密度指数：形状指数在描述三维图像时的推广

摘要

针对将形状指数(SI)应用于三维图像时缺乏对应的推广形式，常通过计算三维图像的3个截面的 SI 来组合表达，导致在肠道肿瘤检测等应用中造成了大量的误检的问题，研究了三维情形 SI 的推广.首先选取球坐标系表达的单位球面以消除灰度变化尺度的影响；然后分析了球面的6个等价区域，并选取其一作为灰度变化的表征区域；由于 SI 原有的表达式不利于推广到三维空间，因此推导了一种等价的表达式，并通过分析此表达式在三维情形的推广，得到了描述三维图像局部灰度变化的指标——密度指数(DI).通过研究 DI 所表征区域的几何特性，得到了一条具有重要性质的曲线——逆Z线，并分析了其上典型特征点所对应的灰度变化模式.仿真实验结果表明，对于肠道肿瘤检测的典型情况，使用DI检测的误检率明显低于SI.%When applying to the quantifying intensity variation of the neighborhood of a voxel in a 3D image, shape index (SI) lacks an extended form and currently uses the combination of the three computed SI values based on three orthogonal sections of the neighborhood, which results in massive false detection. To cope with the problem, the extended form of SI was studied. First, in a spherical coordinates system, an unit sphere was chosen to remove the interference stemmed from the variation of intensity scale; Second, in the unit sphere, 6 equivalent regions were analyzed and one of them was selected as the representative region; Third, because the original cal-culation formula of SI is hard to extend, an equivalent formula of SI was deduced and it was extended to the case of describing the variation of intensity for a local region of a 3D image and the derived index is density index (DI); Fourth, by analyzing the geometrical properties of the definition domain of DI, a curve with important qualities— inverse Z line was introduced and the intensity variation patterns of some typical points in it were studied. The simulation results show that the false detection rate of DI is much lower than SI for the typical cases of polyp de-tection in colon walls.