Topological features of an object are fundamental in image processing. In many applications,including medical imaging, it is important to maintain or control the topology of the image. Howeverthe design of such transformations that preserve topology and geometric characteristics of the inputimage is a complex task, especially in the case of parallel processing.Parallel processing is applied to accelerate computation by sharing the workload among multipleprocessors. In terms of algorithm design, parallel computing strategies profits from the naturalparallelism (called also partial order of algorithms) present in the algorithm which provides two main resources of parallelism: data and functional parallelism. Concerning architectural design, i...