Ph.D. thesis : Impreciseness in Geometric Shape Approximation
Advisor: Prof. Dr. Helmut Alt
I study different variantions of geometric shape approximation problems under the assumption that the input is not known exactly. Most of the previous work on geometric shape approximation assume that the input is known exactly. In practice, however, this is often not the case. In many cases, geometric data comes from measurements of continuous real-world phenomena and the measurements devices have finite precision. This impreciseness of geometric data has been studied lately, and quite a few algorithms that handle imprecise data have been given for fundamental geometric problems.
As a part of my thesis I intend to study different similarity measures with imprecise data. Another intension of my thesis is to study approximation of geometric shapes, since substituting a complex geometric object by a simpler one is motivated by many applications.