Skeletons, Object Shape, Statistics - Pizer, Stephen M.; Marron, J. S.; Damon, James N.; Vicory, Jared; Krishna, Akash; Liu, Zhiyuan; Taheri, Mohsen (Frontiers in Computer Science, 2022)
Objects and object complexes in 3D, as well as those 2D, have many possible representations. Among them skeletal representations have special advantages and some limitations. For the special form of skeletal representation called “s-reps”, these advantages include strong suitability for representing slabular object populations and statistical applications on these populations. Accomplishing these statistical applications is best if one recognizes that s-reps live on a curved shape space. Here I will lay out the definition of s-reps, their advantages and limitations, their mathematical properties, methods for fitting s-reps to single- and multi-object boundaries, methods for the statistics of these object and multi-object representations, and examples of such applications involving statistics. While the basic theory, ideas, and programs for the methods described in this paper and while many applications with evaluations have been produced, there remain many interesting open opportunities for research on new areas of application and further methodological developments, many of which are explicitly discussed here.