Discovering Octobit-Based Formulas for Shape Descriptors Using Selection-Based Regression

In this research, we address the gap in deriving formulas for 3D object shape descriptors using octo-bit patterns, a method that analyzes groups of eight adjacent voxels. We leverage linear regression, both with and without variable selection, to generate interpretable formulas for various descriptors such as Euler characteristic, enclosing surface, contact surface, volume, as well as simplexes and tetra-voxels. By focusing exclusively on octo-bit combinations, we derive computationally efficient formulas that require only a single multiplication of the coefficient vector with the input data, eliminating the need for additional algorithms to compute these descriptors. For the learning stage of our regression models, groups of random 3D objects of different resolutions were used. Our approach is validated using 3D voxelized objects and the diverse BraTS 2020 brain tumor dataset. We achieve a 100% success rate across 2,000 new equations for each shape descriptor, offering an alternative method for deriving linear expressions using octo-bits to measure descriptors.