Acta Stereologica



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Klaus Kayser, Konrad Sandau, Gerhard Böhm, Dietmar Kunze & Jürgen Paul

Hierarchical texture analysis of soft tissue tumors using attributed graphs

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Histological slides of six soft tissue tumors of various cell types were Feulgen stained. The cell types include malignant fibrous histiocytoma, fibrosarcoma, and osteosarcoma. The two dimensional texture of the tumors was analyzed as follows: the centers of gravity of tumor cells were defined as vertices. Tumor cells fulfilling the neighborhood condition of O'Callaghan were connected by edges. Features of tumor cells such as nuclear area, integrated optical density, maximum and minimum nuclear diameter were associated to the vertices and the difference of features of neighboring vertices were associated to the edges. The result is an edge and vertex attributed graph. The minimum spanning tree (MST) was calculated from the attributed graph for various attributes. Decomposition of the MST was performed by rejecting those edges from the MST exceeding the mean value added by twice of the standard deviation of the corresponding attribute. The procedure decomposes the MST into several clusters which contain characteristic structural properties. The center of gravity of the clusters was defined as vertex of a new -higher order- graph, and the procedure for constructing a new MST was repeated. First results of the analyzed soft tissue tumors reveal characteristic structural properties of the soft tissue tumors being preserved in the MST of different order.

Keywords : attributed minimum spanning tree, cluster tree, graph theory, soft tissue tumors

To cite this article

Klaus Kayser, Konrad Sandau, Gerhard Böhm, Dietmar Kunze & Jürgen Paul, «Hierarchical texture analysis of soft tissue tumors using attributed graphs», Acta Stereologica [En ligne], Volume 9 (1990), Number 2 - Proceedings of the seventh workshop on quantitative image analysis - Freiburg 90 - Dec. 1990, 189-195 URL :

About: Klaus Kayser

Department of Pathology, Thoraxklinik, D-6900 Heidelberg, GDR

About: Konrad Sandau

Institute of applied Mathematics, University Stuttgart-Hohenheim, GDR

About: Gerhard Böhm

Institute of Pathology, University, A-1000 Wien, Austria

About: Dietmar Kunze

Institute of Pathology, Medizinische Akademie, Dresden, GDR

About: Jürgen Paul

Cambridge Instruments, Heidelberg-Nuβloch, GDR