测量分形维数。对边缘处理函数的敏感性。

Cross S S, Cotton D W, Underwood J C

Department of Pathology, University of Sheffield Medical School, U.K.

Anal Quant Cytol Histol. 1994 Oct;16(5):375-9.

The fractal dimension is a useful tool in quantitative histology and cytology, and its measurement is easily implemented on computerized image analysis systems. However, the optimal conditions for capture of images and the effect of image-processing functions on the measurement of the fractal dimension have not been reported. Edge-processing functions were applied to images of Euclidean (square) and fractal (Koch island, renal angiogram) objects. The fractal dimension of processed images was measured using implementation of the box-counting method, and the area of thresholded image was also recorded. The method was shown to be accurate, with errors of < 1.5% for objects with known fractal dimensions, and highly reproducible, with a reliability coefficient of 0.972 (95% confidence limits of 0.868-0.987). The fractal dimension of the fractal images showed a marked (> 15%) reduction when a binary noise reduction function was applied with the minimum neighbors limit set above 3. In contrast, the fractal dimension of the Euclidean square was unchanged by this function. The reduction in fractal dimension was due to the erosion of complex convolutions at the edge of the fractal objects. Edge-processing functions should be avoided when manipulating images of fractal objects.

分形维数是定量组织学和细胞学中的一种有用工具，并且其测量在计算机图像分析系统上易于实现。然而，图像采集的最佳条件以及图像处理功能对分形维数测量的影响尚未见报道。边缘处理功能应用于欧几里得（正方形）和分形（科赫岛、肾血管造影）物体的图像。使用盒计数法测量处理后图像的分形维数，并记录阈值图像的面积。结果表明该方法准确，对于已知分形维数的物体误差<1.5%，且具有高度可重复性，可靠性系数为0.972（95%置信限为0.868 - 0.987）。当应用二进制降噪功能且最小邻域限制设置在3以上时，分形图像的分形维数显著降低（>15%）。相比之下，该功能对欧几里得正方形的分形维数没有影响。分形维数的降低是由于分形物体边缘复杂卷积的侵蚀。在处理分形物体的图像时应避免使用边缘处理功能。