Reconstruction of a Destroyed 'Dead Leaves' Tessellation from its Fragments via the Puzzle Fitting Function

摘要

Abstract. An isotropic ensemble of a large number of puzzle pieces is given. These pieces are separate, homogeneous particles of maximum diameter L_0. Then, in respect to their analysis, the so-called puzzle fitting function Φ(r,L_0) can be determined from elastic scattering experiments of (electromagnetic) waves of a certain wavelength, followed by a discussion of the behavior near the origin. The latter yields either Φ(0,L_0) < 1 or Φ(0,L_0) ≥1- If the second relation is fulfilled, the origin of the particles can be traced back to a destroyed tessellation, based on a 'Dead Leaves' model (DLm) of a certain grain shape. This approach is explained in more detail for hemispherical grains of constant radius R, making possible practical applications in several fields, for example in archeology, biology, geography and materials science. The method can be seen as part of the large field of automatic image analysis, although no image material is made use of directly.