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The paper discusses algorithms for extracting essential properties of binary objects in digital images which are either based on distance transforms defined by different metrics or algorithms based on simple shape deformations. Thinning algorithms define one-way simple deformations. Two-way simple deformations transfer object points into background points and vice versa, without destroying the image topology. This article reviews contributions in this area with respect to properties of algorithms and characterizations of simple points, and informs about a few new results. A main intention of this article is the comparative discussion of experimental results and theoretical equivalences.