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We present a self-consistent framework to perform the wavelet analysis oftwo-dimensional statistical distributions. The analysis targets the 2Dprobability density function (p.d.f.) of an input sample, in which each objectis characterized by two peer parameters. The method performs a probabilisticdetection of various `patterns', or `structures' related to the behaviour ofthe p.d.f. Laplacian. These patterns may include regions of local convexity orlocal concavity of the p.d.f., in particular peaks (groups of objects) or gaps.In the end, the p.d.f. itself is reconstructed based on the least noisy (mosteconomic) superposition of such patterns. Among other things, our method alsoinvolves optimal minimum-noise wavelets and minimum-noise reconstruction of thedistribution density function. The new 2D algorithm is now implemented andreleased along with an improved and optimized 1D version. The code relies onthe C++11 language standard, and is fully parallelized. The algorithm has arich range of applications in astronomy: Milky Way stellar population analysis,investigations of the exoplanets diversity, Solar System minor bodiesstatistics, etc.

Statistical detection of clumps and gaps in a random sample by continuous wavelet transforms: the 2D case