利用廣義交叉驗證法決定板條插補法之參數及三維超音波影像的無母數影像細胞單元分群法

Abstract

本研究的目的為利用多張二維腦瘤的超音波影像重建出腫瘤於腦部在三維的相對位置，目的是在臨床應用上能讓醫生明確的知道腫瘤的確切位置，進而提高醫生開刀的準確性。 由於多張的二維超音波影像並非規則的平行切面，所以我們在做影像分割前會先對其作插捕成三維的規則的平行切面，使得許多快速的二維影像處理方法能夠直接地推廣到三維影像上。我們做插補所使用的方法為板條插補法，同時使用了廣義交叉驗證法來決定控制點的個數。 我們接著將分水嶺轉換和影像細胞單元的想法推廣到三維影像上來進行影像切割。首先使用高斯平滑法濾雜訊，再利用Sobel 濾波器求出每個像素的梯度值。接著，經由分水嶺轉換將影像上近似的影像及影像上梯度絕對值小的那些像素聚集起來形成影像細胞單元。最後，影像細胞單元應用無母數的假設檢定和分類法進行合併或分裂，找出腫瘤最後的邊界。我們稱之為無母數的影像細胞單元分群法，並進行模擬與實證研究，證實這個方法的實際可行性。

This study is aimed to segment the tumor in 3D by a volume of 2D ultrasound images. This segmentation can provide the location information of tumor for doctors during operation and improve the accuracy of operation. Because the images obtained by 2D ultrasound scans are irregularly spaced most of the time, it is necessary to interpolate them into regularly spaced 3D images so that image processing techniques for 2D images can be generalized directly with fast computation speed. Spline interpolation is used in this study. Generalized cross validation is proposed to decide the size of control lattice in interpolation. After interpolation, we will generalize watershed transform and cell based approaches to 3D images. Gaussian smoothing is first applied to denoise the images. Sobel filters are then used to estimate the gradient. Based on the absolute values of gradients and the regularization term of the image intensities, image cells are obtained by watershed transform. Finally, cells are merged or split to locate the tumor by a new method with nonparametric testing and divisive clustering. This is called “nonparametric cell clustering” in this study. Simulation and empiric studies are performed for this new approach. The results are promising according to these studies.