Multi-Objective Optimization in Image Approximation

There are two common ways for the representation of images - as pixels (raster graphics) or as a list of geometric primitives (vector graphics). Both ways have their advantages and disadvantages and in some situations conversion between them is needed. Conversion from vector graphics to raster graphics is relatively easy and it is done by a process called rasterization. The opposite conversion (from raster to vector) is much harder and less reliable. The process is called vectorization and in the case of images, it is related to color reduction and information loss. The goal in this research is 16M colors bitmap images to be approximated with 12 colors vectorized form in which the base primitive is an ellipse. The process of vectorization is done with genetic algorithms as one of the most efficient metaheuristic tools for global optimization. The evaluation of the fitness value in the evolution process implemented in the genetic algorithms uses three different objective functions: 1) Average Euclidean distance between the pixels of the original image and the approximated image; 2) The size of the blanks spaces in the approximated image; and 3) The number of graphic primitives used for the approximation.