“Geometrical methods in computer graphics and image processing”
The aim of the project is to develop effective multiresolution methods applied to two areas: computer graphics and image processing. The fractal approach and the so-called inverse subdivision will allow modeling and coding of fractal 2D and 3D shapes, and their multiresolution representation. However, wavelet approach applied to digital images will lead to new algorithms for image processing, in particular, noise reduction, edge detection, segmentation, and consequently, to understanding of their content.
The project in the part of multiresolution methods includes two research tasks:
1. Fractal modeling and fractal coding of 2D and 3D shapes and their multiresolution representation,
2.The effective geometrical approximation of digital images and their processing. Fractal modeling and fractal coding will be based on the relationship between coefficients of an IFS (Iterated Function System) and a subdivision scheme, and their combination with the new ideas presented in 2006 by Barnsley in the monograph entitled “Superfractals”. Multiresolution representation of graphical objects will be obtained on the basis of the possibility of the inverse subdivision scheme presented by Bartels in 2000. Encoding and processing of digital images will be based on modern tools – geometrical wavelets, which enables the analysis of images in a geometrical way, similar to the way the image is received by the Human Visual System. With this approach, we can develop a highly effective tools for noise reduction, edge detection, segmentation and compression. This part of the project is a continuation of the research presented in the doctoral dissertation of A. Lisowska.