Zernike moments and descriptors for 3D object processing

更深入地理解微观水平上的生物过程的机制，如分子识别，需要描述三维物体及其相互作用的模型。同样，在宏观层面上，形状和形状变化是理解生长和发育的关键第一步。这一点已经得到认可，生物成像在全球范围内的研究工作正在增加，并提供了令人惊叹的图像和许多重要生物过程的新见解。一张照片胜过千言万语。为了有效地存储和索引3D图像，需要一个强大的形状描述方法。植物是极具挑战性的对象，因为它们具有复杂的形状，与所谓的星形对象（在计算上更容易处理）有很大的不同。基本的数学框架已经推导出允许多种3D形状和分布被描述的Zernike矩。随着进一步的发展，这种方法可以变得更有效，同时包括额外的属性。拟议的研究将建立在目前的原理证明发展的基础上，并将其转化为强大的代码，以有效地比较分子形状。有待研究的进一步改进措施将包括将目前的方法扩大到四个维度，其中时间在第四个坐标中显示。这将允许在同一框架内对形状变化（运动、变形、生长）进行建模。此外，可靠的方法分割的对象将进行调查。这些发展将使形状能够在空间中组装，并在形状数据库中扫描丢失的组件。这种增强将允许灵活的形状拟合，在成像，X射线散射，特别是EM中的应用。

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.