The topic of the thesis is the description, implementation, and comparison of two filters for edge-preserving smoothing as a preprocessing step for image segmentation.

The student started with very limited prior knowledge of image processing and initial difficulties with mathematical writing. However, she improved greatly during the short eight-month period she had to write the thesis. A significant amount of time was spent working on mathematical notions, keeping the use of symbols clear, maintaining the dimensions of function domains, ensuring clear descriptions of basic image processing concepts, and working on the correct use of illustrative images. Even after this hard work, there are several areas that could have been executed better, and various mistakes remain.

- The language is sometimes too informal for academic writing. It also contains typographical errors, such as missing spaces before parentheses, a period left on the next line on page 33, an incorrect dash after a bullet point on page 38, etc. Words like "seemed" or "appeared" are sometimes used instead of clear, definitive statements.
- The description of equation (2.4) on page 17 is erroneous; there should not be a cubed power (3) in w.
- Page 21: Impulse noise is not necessarily a type of multiplicative noise; it is rather a separate type.
- Pages 33, 34: Local thresholding and multi-level thresholding are mixed together.
- The table of contents is inconsistent; entries like "Otsu Segmentation of filtered images at Gaussian Noise Level 0.1" and others appear twice with different page numbers or figures.

Not completely fulfilling the last goal is not the fault of the student. The artifacts presented in the literature were obvious, but we were unable to reproduce them ourselves, and even the authors of those publications did not provide assistance in reproducing them.

The student did not upload her Matlab codes along with the thesis PDF, which prevents testing the algorithm on other data or evaluating the quality of her coding.

I recommend the thesis for defence.

The thesis deals with edge-preserving image smoothing, subsequently used for image segmentation.

The main part of the thesis consists of three chapters, i.e., chapters 2–4.

Chapter 2 thoroughly summarizes theoretical knowledge associated with the image processing techniques used further, including many illustrative figures. Chapters 3 and 4 then comprise the practical part of the thesis.

The two edge-preserving smoothing techniques investigated by the author are Modified Rotating Anisotropic Gaussian filter (Modified RAG or MRAG) and Bilateral filter. The work presented application of the filters on sample images which were intentionally corrupted with Gaussian noise and, consequently, their ability to preserve the edges in the image while smoothing it was discussed both qualitatively/visually and quantitatively. In terms of quantitative analysis, I highly appreciate the use of PSNR and SSI metrics and the amount of work that has been done. Overall, the author proved both qualitatively and quantitatively that MRAG generally outperforms bilateral filter as a tool for edge-preserving smoothing. Let us mention that the subsequent segmentation and gradient-based analysis also supported this conclusion. Overall, MRAG seems very promising as a subject of further use and investigations.

While the thesis is (for the most part) written well in terms of formal linguistics and the sections are well organised, the work also contains mistakes, inaccuracies and inconsistencies, especially regarding the terminology of some of the image processing techniques. Let us list some of them:
- p. 13, Section 1.2: “linear filters, also known as isotropic filters”. These two terms are not interchangeable!
- There are paragraphs throughout the work where some facts are redundantly reiterated again and again, while not giving any additional information value.
- All the equations and formulas are labeled with numbers, but most of them are not referenced to in the text.
- It is a good custom to emphasise newly defined terms by using italics.
- p. 16: The last paragraph should have appeared after the definition of RGB image, not beforehand.
- p. 17, under formula (2.4): w should equal 2^beta; not (2^beta)^3.
- p. 20: You state “…w is the maximum pixel intensity”. It should be “w-1”.
- p. 22: Formula (2.20) is weird.
- p. 22, beginning of Section 2.3: “Image filtering, also known as image smoothing”. These two terms are not interchangeable!
- p. 23, beginning of Subsection 2.3.1: “A kernel is a small matrix that has different sizes”. Kernels don’t even have to be square, they can have different shapes.
- p. 24: Figure 2.8 is too small.
- p. 26: “A 3x3, 5x5, or 7x7 kernel…”. Kernel of any size can be used in median filter.
- p. 35: Function f in equation (2.45) should have two variables, therefore, f(x) and f(y) in the formula do not make any sense (it should be f(x,y) instead).
- p. 37: In definition of PSNR you state “PSNR is calculated as the mean squared error (MSE)

between the original and degraded images”, but the formula (2.54) given below does not correspond to the sentence (on the other hand, the definition given by the formula is correct).
- In definition of SSIM you say “…two means, standard deviations and one covariance value are computed from the images.” but there are 3 standard deviations and 2 covariance values in the formula.
- pp. 42,43: In Figures 3.3–3.5 there should be sigma_x and sigma_y instead of sigma_r and sigma_s.

Also, I consider it a big drawback of the work that the corresponding MATLAB code has not been attached. Only some parts were shown in the Subsection 3.2.1, but these are insufficient (for example, Step 3 from MRAG algorithm would not work, because angle “theta” is not defined and vector called “angles” is not used further. Moroever, “angles” are given in degrees and not in radians, so MATLAB would not interpret them correctly).

I admire the long list of used references. I found out that two of the references (numbers 7 and 8) are not referenced to in the text, but I believe this was just an overlook and that the text discussed also these two sources. Also, the reference number 11 is not very informative.

Overall, while containing shortcomings, the work also presented many interesting, promising and adequate results. I consider the goals of the thesis fulfilled and recommend it for the defence with grade “C / good”. Topics for thesis defence:

1. Explain the difference between linear and isotropic filters. Give an example of a filter that is 1) linear and isotropic and then a filter that is 2) linear and anisotropic
2. Explain the difference between “image filtering” and “image smoothing” and describe their relationship.