使用 Kirsch 边缘检测的核分形分析的 Box-Counting 方法的外截止值。
Outer Cutoff Value for the Box-Counting Method for Fractal Analysis of the Nucleus Using Kirsch Edge Detection.
机构信息
Department of Bioscience and Laboratory Medicine, Hirosaki University Graduate School of Health Sciences, Hirosaki, Japan,
Department of Bioscience and Laboratory Medicine, Hirosaki University Graduate School of Health Sciences, Hirosaki, Japan.
出版信息
Acta Cytol. 2021;65(2):186-193. doi: 10.1159/000512096. Epub 2020 Dec 10.
OBJECTIVE
The complexity of chromatin (i.e., irregular geometry and distribution) is one of the important factors considered in the cytological diagnosis of cancer. Fractal analysis with Kirsch edge detection is a known technique to detect irregular geometry and distribution in an image. We examined the outer cutoff value for the box-counting (BC) method for fractal analysis of the complexity of chromatin using Kirsch edge detection.
MATERIALS
The following images were used for the analysis: (1) image of the nucleus for Kirsch edge detection measuring 97 × 122 pix (10.7 × 13.4 μm) with a Feret diameter of chromatin mesh (n = 50) measuring 17.3 ± 1.8 pix (1.9 ± 0.5 μm) and chromatin network distance (n = 50) measuring 4.4 ± 1.6 pix (0.49 ± 0.18 μm), and (2) sample images for Kirsch edge detection with varying diameters (10.4, 15.9, and 18.1 μm) and network width of 0.4 μm.
METHODS
Three types of bias that can affect the outcomes of fractal analysis in cytological diagnosis were defined. (1) Nuclear position bias: images of 9 different positions generated by shifting the original position of the nucleus in the middle of a 256 × 256 pix (28.1 μm) square frame in 8 compass directions. (2) Nuclear rotation bias: images of 8 different rotations obtained by rotating the original position of the nucleus in 45° increments (0°, 45°, 90°, 135°, 180°, 225°, 270°, and 315°). (3) Nuclear size bias: images of varying size (diameter: 190 pix [10.4 μm], 290 pix [15.9 μm], and 330 pix [18.1 μm]) with the same mesh pattern (network width: 8 pix [0.4 μm]) within a 512 × 512 pix square. Different outer cutoff values for the BC method (256, 128, 64, 32, 16, and 8 pix) were applied for each bias to assess the fractal dimension and to compare the coefficient of variation (CV).
RESULTS
The BC method with the outer cutoff value of 32 pix resulted in the least variation of fractal dimension. Specifically, with the cutoff value of 32 pix, the CV of nuclear position bias, nuclear rotation bias, and nuclear size bias were <1% (0.1, 0.4, and 0.3%, respectively), with no significant difference between the position and rotation bias (p = 0.19). Our study suggests that the BC method with the outer cutoff value of 32 pix is suitable for the analysis of the complexity of chromatin with chromatin mesh.
目的
染色质的复杂性（即不规则的几何形状和分布）是癌症细胞学诊断中考虑的重要因素之一。使用 Kirsch 边缘检测的分形分析是一种用于检测图像中不规则几何形状和分布的已知技术。我们检查了使用 Kirsch 边缘检测的分形分析中用于检测染色质复杂性的盒计数（BC）方法的外部截止值。
材料
对以下图像进行了分析：（1）用于 Kirsch 边缘检测的核图像，大小为 97×122pix（10.7×13.4μm），Feret 直径的染色质网格（n=50）大小为 17.3±1.8pix（1.9±0.5μm），染色质网络距离（n=50）大小为 4.4±1.6pix（0.49±0.18μm），（2）用于 Kirsch 边缘检测的不同直径（10.4、15.9 和 18.1μm）和网络宽度为 0.4μm 的样本图像。
方法
定义了三种可能影响细胞诊断中分形分析结果的偏倚。（1）核位置偏倚：通过在 256×256pix（28.1μm）正方形框架的中间位置沿 8 个罗盘方向移动核的原始位置，生成 9 个不同位置的图像。（2）核旋转偏倚：通过以 45°增量（0°、45°、90°、135°、180°、225°、270°和 315°）旋转核的原始位置，获得 8 个不同旋转的图像。（3）核尺寸偏倚：具有相同网格模式（网络宽度：8pix[0.4μm]）的不同尺寸（直径：190pix[10.4μm]、290pix[15.9μm]和 330pix[18.1μm]）的图像，在 512×512pix 正方形内。对每个偏倚应用不同的 BC 方法（256、128、64、32、16 和 8pix）的外部截止值，以评估分形维数并比较变异系数（CV）。
结果
BC 方法的外部截止值为 32pix 时，分形维数的变化最小。具体来说，使用 32pix 的截止值时，核位置偏倚、核旋转偏倚和核尺寸偏倚的 CV<1%（分别为 0.1、0.4 和 0.3%），位置和旋转偏倚之间没有显著差异（p=0.19）。我们的研究表明，BC 方法的外部截止值为 32pix 适用于分析具有染色质网格的染色质复杂性。
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