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Fig. 1.


Statistical characteristics of the spatial distribution of a set of points obtained by means of a GRF and a complete spatial random point process (CSRPP). Top-left panel: histogram of nearest neighbor distances of the peaks of a simulated zero-mean unit-variance GRF with size 500 × 500 pixels and autocorrelation function given by a circular Gaussian with dispersion set to three pixels. Since in this GRF the peaks have coordinates given by integer numbers, in order to mimic a continuous spatial distribution, they have been added to a uniform random number taking its value in the range (−0.5, +0.5]. Bottom-left panel: sample pair correlation function ρ(r) of the peaks in the same GRF. Top-right and bottom-right panels: figures corresponding to the left panels for a CSRPP with the same sizes and containing a number of points equal to the number of peaks as in the GRF. The red lines provide the corresponding theoretical PDFs due to a CSRPP.

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