04/02/2020 – Talk by Vasileios Drakopoulos

Time: 14:15
Location: Meeting Room B, Building Zeta
Speaker: Vasileios Drakopoulos
Abstract: Fractal interpolation offers an alternative to traditional interpolation techniques, aiming primarily at data which present detail at different scales or some degree of self-similarity. These characteristics, often intrinsic in natural objects, imply an irregular and non-smooth structure which is inconvenient to capture by elementary functions such as polynomials. 
Specifically, a fractal interpolation function, as defined by M. F. Barnsley and other researchers, can be considered as a continuous function whose graph is the attractor of an appropriately chosen iterated function system. If this graph, usually of non-integral dimension, belongs to the three-dimensional space and has Hausdorff – Besicovitch dimension between 2 and 3, then the resulting attractor is called fractal interpolation surface. 
During this talk, we discuss the theory and applications of fractal interpolation surfaces constructed by bivariate functions on rectangular grids. As far as the theory is concerned, we focus on two important issues: (a) The ensurance of continuity, which is in general a more complicated task than in the case of fractal interpolation functions on the plane, and (b) the identification of the vertical scaling factors which are the only free parameters in such a construction. As far as the applied part is concerned, we present several practical applications of fractal interpolation surfaces, including image compression, 3D data representation and medical imaging.