CIF: Small: Theory of Multiresolution Classification with Bases and Frames

从分子、细胞到器官的所有尺度的生物系统成像的最新进展，使生物学家和临床医生有机会在前所未有的水平上观察过程和相互作用，从而收集了大量的高维数据。因此，对这些已经容易出错、不可重现和主观的数据集的目视检查也变得不切实际。因此，迫切需要开发系统来自动化这种分析，并挖掘人眼看不到的相互作用。过去几年，分类任务一直是该小组几个项目的核心，包括确定苍蝇胚胎的发育阶段，识别干细胞畸胎瘤中H&P；E染色的组织类型，以及诊断中耳炎。由于一种准确而高效的自动分类算法将对生物学家和临床医生大有裨益，人们开发了一种多分辨率(MR)分类算法，并在每个问题中出现了一致的趋势：1.MR分类总是比非MR版本更好；2.冗余MR变换帧，总是比无冗余的基础更好。这种跨数据集和应用程序的一致性表明，MR有能力对生物医学图像分类性能产生重大影响。研究人员因此研究MR分类，以获得对其基础的基本了解，特别是以下两个问题：1.MR分类何时/为什么起作用？2.MR框架分类何时/为什么起作用？这些问题是通过建立一个测量论分类理论来解决的，该理论是一个提出和研究现实世界分类问题的数学严格框架。

Recent advances in imaging of biological systems at all scales, from molecular and cellular up to organ levels, have given biologists and clinicians opportunities to observe processes and interactions at a never-before-seen level, leading to the collection of huge amounts of high-dimensional data. As a result, the visual inspection of these data sets,already error-prone, nonreproducible and subjective, has become impractical as well.There is thus an acute need for the development of systems to both automate this analysis, as well as mine interactions not visible to the human eye.The task of classification has been at the heart of several of the group's projects in the past few years, including the determination of developmental stages in fly embryos,the recognition of H&E-stained tissue types in stem-cell teratomas, and the diagnosis of otitis media. As an accurate and efficient algorithm for automated classification would have been of great use to biologists and clinicians, a multiresolution (MR) classificationalgorithm was developed and, in each of the problems, consistent trends emerged:1. MR classification always performed better than the no-MR version;2. Redundant MR transforms frames, always performed better than thenonredundant ones bases. This consistency across data sets and applications indicates that MR has the power to make a significant impact on biomedical image classification performance. The investigators thus study MR classification to gain fundamental understanding of its underpinnings, in particular, the following two questions:1. When/why does the MR classification work?2. When/why does the MR frame classification work?These questions are approached by setting up a measure-theoretic theory ofclassification as a mathematically rigorous framework within which to pose andinvestigate real-world classification problems.