测绘地理信息   2017, Vol. 42 Issue (4): 77-80 0
 顾及分形理论的多特征海底底质分类 [PDF全文]

1. 武汉大学动力与机械学院，湖北 武汉，430072;
2. 武汉大学测绘学院，湖北 武汉，430079

Seabed Classification Based on Multiple Features of Fractal
ZHANG Hongmei1, ZHANG Yiting2, HE Linbang2
1. School of Power and Mechanical Engineering, Wuhan University, Wuhan 430072, China;
2. School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China
Abstract: Aimed at the poor seabed classification reliability of traditional single fractal dimension, this paper puts forward a seabed classification of considering fractal dimension, lacunarity and multi-fractal. Combining gray statistical information such as mean value, standard deviation and median, a full feature vector is constructed and principal component analysis is carried out on later sediment classification work. The method of our proposed is applied to the Jiaozhou bay, and reliable experiment results have been obtained.
Key words: seabed classification     fractal     lacunarity     multifractal     principal component analysis

1 回波强度特征提取 1.1 分形维数

 $d = \mathop {\lim }\limits_{\varepsilon \to 0} \left[{{\rm{log}}N(\varepsilon )/{\rm{log}}\left( {\frac{1}{\varepsilon }} \right)} \right]$ (1)

 ${n_r}(i, j) = l-k + 1$ (2)

 ${N_r} = \sum\limits_{i, j} {{n_r}(i, j)}$ (3)

 $D = \lim \frac{{\log ({N_r})}}{{\log (1/r)}}$ (4)

3种典型底质如图 1所示，DBC方法分形维数计算结果如下：沙为2.18，泥为2.33，砾石为2.87。

 图 1 三种典型海底底质灰度图 Figure 1 Grey-Scale Maps of Three Typical Sediments

1.2 空隙

 $C(L) = \frac{{M(L)-N(L)}}{{M(L) + N(L)}}$ (5)

 $M\left( L \right) = \frac{P}{{{N_r}}}, N\left( L \right) = \frac{{{N_r}}}{P}$ (6)

 $C\left( L \right) = \frac{{{P^2}-{N_r}^2}}{{{P^2} + {N_r}^2}}$ (7)

1.3 多重分形

 $\mathop {\lim }\limits_{r \to 0} {\mu _r}(x)\sim {r^a}$ (8)

 ${\mu _r}\left( {i, j} \right) = {n_r}\left( {i, j} \right)/{N_r}$ (9)

 $\chi \left( {q, r} \right) = \sum {[{\mu _r}\left( {i, j} \right)]^q} \approx {r^{\tau (q)}}$ (10)

 $(q-1)D(q) \equiv \tau (q) = \mathop {\lim }\limits_{r \to 0} \frac{{{\rm{In}}\chi (q, r)}}{{{\rm{In}}r}}, q \ne 1$ (11)

1.4 灰度基本统计量

 $u = \frac{1}{{mn}}\sum\limits_{i = 1}^m {\sum\limits_{j = 1}^n {{x_{ij}}} }$ (12)

 $\sigma = \sqrt {\frac{1}{{mn}}\sum\limits_{i = 1}^m {\sum\limits_{j = 1}^n {{{\left( {{x_{ij}}-u} \right)}^2}} } }$ (13)

2 特征向量主成分分析及分类

 $\boldsymbol{X} = \left[{\begin{array}{*{20}{c}} {{x_{11}}}& \cdots &{{x_{1p}}}\\ \vdots &{}& \vdots \\ {{x_{n1}}}& \cdots &{{x_{np}}} \end{array}} \right]$ (14)

 ${\boldsymbol{Y}_i} = {a_{i1}}{\boldsymbol{X}_1} + {a_{i2}}{\boldsymbol{X}_2} + \cdots + {a_{ip}}{\boldsymbol{X}_p}$ (15)
 $\mathit{\boldsymbol{Y}} = \mathit{\boldsymbol{X \boldsymbol{\varPhi} }}$ (16)

 ${x_0} = \frac{{x-{\rm{ave}}}}{{{\rm{std}}}}$ (17)

 $\boldsymbol{R} = \frac{{\boldsymbol{X}_0^{\rm{T}}{\boldsymbol{X}_0}}}{{n-1}}$ (18)

 ${s_i} = \frac{{{b_i}-{a_i}}}{{\max ({a_i}, {b_i})}}$ (19)

3 底质分类实验结果与分析

 图 2 多特征样本主成分图(左)及分类图(右) Figure 2 Diagram of Principal Component of Multi-feature Sample (Left) and Clustering Result (Right)

 图 3 传统方法样本主成分图(左)和样本分类图(右) Figure 3 Diagram of Principal Component of Traditional Method (Left) and Clustering Result (Right)

 图 4 多特征分类方法(左)与传统方法(右)分类结果的轮廓系数指标图 Figure 4 Silhouette Coefficient Index of Multi-feature Classification (Left) and Traditional Classification (Right)

4 结束语

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