Zernike moments and descriptors for 3D object processing

A deeper understanding of mechanisms that underlie biological processes at the microscopic level, such as molecular recognition, requires models for describing three dimensional objects and how they interact. Similarly at the macroscopic level, shape and shape changes are a crucial first step in understanding growth and development. This has been recognised and biological imaging is enjoying an increased research effort worldwide and is providing stunning images and many new insights into important biological processes. A picture can say more than a thousand words. To store and index 3D images efficiently, a powerful shape description method is required. Plants represent highly challenging objects as they have convoluted forms that deviate significantly from so-called star-shape objects (which are computationally easier to handle). The underlying mathematical framework has been derived to allow many kinds of 3D shapes and distributions to be described by Zernike moments. With further development this approach can be made more efficient whilst including additional properties. The proposed research will build on the current proof-of-principle developments and translate them into robust code for efficiently comparing molecular shapes. Further enhancements to be investigated will include the extension of the current methodology to four dimensions, in which time is presented in the fourth coordinate. This will allow for shape changes (motion, deformation, growth) to be modeled within the same framework. In addition, reliable approaches for the segmentation of objects will be investigated. These developments will enable shapes to be assembled in space and missing components scanned for in shape databases. This enhancement will allow for flexible shape fitting, with applications in imaging, X-ray scattering and especially EM.

The description of 3D objects in a concise mathematical framework has only rather recently become suited for efficient comparisons, thanks to developments made mainly by computer scientists working on content-based web search methods. As biological imaging continues to build up 2D and 3D views of biological entities, it it crucial to develop computational approaches to efficiently search for and compare these objects. In this project we wish to build on and extend the state-of-the-art methodology we have developed for molecular shape descriptors (proteins, ligands) to suit the needs of the biological plant imaging community. This proposal focusses on the use of Zernike polynomials which have been used with success in 2D and very recently also for some 3D problems. They have a number of important advantages over other approaches such as being region rather than surface based and possessing powerful rotationally invariant features. We will evaluate their use in biological imaging, mainly the optical projection tomography and microscopy images but also for unmodelled crystallographic electron density interpretation. This will enable us to exploit our recent proof-of-principle prototype and to transform this into a robust and efficient tool for biological imaging. Such tools are important for the study of whole plant growth and development. In addition, we will investigate an extension of this approach to include elasticity, i.e. to allow for deformation, and to take this into account during shape comparison.