Growing 3D clouds from 2D maps via full spherization

In this work, we present a novel framework for constructing three-dimensional (3D) objects from two-dimensional (2D) maps, tailored for the analysis of complex structures in the interstellar medium (ISM). The framework extends the Abel transform and the AVIATOR algorithm. By expanding medial-axis trees along the $z$-coordinate and transforming circular components into spheres, we generate 3D objects from 2D flux slices while preserving key structural features such as filament intersections, the spatial distribution of bright cores, and filamentary twists. The framework introduces multiple expansion strategies--random, fiducial, and physical--allowing for different interpretations of the underlying 3D structures. While the column density probability density function (PDF) remains largely invariant across different construction methods, the high degree of freedom in the 3D expansion poses challenges in accurately recovering true spatial configurations in complex regions. Our work provides a flexible, extensible platform for exploring the 3D organization of ISM structures, with potential applications in star formation and molecular cloud analysis.