HRUBÝ, J. 3D rekonstrukce scény pomocí Cliffordových algeber [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2018.
The thesis presents Conformal Geometric Algebra as a tool for solving selected problems in robotics, namely binocular vision and inverse kinematics. Theoretical part introduces CGA as a 'tool of trade' to be used in the practical part. Conformal Geometric algebra is well set in the underlying framework of Clifford Algebra. Practical part of the thesis consists of two subsections addressing selected problems in Robotics. In the Inverse Kinematics section, the problem and its solution is outlined within the conventional framework of R^{3} euclidean space, then it is represented in the CGA scope. Comparing these two approaches, the student has shown that, the CGA approach does avoid difficulties which may appear in the conventional approach and, the Inverse kinematics problem has an intuitive geometric meaning. In the last section the student applies the framework of CGA to address one of the major issues in computer vision -- binocular vision. Pinhole camera model was formulated in CGA and applied to the problem of line pose estimation in R^{3} in binocular vision. Calculations have been carried out to show that solving the problem of binocular vision in CGA is viable and effective, this section may be viewed as an opening proposal for further research. The student has shown he is familiar with CGA and presented the algebra in a way which is sufficient for addressing problems in the second part, where the two problems of binocular vision and inverse kinematics are outlined and subsequently solved.
| Kritérium | Známka | Body | Slovní hodnocení |
|---|---|---|---|
| Splnění požadavků a cílů zadání | A | ||
| Postup a rozsah řešení, adekvátnost použitých metod | A | ||
| Vlastní přínos a originalita | A | ||
| Schopnost interpretovat dosažené výsledky a vyvozovat z nich závěry | A | ||
| Využitelnost výsledků v praxi nebo teorii | A | ||
| Logické uspořádání práce a formální náležitosti | A | ||
| Grafická, stylistická úprava a pravopis | A | ||
| Práce s literaturou včetně citací | A | ||
| Samostatnost studenta při zpracování tématu | A |
The student defines a general geometric algebra at first and then he describes a particular one in more detail. At the end two concrete applications are given. I have not found any mistake but I have the following comments. The general definition is very technical, based on formal language with a specific formal grammar. This is a possible and elementary way but one has to be very careful, eg. the associative property of the product is missing on pg 22, the reduction of the concatenation in def 1.20 is not mentioned. The part about conformal geometric algebra is also very technical. However some of the computations are superfluous the other, more important, are cited only. For example the computation of scalar products on pg 34 - 37 can be done all at once. On the other hand, the proof of outer representations of spheres and planes is important and it would take a few lines but this is missing. Concerning the last part of the thesis I would like to see an application on a concrete example. This is definitely the weakest point of the this text and that is basically why I recommend the evaluation by B.
| Kritérium | Známka | Body | Slovní hodnocení |
|---|---|---|---|
| Splnění požadavků a cílů zadání | B | ||
| Postup a rozsah řešení, adekvátnost použitých metod | B | ||
| Vlastní přínos a originalita | B | ||
| Schopnost interpretovat dosaž. výsledky a vyvozovat z nich závěry | A | ||
| Využitelnost výsledků v praxi nebo teorii | B | ||
| Logické uspořádání práce a formální náležitosti | A | ||
| Grafická, stylistická úprava a pravopis | A | ||
| Práce s literaturou včetně citací | A |
eVSKP id 105694