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Many shapes can be described very well in terms of an axis. Examples are the stick figure drawings of man and animals from ancient times. We would like to give a natural (intuitive) definition of axis for cylindrical shapes. For 2D shapes, the medial axis is a good candidate, though it is sensitive to perturbations. For 3D shapes, the medial scaffold is often complicated surfaces and does not match people's intuitions very well. In this paper, we give a new definition of axis for generalized cylinders. This approach uses a regression point of view, defining the axis as a minimization point of a global energy function. We prove the existence of a solution and give the equations of the minimization point and stability conditions. We also apply the definition to some real and artificial examples. Our goal is to produce natural (intuitive) shape descriptions for 2D and 3D shapes. We believe that is essential for building general object recognition systems. It would be also useful in shape classification and compression.