Cross-Correlation and Fractal Analysis in the Images Diatoms Symmetry

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The manuscript entitled “Cross-correlation and Fractal Analysis in the Images Diatoms Symmetry” by R. Pestana-Nobles proposed a set of methods to analyze diatom images based on fractal dimension and cross-correlation. These methods present the baseline of the technique for diatom automatic identification. The manuscript is well structured with plain language.

In spite of my generally positive opinions, I do have some concerns on the manuscript.

1) Deepened discussions are somehow missing in the entire text. In the ‘Results & Discussion’ session, the authors present more outcomes and, to a lesser extent, explanations of the experiments than discussions on the pros and cons and their application or perspectives on diatom identification. For instance, in ‘3.3 CC between diatoms’, the authors only have 2 paragraphs, one for method description and one for figure caption! Not a single word on discussion. It is far from enough for a research paper.

This paragraph was added:

The similarity between diatoms is shown in a heat map in figure 8. The heat map was generated q between all the previously selected diatoms where red represents a poor similarity and blue color a high similarity. The central line value is zero indicating total similarity; higher zero values q were found for any pair of diatoms; this shows that the q parameter suggests a good differentiator between diatoms.

Diatoms 6 to 9 and 15 to 17 show high similarity (see figure 8), but the Theta values, although close to zero, could be due to imperfections in the images and not show the fundamental differences between them, so it is essential to combine the Teta parameter with other ways of measuring the differences between it, as is the case of Nf. In any case, if we review the use of all the parameters for the classification in the principal components analysis, we see a total separation between the diatoms 6 to 9 and 15 to 17 (see Figure 6 a).

2) The authors chose 50 diatom images of standard focus for analysis (Fig. 1). However, the valves of most diatom species are not plain, which means one focus could only capture a part of traits of diatom valves. This will definitely bias the experiments in the manuscript. I would suggest the authors to stack different focuses into one merged image to avoid the bias. The different focuses of diatom images are also available from ADIAC.

The procedure tries to create a simple tool for the analysis of diatoms, what the reviewer indicates may be true, but among very similar diatoms, the system can fail but it must recognize that concept is powerful since it works adequately among classes of diatoms. The reviewer's recommendation will be considered for future publication.

3) Fractal dimension analysis (Nf) is introduced in this study. But I do not see much sentences on Nf, neither explanations (why did you choose it? what does it mean in the analysis? What is the significance of Nf in Fig. 4? etc.) nor further discussions. Please note that this method is addressed in the title, so you need to concentrate more on it as you did for CC.

In short, I think the manuscript fits the scope of the journal and suggest a moderate revision before acceptance.

Line 31-38: Too much on microalgae. Focus on diatoms please.

The content about microalgae was removed.

This paragraph was added: The combination of the Nf parameter with the self-similarity describes the space of morphological differences of diatoms. Nf in geometry whose basic structure, fragmented or irregular, is repeated at different scales. Those diatoms whose dimension is fractional are easily differentiated from those that do not with this type of parameter. The fact that the diatom has self-similarity means that it can be easily measured in the case of fractional similarity; the fractal is the appropriate parameter.

Line 45: ‘…it’s by diatoms’ should be ‘the 40% oxygen is produced in aquatic environments by diatoms’

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Line 47: ‘…have been increasing. [4, 13].’ should be ‘…have been increasing [4, 13].’

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Line 117: delete ‘3. Results’

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Line 123: I guess ‘de’ here should be ‘the’?

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Line 159-167: Is this paragraph a result or a discussion? It is more like a figure caption. Why do you put a figure caption in the main text? It is the same for the paragraph from Line 239 to 241.

This paragraph was added:

Two diatom images, I3 and I34, were used how examples using all the preprocessing steps to calculate the q projection (see figure 3a and 3b, respectively). Figure 3 shows the original images after edge detection and centering (B), and each symmetry operation applied (PSv, R180, PSo) for the two diatoms images. Also, the CC for each symmetry operation is shown in figure 3(a,b) (see blue circles in the bottom left), where the red line represents the CCauto for each image (I3 and I34). Additionally, three lineal correlation plots for the CCauto vs. CC calculated for each symmetry operation are shown in figure 3(a,b) (bottom right). Lastly, the Nf and  values are reported on the top right of figure 3(a,b).

 The similarity between diatoms is shown in a heat map in figure 8. The heat map was generated q between all the previously selected diatoms where red represents a poor similarity and blue color a high similarity. The central line value is zero indicating total similarity; higher zero values q were found for any pair of diatoms; this shows that the q parameter suggests a good differentiator between diatoms

Line 187: Have the authors ever indicated what ‘PC’ is before the abbreviations were used?

This paragraph was modified:

For this, a reduction of the dimensionality of the variables was generated through a Principal Component Analysis (PCA), as shown in figure 4d. In this case, 2 components have been extracted since 2 components had eigenvalues greater than or equal to 1.0. Together they explain 85.1% of the variability in the original data. The first Principal Component (PC1) has a 55% variability with an eigenvalue of 2,2, and the second Principal Component (PC2) has a 30% variability with an eigenvalue of 1,2. Therefore, these are the two principal components, with the most significant being able to improve the separation between diatom species as evidenced in figure 4d

Line 203: How did the authors ‘resize’ a diatom image to a square figure? An explanation is necessary here.

This paragraph was added:

Where the image is resized to a square image (254x254) in order to match the dimension of the vector found with and without the symmetry operation (CC) to CCauto,

Line 204: ‘…Shift’ is ‘…shift’ ?

done

Line 21: ‘… generated ranges θ lower than the θ…’ should be ‘…generated θ ranges lower than those for…’.

This paragraph was added:

In this case, the symmetry operations used above (Psv, PSo, and R180) generated θ ranges lower than those for range for the preprocessing steps used in figure 4

Figure 4. It is too crowded when you put all the numbers in a tiny area, making the figure unreadable and less informative. I would propose the authors use dots in different colors, instead of numbers, to avoid such situation. Besides, most dots are within the circular quadrants (except 1 point in θPSo), it is therefore more reasonable to only draw this sector rather than the whole semicircle.

done

Figure 8. Why the upper-left and the lower-right parts are of different color? One would suppose that these two parts mirror each other. For instance, the similarity of diatom #14 and #35 is same with that of diatom #35 and #14. But this is not the case in Fig. 8. Why? Could the authors present a convincing explanation or discussion?

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The figure 8, the image is not two parts that mirror each other because the theta value is calculated based on the CCauto of the reference image; when changing the role of the images, the CCauto is different, and therefore the value of the projection is a bit different. This is seen more markedly between very different diatoms than between similar ones, where the figure's mirror effect can be seen.

Comments and Suggestions

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This manuscript presents an innovative approach to the identification of diatoms.

This is valuable information in the context of the difficulties associated with the identification of this taxon.

The methods seem to be sound. I found the manuscript quite well-written and interesting however some points need to be amended.

The methods seem to be sound. I found the manuscript quite well-written and interesting however some points need to be amended.

The manuscript requires minor editorial corrections, as in many places there are no spaces where they should be, or they are double. In Graph 4, the axes for PC1 and PC2 should be unified. This graph requires the font for the points to be enlarged to make it more readable.

Done

I am not sure about the type of article the authors have chosen. The content is more like a 'Protocol' or 'technical note' to me.

 Article

I realize that the method proposed by the authors is new, but I miss the reference to others in the discussion. The combination of results and discussion is valid, but there is little discussion. Perhaps by choosing a different type of article this could be avoided.

The discussion was expanded

In the summary, I miss even a piece of short information on how these methods, compared to others, improve the techniques of diatom identification.

This paragraph was added:

This methodology to classify diatoms differs from others in that only simple parameters are determined, and complex algorithms are unnecessary, as in deep learning. Since these parameters are calculated based on the natural symmetry of the entities and the complexity of their structure, we can call this the diatom fingerprint.