The thesis is devoted to the application of quaternion and Clifford algebras in color and multispectral image processing, with particular emphasis on edge detection. The author studies the principles of the Quaternion Fourier Transform (QFT), quaternion convolution, and Clifford convolution, and investigates their practical effectiveness through a comprehensive experimental study.

The introductory chapters provide a solid overview of quaternion algebra, Clifford (geometric) algebra, convolution operators, and hypercomplex Fourier transforms. These chapters establish the necessary mathematical background and provide a suitable foundation for the subsequent development of the proposed methods.

One of the main strengths of the thesis is its extensive experimental evaluation. The author systematically investigates a range of quaternion- and Clifford-based edge-detection approaches. Particular attention is devoted to different strategies for encoding the real part of quaternions, as well as to the influence of various color spaces. The proposed methods are evaluated on natural images using quantitative measures. 

The most notable contribution of the thesis is presented in Chapter 7, where the author extends the Clifford-algebra-based convolution framework from conventional RGB images to five-band multispectral imagery. Two original encoding schemes within the algebra Cl(3,0) are introduced and compared in detail.  This part of the thesis represents an original contribution that goes beyond the implementation of existing methods and clearly demonstrates the author's ability to develop, analyze, and experimentally validate novel research ideas.

The submitted Master's thesis deals with the application of quaternion and Clifford algebras to edge detection in color and multispectral images. The author first introduces the mathematical foundations of quaternions, Clifford algebras, hypercomplex convolutions, and Fourier transforms. Subsequently, several edge detection methods based on quaternion and Clifford algebra are implemented and experimentally compared.

The thesis includes testing of the proposed edge detectors on both RGB and YUV color space representations. The methods are evaluated using five color images and subsequently verified on a single multispectral image.

The topic of the thesis can be considered moderately challenging and highly relevant from both scientific and application-oriented perspectives. All objectives defined in the assignment have been fulfilled, although the practical part could have been more extensive.

The author follows a systematic and methodologically sound approach. The work begins with an analysis of the theoretical background, followed by the implementation of the proposed methods and their experimental evaluation. A reference edge detector was selected for comparison. However, for a more comprehensive assessment of the effectiveness of the proposed approach, I miss a comparison with a conventional edge detector applied directly to RGB images.

I consider the most significant contribution of the thesis to be the verification of Clifford convolution on five-band multispectral data, including the use of derived parameters obtained from the original image channels. Nevertheless, I do not agree with the explanation of the spatial shift between spectral bands presented on page 63. In my opinion, the displacement of individual channels is primarily caused by the camera design and optical arrangement rather than by vibrations during image acquisition.

The achieved results are presented in a clear and understandable manner, and the author draws appropriate conclusions from them. Some figures, particularly Figures 7.5 and 7.6, could benefit from inverted color mapping to better highlight the observed details.

The author works with relevant scientific literature, which appropriately supports both the theoretical and experimental parts of the thesis. References are used adequately and demonstrate familiarity with the current state of the art.

The submitted thesis successfully combines applied mathematics with computer image processing. The author has demonstrated the ability to independently study advanced mathematical concepts, implement them in a programming environment, and critically evaluate the obtained results.

My main reservation concerns the reproducibility of the work. The thesis states that the source codes will be made publicly available on GitHub after the defense; however, at the time of writing this review, the repository is not yet available, and therefore the implementation cannot be independently verified.

Overall, I consider the thesis to be a valuable contribution that fulfills the requirements of a Master's thesis and demonstrates the author's analytical and technical skills. Topics for thesis defence:

1. Can the principle of quaternion-based image representation be applied to color spaces other than RGB, such as HSV, and how would such a modification affect the edge detection performance and characteristics?
2. Why was no direct quantitative comparison performed between the proposed methods and commonly used edge detectors, such as the Sobel, Prewitt, or Canny algorithms applied to RGB images?