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The hybrid cellular automaton method has been successfully applied to topology optimization using a uniform strain energy density distribution approach. In this work, a new set of design rules is derived from the first-order optimality conditions of a multi-objective problem. In this new formulation, the final topology is derived to minimize both mass and strain energy. In the hybrid cellular automaton algorithm, local design rules based on the cellular automaton paradigm are used to efficiently drive the design to optimality. In addition to the control-based techniques previously introduced, a new ratio technique is derived in this investigation. This work also compares the performance of the control strategies and the ratio technique.

The study of cerebral microvascular networks requires high-resolution images. However, to obtain statistically relevant results, a large area of the brain (several square millimeters) must be analyzed. This leads us to consider huge images, too large to be loaded and processed at once in the memory of a standard computer. To consider a large area, a compact representation of the vessels is required. The medial axis is the preferred tool for this application. To extract it, a dedicated skeletonization algorithm is proposed. Numerous approaches already exist which focus on computational efficiency. However, they all implicitly assume that the image can be completely processed in the computer memory, which is not realistic with the large images considered here. We present in this paper a skeletonization algorithm that processes data locally (in subimages) while preserving global properties (i.e., homotopy). We then show some results obtained on a mosaic of three-dimensional images acquired by confocal microscopy. Index Terms--Chamfer map, digital topology, image mosaic, medial axis, skeleton, topological thinning.