Centre de Morphologie Mathématique, Ecole des Mines de Paris, 77305 Fontainebleau, France.
IEEE Trans Image Process. 2001;10(7):1010-9. doi: 10.1109/83.931095.
This paper presents an algorithm based on mathematical morphology and curvature evaluation for the detection of vessel-like patterns in a noisy environment. Such patterns are very common in medical images. Vessel detection is interesting for the computation of parameters related to blood flow. Its tree-like geometry makes it a usable feature for registration between images that can be of a different nature. In order to define vessel-like patterns, segmentation is performed with respect to a precise model. We define a vessel as a bright pattern, piece-wise connected, and locally linear, mathematical morphology is very well adapted to this description, however other patterns fit such a morphological description. In order to differentiate vessels from analogous background patterns, a cross-curvature evaluation is performed. They are separated out as they have a specific Gaussian-like profile whose curvature varies smoothly along the vessel. The detection algorithm that derives directly from this modeling is based on four steps: (1) noise reduction; (2) linear pattern with Gaussian-like profile improvement; (3) cross-curvature evaluation; (4) linear filtering. We present its theoretical background and illustrate it on real images of various natures, then evaluate its robustness and its accuracy with respect to noise.
本文提出了一种基于数学形态学和曲率评估的算法，用于在噪声环境中检测管状模式。这种模式在医学图像中非常常见。血管检测对于计算与血流相关的参数很有趣。它的树状结构使其成为不同性质的图像之间配准的有用特征。为了定义管状模式，我们根据精确的模型进行分割。我们将血管定义为明亮的、分段连接的、局部线性的模式，数学形态学非常适合这种描述，但其他模式也符合这种形态描述。为了将血管与类似的背景模式区分开来，我们进行了交叉曲率评估。它们被分离出来，因为它们具有特定的类高斯轮廓，其曲率沿着血管平滑变化。直接从这种建模中导出的检测算法基于四个步骤：（1）降噪；（2）具有类高斯轮廓的线性模式改进；（3）交叉曲率评估；（4）线性滤波。我们介绍了它的理论背景，并在各种性质的真实图像上进行了说明，然后评估了它对噪声的鲁棒性和准确性。
