Rasterable pointsets
Hans Giger · Journal of Microscopy · 1972
SUMMARY A very general class ℛ of pointsets is introduced which is named rasterable. The term ‘rasterable’ designates the important property of these pointsets that they can be represented by the raster of those points of a lattice belonging to the pointset. This representation concerns the Minkowski measures and has to be interpreted in a statistical sense. It is shown that the directional Minkowski measures for rasterable pointsets can be interpreted as coefficients of the expansion of the corresponding correlation function. It follows that the well‐known Wiener spectrum of a two‐dimensional texture, which equals the Fourier transformation of a reduced correlation function, does not preserve the topological properties of the pointset. The described representability of a pointset by a point picture may clarify the property of the pointset to be ‘normal’ in the common sense of the word. If one knows the pathological appearances in the theory of pointsets this clarification is of special interest.