Approximation and Rough Classification of Letter-Like Polygon Shapes
|Title:||Approximation and Rough Classification of Letter-Like Polygon Shapes|
|Book:||Rough Sets and Intelligent Systems - Professor Zdzislaw Pawlak in Memoriam - Volume 1|
|Editor:||Andrzej Skowron, Zbigniew Suraj|
|Organization:||Blekinge Institute of Technology|
|Department:||School of Engineering - Dept. of Mathematics & Natural Sciences (Sektionen för ingenjörsvetenskap - Avd.för matematik och naturvetenskap)
School of Engineering S-371 79 Karlskrona
+46 455 38 50 00
|Abstract:||It is a privilege for the author to be involved in composing a book chapter in the anthology devoted to the life and scientific occupation of Professor Zdzisław Pawlak. The author made a personal acquaintance with the outstanding scientist Professor Pawlak and still remembers him as a warm and gentle human being. Professor Pawlak’s theory of rough sets was taught to students during the courses in Computational Intelligence established at Blekinge Institute of Technology in Karlskrona, Sweden. In some Master of Science theses, the principles of rough set theory were
discussed in the aspects of technical applications. In this context, we can feel that the theory is still alive and very useful.
In this work, we recall again the basics of rough sets to apply them to the classification of discrete two dimensional point sets, which form the shapes resembling some letters. These possess very irregular patterns and cannot be approximated by standard curves without committing large errors. Since the approximation of letter-like point sets is required by the latter classification of their shapes then we, due
to own model, wish to find a continuous curve which fits best for each distribution of points. To accomplish the thorough approximation of finite point sets, we test parametric s-truncated functions piecewise, which warrants a high accuracy of approximating.
By operating on the functions, replacing samples of points obtained during experiments carried out, we are able to adopt the rough set technique to verify decisions about the primary recognitions of the curves’ appearance as letter shapes. Even if the curves are stretched and shaped differently in the plane, we will
divide them in classes gathering similar objects. Our investigations have not a character of pure art — on the contrary— their results are utilized in the classifications
of internet packet streams or the analysis of wave signals typical of, e.g., medical examinations.
|Keywords:||S-truncated parametric function, Approximation of letter-like point sets, Rough classification, Indiscernibility relation, Lower approximation, Upper approximation|
|Note:||Series: Intelligent Systems Refeence Library|