The thesis covers methods for image segmentation. Fuzzy segmentation is based on the thresholding method. This is generalized to accept multiple criteria. The whole process is mathematically based on the free algebra theory. Free distributive lattice is created from poset of elements based on image properties and the lattice members are represented by terms used by the threshoding. Possible segmentation results compose the equivalence classes distribution. The thesis also contains description of resulting algorithms and methods for their optimization. Also the method of area subtracting is introduced.