In this paper we introduce the generalized exponential sampling series of bivariate functions and establish some pointwise and uniform convergence results, also in a quantitative form. Moreover, we study the pointwise asymptotic behaviour of the series. One of the basic tools is the Mellin--Taylor formula for bivariate functions, here introduced. A practical application to seismic waves is also outlined.

In this paper, we take advantage of the reconstruction properties of the sampling Kantorovich (SK) algorithm to estimate the volume of the human brain for the quantification of Alzheimer's biomarkers. At first, the goodness of the reconstructions is evaluated, comparing it to different interpolation methods by means of the Peak Signal to Noise Ratio (PSNR) index; then the stereological Cavalieri/Point‐counting technique is used to infer volumetric data starting from the knowledge of the planar sections. The comparison of the achieved results with synthetic references confirms the good performances of the new methodology.