Physics-based measurements, reflective measurements and meta-measurements for nonrigid and deformable shapes with application to structural proteomics and macromolecular docking

Non-rigid shapes are generally known as objects where the three dimensional geometry may deform by internal and/or external forces. Deformable shapes are all around us, ranging from macromolecules, to natural objects such as the trees in the forest or the fruits in our gardens, and even human bodies. The development of measurements to accurately describe such non-rigid shapes has wide application. It follows that, when aiming to perform measurement of non-rigid shapes, one need to ensure that the intrinsic geometries are preserved in the presence of deformations. This paper introduces physics-based techniques for the measurements of such deformable shapes. Our work is based on the idea of heat propagation through a surface. Specifically, we introduce so-called multi-measurements to measure the distance between two points on an object and reflective measurements that allows for the exploration of a region around a point. Further, we introduce two novel meta-measurements that extend the bag of features concept. We illustrate our methodology in the context of structural proteomics and molecular docking.