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 #x3c;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.
Acta Cytologica

中文翻译：

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使用Kirsch边缘检测对核进行分形的盒计数方法的外部截止值

目的：染色质的复杂性（即不规则的几何形状和分布）是在癌症细胞学诊断中考虑的重要因素之一。使用Kirsch边缘检测进行分形分析是一种检测图像中不规则几何形状和分布的已知技术。我们使用盒式计数（BC）方法使用Kirsch边缘检测对染色质的复杂性进行分形分析，研究了外部截止值。材料：以下图像用于分析：（1）用于Kirsch边缘检测的核的图像测量为97×122 pix（10.7×13.4μm），染色质网的费雷特直径（ n = 50）测量为17.3±1.8 pix （1.9±0.5μm）和染色质网络距离（ n= 50）测量4.4±1.6像素（0.49±0.18μm），以及（2）具有不同直径（10.4、15.9和18.1μm）和网络宽度0.4μm的Kirsch边缘检测的样本图像。方法：定义了三种可能影响细胞学分形分析结果的偏倚。（1）核位置偏差：通过在8罗盘方向上将256×256 pix（28.1μm）方形框中间的核的原始位置移动而生成的9个不同位置的图像。（2）核旋转偏差：通过以45°增量（0°，45°，90°，135°，180°，225°，270°和315°）旋转核的原始位置而获得的8种不同旋转的图像）。（3）核尺寸偏差：具有相同网格图案（网络宽度：8像素[0.4μm]的各种尺寸（直径：190 pix [10.4μm]，290 pix [15.9μm]和330 pix [18.1μm]）的图像]）在512×512像素正方形内。BC方法的不同外部截止值（256、128、64、32、16结果：外部截止值为32 pix的BC方法导致分形维数变化最小。具体而言，在临界值为32 pix时，核位置偏差，核旋转偏差和核尺寸偏差的CV为＃x3c； 1％（分别为0.1％，0.4％和0.3％），位置之间无显着差异和旋转偏差（ p = 0.19）。我们的研究表明，外部截止值为32 pix的BC方法适用于分析染色质与染色质网格的复杂性。
细胞学学报