為了控制動物的複雜行為，數以萬計的基因在大腦的不同位置同時運作著。近年來隨著基因體學(Genomics)、資訊科學、奈米科技與生醫影像資訊等學門的發展，我們已逐漸接近生物學中最複雜的問題的核心：「大腦到底是如何完整運作的?」為了闡明中樞神經系統的建立、發展及功能性，我們必須要從神經間的連接關係開始著手。在生物學家汲汲於從顯微影像中擷取資訊以利探究神經間連結關係的同時，我們則可透過建立處理此類三維影像的演算法來提供一臂之力。

為了完成這樣的目標，我們將相關研究工作分為三個子目標來進行：(1) 高解析度的影像貼合，(2) 多重尺度(multiscale, 或level-of-detail)的網格點表面模型(mesh surface model)重建，及(3)正確的體資料建模。我們預計在將來的相關研究中完成第三個子目標，而這份論文將只著重於前兩項；也就是說，我們主要會探討如何從多個待合併的原始影像堆疊建立一組高解析度的多重尺度網格點表面模型。我們希望最終所獲得的網格點表面模型除了能作為神經傳導路經的三維地圖參考之外，同時也能便於銜接原始影像堆疊與該堆疊的面資料表示方式(surface representation)。

至於影像貼合的問題，由於共焦顯微鏡螢光影像所特有的「光漂白(photobleaching)效應」，在貼合過程中，我們應該給予「較早成像」的顯微影像較大的混合係數。由此，我們定義了一個多重解析度下最佳混合係數的估測問題，而這個問題則可並利用二次最佳化(quadratic programming)及一組代表生物限制的線性限制式來求解。依據我們的所提出的最佳化架構，這樣的做法也能輕易地延伸，並與不同狀況下可能遭遇的不同限制式(case-dependent constraint)進行整合。

其次，我們建立了一個由粗糙至精細(coarse-to-fine)的演算法，以便從生物影像堆疊來重建半規則(semi-regular)的多重尺度(multiscale)網格點表面模型。此外，我們也希望能透過這樣的方式，讓所建立的模型的三維結構特徵點能與二維原始影像上的輪廓點相符合，並能同時適合資料壓縮及傳輸。在我們的作法中，由於調整內插點位置的機制與該點的鄰近區域的幾何關係有關，因此，某些程度上我們的作法相當於建立一個三維表面上的不均勻(non-uniform)濾波器，這也有別於過去文獻所提及的觀念。

最後，我們的實驗結果顯示我們所提出的方法不僅能獲得品質良好的貼合影像，而所建立的三維網格點表面模型也適合在低碼率(low bit-rate)的環境下進行傳輸。

Thousands of genes operate in the brain, each at a different time and space, to control complex behaviors of an animal. Recent advances in genomics, computer science, nanotechnology and bioimage informatics could be brought together to answer one of the most complex questions in biology—how does a complete brain work? A key step towards understanding the development and function of the central nervous system is to characterize the physiology of interconnected neurons. It is because of that the wiring patterns of nervous system are characterized by specific synaptic connections, and the interactions among synaptic inputs enable neurons to compute the overall consequence of various stimuli and provide the cellular basis of cognitive processes and behavior. While biologists are exploring the inter-connections among neurons by trying to draw useful information from microscopy images, scientists of engineering background can assist in this worldwide research work by developing algorithms of 3D image processing.
In order to carry out these goals, three important sub-goals should be achieved first. They are (1) high-resolution image mosaicing, (2) multiscale (level-of-detail) mesh surface reconstruction, and (3) accurate volumetric modeling. The third part will be dealt with elsewhere in the future, and this research is focused on the first two parts. That is, we focus on the way to reconstruct a high-resolution multiscale mesh surface from the to-be-combined source image volumes. We hope the obtained mesh surfaces can not only act as a 3D roadmap for neural pathways, but also can connect image volumes and the surface representation thereof.
As for mosaicing problem, due to photobleaching effect, earlier-acquired images should be given more weight than later-acquired images in the mosaicing process. We incorporate these properties into a mosaicing procedure and define a multi-resolution optimum blending parameter estimation problem that can be solved by quadratic programming with linear constraints. The perceptual quality of the resulting mosaic images is compared with that of the results derived by Burt and Adelson's algorithm and the MosaicJ algorithm. Based on the proposed optimization framework, it would be easy to extend the proposed method to other scenarios with case-dependent constraints.
Next, we develop a coarse-to-fine algorithm that can reconstruct semiregular mesh surfaces from biomedical image stacks in a multiscale fashion, and the 2D contour information can be integrated with 3D structure features at the same time. The developed method first extracts the 3D structural features via wavelet analysis, and then a registration-based subdivision procedure succeeds to evaluate the optimal position of each newly interpolated vertex. Because low-passed components belonging to the coarsest domain are extracted and isolated in advance, the obtained coarsest mesh would mix less high-frequency components than typical methods. Moreover, the proposed registration-based subdivision method guarantees that each newly interpolated vertex would have its own subdivsion parameter depending on the behaviors of neighboring vertices. It means that this strategy delivers vertices to where they are supposed to be by developing a non-uniform filter.
Finally, the proposed method can be applied to scalable/progressive transmission, and the experimental results show that it performs well even in low bit-rate circumstance.

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