Bayesian Inference for Post-Processing of Remote-Sensing Image Classification

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This article focusses on improving pixel-based classification results with Bayesian smoothing. The manuscript needs some major revision.

The main problem of the article is that there is no reference, and therefore, it is not possible to evaluate if smoothing improves the results (case: no smoothing) or not. In principle, you have a good case by having three different methods and possibility to compare them. For example, you could create manually a reference area that allow you to use standard measures for quality inspections. In addition to measures, you can illustrate some details with a figure/figures that reveals differences of the methods. Without this kind of scientific proof you cannot easily make conclusions, such as  “Bayesian smoothing provides an objective way to post-process the results of machine learning classification” (in Discussion section).

In the Results section you should not introduce new theories (here Gaussian smoothing and bilateral filter) but the introduction should happen in the Methods section. Reserve the Results section for results only.

In following I highlight some minor comments.

In line 124, you talk about a data cube. However, smoothing is applied to classification results that is just a single layer instead of a data cube.

Line 133. I’m not sure what do you mean with “linear stretches”.

When you use quantile and quartile, notice that quartile has only thresholds 25%, 50% and 75%. In your case it’s better to use quantile all the time. Since there are many methods how to compute quantiles, you could mention which one you use.

In Table 2, the value for Clear Cut Burned Area should be 9 instead of 10 (see table 1).

Mention that the values in table 3 are percentages. Notice that “no smoothing” and “bilat” don’t sum up into 100% (but this can be a rounding problem).

Comments on the Quality of English Language

Some terms could be improved (see my general comments).

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Summary

The authors present a method for post-processing smoothing of land cover classification results. Post processing smoothing is an important step for reducing misclassifications and the salt-and-pepper effect common when using pixel classification techniques. The proposed method uses Bayesian smoothing by estimating the class likelihoods from the classification of the surrounding pixels. The class likelihood is then used to update the classifier output (the priors) to produce the smoothed classification (the posteriors). This technique allows information from the spatial dimension (which is ignored in pixel classification methods) to be incorporated into models. The method improves post-processing re-classification of pixels in borders between areas of differing land covers. Many existing methods result in "blurred" borders. The proposed method aims to produce sharp borders consistent with the actual changes in land cover. The authors provide an implementation of their method in an R package (called sits), thus making it readily available to researchers. Overall, I think the paper makes a useful contribution but it needs some revisions to improve the understandability and to better highlight the novelty of the work.

 

General Comments

The paper is light on citations in places and makes a few claims that are not shown in the results or backed up by citations. These include:

• The need for image post-processing in general (lines 19-24)
• The claim that other post-processing methods don't work well at class boundaries (lines 219-224)
• The claim that most post-classification procedures use ad-hoc parameters which are not directly linked to the properties of the data (lines 214-215)

 

In lines 46/47, the authors state "Usually, it [the ground truth] is composed of non-contiguous locations; therefore, no spatial neighbourhood context is available to train f [the classification function]." While this can be the case, it isn't obvious that it is "usually" the case, so the statement needs clarifying and/or references. As a contrary example, if labels were acquired from field studies or farmer questionnaires, we would expect entire blocks (fields etc) would be labelled, so contiguous information would be available in some locations. Presumably, this statement (and therefore the work) makes some assumptions about how the ground truth labels have been acquired, so I suggest stating these assumptions to back up this statement.

 

If space permits, a brief discussion of other image classification methods (such as using OBIA to split the image into land parcels and semantic segmentation methods) could be included. This could then discuss the advantages of pixel classification methods and/or when these methods are needed, and thus reinforce the requirement/usefulness of post-processing methods.

 

Additionally, the introduction lacks a discussion of existing post-processing methods (although there is a limited discussion of some of these in the discussion). In particular are there any other methods that use Bayesian methods? (From the discussion in lines 246-248 it would appear that there are. If there aren't, maybe state this explicitly). It should also include a brief overview of Bayesian inference/smoothing.

 

The discussion assumes the boundaries between land cover classes are sharp (or crisp), so post-processing that aims to keep these boundaries sharp is suitable. But some boundaries may be more blurred (e.g. a forest that gradually thins out into shrubland). It would be useful to add a discussion about how well the Bayesian updating process does in these cases. Does it maintain these more blurred transitions or does it tend to enforce sharp transitions?

 

Specific Comments

Section 2.3: I found this section hard to follow, so I recommend editing and expanding it to provide a more detailed explanation of your Bayesian smoothing method. Keep in mind that some readers may not be familiar with Bayesian inference/updating.

• State and explain the general formula for Bayesian updating near the start of the section
• Explicitly describe what you are using as the priors, likelihoods and posteriors
• Use either log or ln consistently (unless you really mean you use a base other than e when you use log)
• Make sure all symbols in the equations are defined/described and avoid using the same symbol in two equations unless it refers to the same values in each equation.
• Equations (2) and (3) both give logit transformations to give x_i,k but one finds the log-odds of p_i,k and the other π_i,k. What is π_i,k? Are the two x_i,k in these equations referring to the same thing (i.e. are the i pixels the same pixels)? If not, it would be better to label these differently and clarify what they refer to.
• Equation (4) tells us that (x_i,k |μ_i,k )=log(p_i,k/(1−p_i,k )), but in equation (2) we are told that this is x_i,k. Please clarify what is meant here.
• Line 57: should this be "log likelihood" rather than "likelihood"?

 

Section 2.4: Are the correct limits used for the integral equation 6? Should this be the integral over α to 1 quantiles (this would make more sense for α in the range 0-1)?

 

The definition of the priors appears to change between sections 2.3 and 2.4. Section 2.3 states the priors are the classification outcome of the pixels and the classifications of the surrounding pixels are used to estimate the class likelihoods. Section 2.4 states that the neighbouring pixels are used to estimate the priors. This seems contradictory. Again, please check you are using terminology consistently.

 

Section 3: For completeness, please state which classifier you used to train the data and how this classifier compares to state of the art (SOTA) classifiers. While the proposed method can clearly be applied to any classifier producing probabilistic outputs, it's relevant/useful to know which one is used. If the classifier used is not particularly SOTA, consider including a justification for using that classifier. This will help readers place your result in context with other results. For example,  it's easier to get a big post-processing improvement to a weak classifier than a well-performing one, but we may still be better off using another SOTA classifier with no post processing - or another post-processing technique.

 

Section 4: The statement in lines 246-248 suggests the proposed Bayesian smoothing method is not new. It references works that have already used this technique - one of which dates back to 2018. To clarify the novelty of the current work, the paper therefore needs to better differentiate between the past uses of Bayesian smoothing and what the authors are proposing - or otherwise justify the need for the current paper.

 

Figures:

• Consider combining Figs 1 and 2 into a single (4-part) figure. Similarly for figures 4 and 5. This would make it easier for readers to follow.
• Similarly, combining figs 3 and 6 would allow readers to directly compare the raw and smoothed results.
• Consider including a figure of a boundary area with the different types of smoothing applied to show the differences between blurred/smoothed boundaries generated by the different post-processing methods.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Please see the attachment.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

N/A

Author Response

 "Please see the attachment."

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

In the introduction (the last paragraph), do not yet reveal the conclusions of your research.

 

In lines 352-353, you wrote: Entropy is a measure of uncertainty used by Claude Shannon in his classic work "A Mathematical Theory of Communication". Add reference.

 

Section 3 includes a lot of texts that, in my opinion, belong to Section 2. Consider moving the descriptions of materials and methods to Section 2 and leave only results in Section 3.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have done an excellent job of revising the manuscript based on feedback from the first review. Substantial changes have been made and the manuscript has been greatly improved. It is now much easier to understand and the novelty and purpose of the paper are also clearer. The paper is now of an acceptable quality for publication and I suggest only a couple of very minor changes:

- Page 2; lines 68-69 - 24 time steps, 10 bands and 4 spectral indices means each pixel would have 24 x 14 = 336 dimensional feature vector, not 2400.

- Page 6; lines 227-228 - please add the location (country and province/state if relevant) of the 20LMR tile.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

All issues have been modified, and the current version can be accepted.

Comments on the Quality of English Language

N/A

Author Response

Please see the attachment

Author Response File: Author Response.pdf