In the present thesis, we will describe and analyse two algorithms for this problem, usually called an inverse problem. One algorithm is based on a full search through the parameter space of the affine mappings. The other is based on a gradient search in the parameter space of the affine mappings where the gradient is obtained by the Kantorovich metric. We describe some variants of these attractor coding methods and compare them with non-fractal coding methods for binary images.
We have found that the gradient search algorithm can be used to improve a good initial solution. A disadvantage of this algorithm is that the number of mappings must be given. Thus, it is less suitable for encoding images. The full search algorithm with its variants can be used to encode binary images. It also has an inverse property regarding the number of affine mappings, which means that if the given image was generated by a set mapping, then under some conditions the algorithm can recover the mappings that generated the given image.
The Kantorovich distance has a high computational complexity and takes considerable time to compute even for small images. We have implemented two algorithms with some variants for the computation of the distance and compared them. We found that they can be used to compute the distance between images.
The underlying notion behind the attractor-based techniques described here is that using a larger parameter space for the affine mappings in the spatial domain should give a better image coding in a rate distortion sense. We have also made some experiments on grey scale images along this line of thought.