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表1 分形纹理特征公式及含义

Tab.1 Formulas and meanings of fractal texture features

特征名称	计算公式	说明
均值	$μ_{FD} = \frac{1}{MN} \overset{M}{\sum_{i = 1}} \overset{N}{\sum_{j = 1}} I_{FD} (i, j)$	计算区域的分形维数的均值
方差	$σ_{FD} = \sqrt[]{\frac{1}{MN} \overset{M}{\sum_{i = 1}} \overset{N}{\sum_{j = 1}} (I_{FD} (i, j) - μ_{FD})^{2}}$	计算区域的分形维数的方差
对比度(CON)	$CO N_{FD} = \overset{L}{\sum_{n = 1}} n^{2} [\overset{M}{\sum_{i = 1}} \overset{N}{\sum_{j = 1}} \tilde{p} (i, j)], \| i - j \| = n$	度量局部区域变化,值越小纹理越均匀
相异性(DIS)	$DI S_{FD} = \overset{M}{\sum_{i = 1}} \overset{N}{\sum_{j = 1}} \tilde{p} (i, j) \|i - j\|$	描述区域内像素与邻近像素的相异性
空隙度(L)	$L_{FD} = \frac{\frac{1}{MN} \overset{M}{\sum_{i = 0}} \overset{N}{\sum_{j = 0}} I_{FD} {(i, j)}^{2}}{(\frac{1}{MN} \overset{M}{\sum_{i = 0}} \overset{N}{\sum_{j = 0}} I_{FD} {(i, j))}^{2}} - 1$	计算区域中分形维数的“块度”,空隙度越大表明区域同质性越强
角二阶矩(ASM)	$AS M_{FD} = \overset{M}{\sum_{i = 1}} \overset{N}{\sum_{j = 1}} {\tilde{p}}^{2} (i, j) \lg [\tilde{p} (i, j)]$ 其中: $\tilde{p} (i, j) = \frac{1}{\sqrt[]{2 π σ_{I_{FD}}}} \exp (- \frac{(I_{FD} (i, j) - μ_{FD})^{2}}{2 σ_{FD}^{2}})$	度量区域的紊乱性,值越小,表明区域越均匀,其中, $\tilde{p} (i, j)$ 为分形维数图像中坐标为 $(i, j)$ 处像素点属于所在类的归一化概率值
熵(ENT)	$EN T_{FD} = - \overset{M}{\sum_{i = 1}} \overset{N}{\sum_{j = 1}} \tilde{p} (i, j) \lg [\tilde{p} (i, j)]$	度量区域内像素的随机性,值越大表明纹理越复杂
同质性(HOM)	$HO M_{FD} = \overset{M}{\sum_{i = 1}} \overset{N}{\sum_{j = 1}} \frac{\tilde{p} (i, j)}{1 + \|i - j\|} \tilde{p} (i, j)$	描述区域内像素分布均匀度
偏斜度(S)	$S_{FD} = \frac{E (x - μ_{FD})}{{σ_{FD}}^{3}}$	描述区域内像素分形纹理值的不对称性
逆差距(IDM)	$ID M_{FD} = \overset{M}{\sum_{i = 1}} \overset{N}{\sum_{j = 1}} \frac{1}{1 + {(i - j)}^{2}} \tilde{p} (i, j)$	类似于同质性,但是更强调区域内像素之间的差异性