Skeletons, Object Shape, Statistics

Objects and object complexes in 3D, as well as those in 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 we 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 measuring 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 are described in this paper and while many applications with evaluations have been produced, there remain many interesting open opportunities for research on comparisons to other shape representations, new areas of application and further methodological developments, many of which are explicitly discussed here.

Automated summary

This article discusses the possible representations of objects and object complexes in 3D and 2D, focusing on the advantages and limitations of skeleton representations, particularly s-reps. It highlights the suitability of s-reps for slabular object populations and statistical applications. The paper also outlines the mathematical properties of s-reps, methods for fitting them to single and multi-object boundaries, and techniques for measuring statistics on these representations. Numerous examples of statistical applications are provided. The article concludes by suggesting various research opportunities and areas for further development.