彈性影像對位演算法在許多方面都已經被使用，在醫學影像上的應用為：臨床診斷、放射治療規劃、影像定位手術、療效評估…等都有其重要性的，為醫學影像研究領域中一個熱門的題目。病理切片影像為判斷疾病特徵、研究病理現象不可或缺的診斷依據，但是其容易受到人為因素、染色和儀器拍攝問題影響，時常造成影像上的扭曲、變形。因此，本論文希望透過彈性影像對位演算法，解決無法使用傳統的剛性影像對位法處理之變形問題。
本論文是研究並使用B-spline的彈性影像對位方法，B-spline的優點為可以局部控制和計算速度較快。此對位方法同時利用多解析度金字塔，從整張圖全局的變形到細部的變形，增加影像對位的精準度。
本論文預計將完成以下幾項工作：
研究B-spline彈性影像對位方法其原理與內容
執行B-spline彈性影像對位演算法
針對影像對位容易發生的四種問題（位移、旋轉、尺度、變形）和病理切片影像，探討彈性影像對位法的功效與會遇到的問題。
分析實驗結果發現利用BUnwarpJ和UnwarpJ（開放源碼程式）進行影像對位演算法，進行影像對位中常出現的問題和真實的病理切片影像後，發現兩種方法的平均準確率差不多，沒有哪種方法特別領先。面對位移問題，在小幅度位移皆可完全對位成功，但是當兩個影像目標物一開始沒有重疊時，會造成對位完全的錯位，這是因為能量項E_img會考慮到兩張影像像素值相減的關係；面對旋轉問題，不論有沒有增加旋轉能量項E_rotation在旋轉順、逆時針30°以內，皆可對位成功，但是當旋轉超過30°以後，對位準確率下降，由於BUnwarpJ和UnwarpJ對位過程是四項能量項的競爭，不會只考慮旋轉問題；在尺度問題，BUnwarpJ和UnwarpJ皆可得到良好的平均準確率（95%以上）。特別值得一提的是，面對傳統剛性影像對位無法解決的變形問題，BUnwarpJ和UnwarpJ平均準確率也都超越90%。BUnwarpJ在能量項方面新增E_cons，同時考慮順向和逆向間影像變形的差異，使得在變形過程中，不會造成大幅度的影像跳動而產生影像失真現象。因此，在選用影像對位方法的時候，會傾向使用BUnwarpJ影像對位方法。
當進行病理切片的影像對位，由於病理切片複雜的綜合變形問題，大幅提高影像對位的困難，使得BUnwarpJ和UnwarpJ平均準確率大約為58%，無法產生有效的對位結果。未來，我們希望透過改良以上兩種演算法，建立能夠應用於病理切片的影像對位方法，規畫可能的改良方式如：加入標記點項目、使用適當的旋度和散度權重。而後，透過改良的演算法，擷取對位過程中變形影像，搭配三維重建技術，建立一套病理切片三維重建演算法。

Elastic image registration has been used in many applications, such as medical diagnosis, planning surgery, radiation therapy planning and evaluation of treatment and other aspects, and it has become a popular research topic in medical image field. In this study, we have investigated two elastic image registration methods on histopathological tissue images. However, image registration of tissue images is challenging, and there are complex deformations and distortion problems, which make traditional rigid image registration techniques perform poor.
Two B-spline models (BUnwarpJ and UnwarpJ) were selected for this study because they were demonstrated to be effective in biological image alignments, and both methods include multi-resolution B-spline optimization strategy. In this study, we have completed the following work,
We have investigated the principle and contents of the elastic image registration method using B-spline models.
We have tested and analyzed two B-spline models in application to synthetic and histopathological images.
We have identified the limitations and strengths of the two B-spline models in our experiments.
In evaluation, the registration accuracies of the two B-spline methods are not significantly different. In adjusting translation distortions, the energy function E_img calculates the difference of the source and target images, and when there is an overlap between an object in the target image and the same object in the source image, BUnwarpJ and UnwarpJ will produce perfect alignments, otherwise, they will fail. Regarding rotation distortion, BUnwarpJ and UnwarpJ were demonstrated to produce good alignment results to adjust rotation effects within 30 degrees. However, for rotation effects greater than 30 degrees, BUnwarpJ and UnwarpJ tend to produce poor registration outputs with or without the rotation energy function. In addition, it is observed that adding the rotation energy tends to cause large deformation problems for registered outputs, especially when dealing with rotation effects greater than 30 degrees. In dealing with scaling deformation, BUnwarpJ and UnwarpJ appear to perform well with registration accuracies more 90%.
Importantly, for shape distortion problems, BUnwarpJ and UnwarpJ outperform rigid registration techniques and produce high registration accuracies (92% for BUnwarpJ and 100% for UnwarpJ). Comparing the two methods, as BUnwarpJ adds an additional energy function E_cons, considering the consistency between the direct and inverse transformation to avoid results containing large distortion, BUnwarpJ appears to generate less registration outputs suffering large deformation. Therefore, we recommend BUnwarpJ for image registration of biological images.
In our experiments on histopathological image alignments, due to complex deformation problems, combining various distortion effects, BUnwarpJ and UnwarpJ perform poor, obtaining 58% for average accuracies. For the future work, we hope to build an useful registration method by adding effective landmark extraction methods and improving the rotation and divergence energy functions for the BUnwarpJ algorithm, and the improved method can be further utilize for building a 3 dimensional histopathological reconstruction model.

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