复杂血管三维图像增强的可逆方向分数设计与处理
Design and Processing of Invertible Orientation Scores of 3D Images for Enhancement of Complex Vasculature
摘要：
噪声图像数据中细长结构的增强和检测与许多生物医学成像应用相关。为了处理2D图像中的复杂交叉结构，引入了2D方向分数$U: \mathbb{R} ^ 2\times S ^ 1 \rightarrow \mathbb{C}$，该分数已经显示了其在各种应用中的用途。在这里，我们将这项工作扩展到3D方向分数$U: \mathbb{R} ^ 3 \times S ^ 2\rightarrow \mathbb{C}$。首先，我们从一个给定的数据集，这是通过一个可逆的相干态类型的变换来实现的方向得分。对于这种变换，我们引入3D版本的2D蛋糕小波，这是复杂的小波，可以同时检测定向结构和定向边缘。在这里，我们介绍了两种类型的蛋糕小波，第一种使用离散傅立叶变换，第二种是在3D广义Zernike基础上设计的，使我们能够计算空间滤波器的解析表达式。最后，我们展示了方向分数变换的两个应用。在第一个应用程序中，我们提出了一个扩展的交叉保持一致性增强扩散通过我们的可逆方向分数的3D图像，我们应用到真正的医学图像数据。在第二个中，我们开发了一个新的tubularity措施，使用三维方向分数和应用的tubularity措施，人工和真实的医疗数据。
英文摘要：
The enhancement and detection of elongated structures in noisy image data is relevant for many biomedical imaging applications. To handle complex crossing structures in 2D images, 2D orientation scores $U: \mathbb{R} ^ 2\times S ^ 1 \rightarrow \mathbb{C}$ were introduced, which already showed their use in a variety of applications. Here we extend this work to 3D orientation scores $U: \mathbb{R} ^ 3 \times S ^ 2\rightarrow \mathbb{C}$. First, we construct the orientation score from a given dataset, which is achieved by an invertible coherent state type of transform. For this transformation we introduce 3D versions of the 2D cake-wavelets, which are complex wavelets that can simultaneously detect oriented structures and oriented edges. Here we introduce two types of cake-wavelets, the first uses a discrete Fourier transform, the second is designed in the 3D generalized Zernike basis, allowing us to calculate analytical expressions for the spatial filters. Finally, we show two applications of the orientation score transformation. In the first application we propose an extension of crossing-preserving coherence enhancing diffusion via our invertible orientation scores of 3D images which we apply to real medical image data. In the second one we develop a new tubularity measure using 3D orientation scores and apply the tubularity measure to both artificial and real medical data.
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