. Also, the caption of Figure 4 (formerly Figure 5) has been completed so that the information is clearer.

Briefly, for each ROI size we checked the autocorrelation in 50 different random positions.  The grain statistics of each ROI was parametrized through the width of the correlation peak. So, we obtained the main and standard deviation of this parameter for each ROI size and the result is plotted in Figure 4. With this test, we are selecting and comparing ROIs with similar characteristics.

This analysis is not performed in typical DIC applications, since pseudospeckle patterns are built for being statistically uniform. Since we are dealing with natural textures, we think it is important that the analyzed regions contain similar information, thus avoiding confusing results.

  7- The lighting conditions of the experiment and the camera configuration (focal length, obturation, etc.) is not indicated in the paper. Please indicate them.

Up to our knowledge, the exact illumination conditions in the box are not relevant for the result, since the final appearance of the image was obtained with the combination of light intensity and exposition time that produced the widest histogram, without overexposed or subexposed areas. This procedure has been added to the text in lines 133-136.

Both the camera model and the objective lens are given in the text, together with the parameters of the experiment (working distance and magnification). Regarding other parameters of the lens, we have specified in the text (lines 135-138) that, since the illumination was controlled by the sensor, the diaphragm was set to the maximum in order to minimize the depth of field.

  8-  In Fig. 11, “sample 2” is missing.

The tittle was cropped. The figure has been replaced. Notice that Figure 11 and 12 have been replaced in order to improve the composition.

  9-  It would be convenient to include the deformation map of at least one specimen.

We have added a new part in the results section in which those maps are shown and explained (lines 317 to 337). They were not included in the previous manuscript because we wanted to make the procedure as simple as possible, but we agree the reviewer that this part add important information regarding the results obtained. The inclusion of the map also leads to some new conclusions that have been added in lines 355-358.

  10-  Since the study raised is very simple (2D DIC, only one camera, measures on one surface, etc.) it is convenient to indicate futures works in the conclusions section.

We agree with the reviewer in adding this information. Therefore, we have added some future work lines to the text (364 to 372). In brief, these lines consist on improving the camera performance and extend the method to the analysis of natural textured surfaces.

Author Response File: Author Response.docx

Reviewer 2 Report

It is an interesting work that could be published after some minor revision.

My main comments concerns on  the significant fluctuations observed in the measurements (see Figs 8-12). The authors have to discuss it and to explain if it is related with the sample or is a part of the experimental procedure.  For the first case they have to describe the material properties that control this instability, while for the case of experimental reason, they must suggest how could be reduces.

Author Response

It is an interesting work that could be published after some minor revision.

My main comments concerns on the significant fluctuations observed in the measurements (see Figs 8-12). The authors have to discuss it and to explain if it is related with the sample or is a part of the experimental procedure.  For the first case they have to describe the material properties that control this instability, while for the case of experimental reason, they must suggest how could be reduced.

Fluctuations are due to both the mathematical method and image noise. In figure 6 the fluctuation for a real scene with synthetic displacement was of 0,045 px. In Figure 8, oscillations are of the order of 0.25 microns or, equivalently, 0,1 px, which is “only” twice the error of the mathematical method. According to our experience in image processing methods, these errors may be due to Gaussian noise in the image and fitting errors in the subpixel calculation algorithms.

Although these fluctuations can be cancelled out by applying smoothing filters in the signal, we preferred to show the data as obtained, since they do not distort the main trend of the result.

These explanations have been added in lines 236-242.

Notice also that, because of the comments of Reviewer #1, the manuscript has suffered many changes. We hope that these changes help to improve the manuscript and you find it suitable for its publication. 

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The changes have been attended. In the current state, the article has improved in quality, especially in terms of the explanation and justification of the methods applied.