本研究計畫之目標在於發展一個以量子力學方法研究大尺度三維生物組織影像重構的方法。根據我們之前的研究(已被Scientific Reports接受，2017)，藉由映射物理空間中的資訊至資料空間，可成功的連結密度泛函理論與機械學習方法兩種不同的理論架構。因此，一種根據能量守恆定理而針對群數以及群邊界的非監督式搜尋方法即被提出。拉氏密度泛函的空間形貌勾勒出群之間的有意義的資料邊界，而哈密頓密度泛函則連結了擁有最相似局域資訊的資料構件。多種由物理至生物系統之跨學科領域的模態辨識問題，已被列舉而出來闡述所提演算法之可行性與準確度。本研究於研究該問題的當代方法之間，實屬一種開創性的嘗試。因此，於本研究計畫中，我們將拓展這個基礎研究到大尺度三維生物組織影像重構這類的實際應用之上。Lucas-Kanade光流法以及像素連結法這兩種當代的相關技術，將被引用於解決影像像格校準以及像素編號等問題方面。同時，在本計畫中我們嘗試將這兩種方法與我們之前的研究工作以及量子力學的數學架構融合與發表。相關的演算法也將於MATLAB以及TensorFlow這兩種截然不同的平台上，針對不同的具體應用與問題解決方法來設計與開發。最終，我們希望本計畫中所實踐的數學理論連結與開發之演算法能在臨床研究與轉譯科學中做出貢獻。 ;The objective of this research proposal is to develop a method of large-scale 3-dimensional image reconstruction of biological tissues using the quantum mechanics. Based on our previous investigations (Scientific Reports, accepted, 2017), a connection between the density functional theory, a sophisticated and pragmatic method in quantum mechanics, and the methods of machine learning was successfully constructed by mapping the information from the physical space to the data space. An unsupervised searching algorithm of the cluster number as well as the corresponding cluster boundaries was proposed based on the principle of energy conservation. Morphologies of Lagrangian density functional reveal significant data boundaries between clusters, while that of Hamiltonian density functional connect the components having the most similar local information. Several interdisciplinary problems of pattern recognition from physical to biological systems were enumerated to elucidate the feasibility and the accuracy of the proposed algorithm. The study is the pioneering attempt to propose such a methodology to solve these issues. Therefore, in this proposal we would like to extend this fundamental study to a pragmatic application on the large-scale 3-dimensional image reconstruction of biological tissues. Two contemporary techniques, the Lucas-Kanade optic flow and the pixel connectivity will be employed to resolve the issues from image film alignment and labeling of pixels. Meanwhile, these employed methods will be combined with our previous work and the mathematical framework of quantum mechanics. The mathematical connection between the employed methods and the quantum mechanics will be carefully derived and published. Then the relevant algorithms will also be constructed on the platforms of MATLAB and TensorFlow for specific applications and problem solutions. Eventually, we hope the proposed mathematical connection and the algorithm can make contribution to the clinical investigation and translational science.
