Géza Makay

Method for automatically segmenting the spinal cord and canal from 3d CT images

We present two approaches for automatically segmenting the spinal cord/canal from native CT images of the thorax region containing the spine. Different strategies are included to handle images where only part of the spinal column is visible. The algorithms require one seed point given on a slice located in the middle region of the spine, and the rest is automatic. The spatial extent of the spinal cord/canal is determined automatically. An extended region-growing technique is suggested for segmenting the spinal canal while active contours are applied if the spinal cord is to be segmented. Both methods work in 2D and use propagated information from neighboring slices. They are also very rapid in execution, that means an efficient, user-friendly workflow. The methods were evaluated by radiologists and were found to be useful (in reducing/eliminating contouring labor and time) and met the accuracy and repeatability requirements for the particular task.

Invariance groups of finite functions and orbit equivalence of permutation groups

Abstract Which subgroups of the symmetric group Sn arise as invariance groups of n-variable functions defined on a k-element domain? It appears that the higher the difference n-k, the more difficult it is to answer this question. For k ≤ n, the answer is easy: all subgroups of Sn are invariance groups. We give a complete answer in the cases k = n-1 and k = n-2, and we also give a partial answer in the general case: we describe invariance groups when n is much larger than n-k. The proof utilizes Galois connections and the corresponding closure operators on Sn, which turn out to provide a generalization of orbit equivalence of permutation groups. We also present some computational results, which show that all primitive groups except for the alternating groups arise as invariance groups of functions defined on a three-element domain.