Underwater Optical Image Recognition Based on Dual Flexible Metric Adaptive Weighted 2DPCA
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摘要: 受观测条件和采集场景等因素影响，水下光学图像通常呈现出高维小样本特性且易伴随着噪声信息干扰，导致许多降维方法对其识别过程中的鲁棒表现力不足。为解决上述问题，该文提出一种新颖的双灵活度量自适应加权2维主成分分析方法(DFMAW-2DPCA)应用于水下图像识别。该方法不仅在建立重构误差和方差之间双层关系中同时使用了灵活的鲁棒距离度量机制，而且能够根据每个样本实际状态自适应学习到与之相匹配的权重，有效增强了模型在水下噪声干扰环境下的鲁棒性并实现识别精度的提升。与此同时，该文设计了一个快速非贪婪算法用于最优解的获取，其具有良好的收敛性。通过3个水下图像数据库中进行大量实验的结果表明，DFMAW-2DPCA在同类方法中具有更为杰出的整体性能。Abstract: Influenced by factors such as observation conditions and acquisition scenarios, underwater optical image data usually presents the characteristics of high-dimensional small samples and is easily accompanied with noise interference, resulting in many dimension reduction methods lacking robust performance in their recognition process. To solve this problem, a novel 2DPCA method for underwater image recognition, called Dual Flexible Metric Adaptive Weighted 2DPCA (DFMAW-2DPCA), is proposed. DFMAW-2DPCA not only utilizes a flexible robust distance metric mechanism in establishing a dual-layer relationship between reconstruction error and variance, but also adaptively learn matching weights based on the actual state of each sample, which effectively enhances the robustness of the model in underwater noise interference environments and improves recognition accuracy. In this paper, a fast nongreedy algorithm for obtaining the optimal solution is designed and has good convergence. The extensive experimental results on three underwater image databases show that DFMAW-2DPCA has more outstanding overall performance than other 2DPCA-based methods.
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1 DFMAW-2DPCA优化求解算法
输入：样本增广矩阵$ {\boldsymbol{A}} \in {R ^{mN \times n}} $，特征维度$ k $和$ p \in \left( {0,2} \right) $，其中样本数据$ {{\boldsymbol{A}}_i} $已完成数据中心化处理。 初始化：$ {{\boldsymbol{V}}^{\left( {t - 1} \right)}} \in {{{R}}^{n \times k}} $，其满足$ {{\boldsymbol{V}}^{\mathrm{T}}}{\boldsymbol{V}} = {{\boldsymbol{I}}_k} $，$ t = 1 $，$ \delta = 0.01 $。 当 不收敛时 执行 1：分别利用式(7)、式(10)和式(11)计算对角矩阵$ {{\boldsymbol{D}}^{\left( {t - 1} \right)}} $，$ {{\boldsymbol{S}}^{\left( {t - 1} \right)}} $和$ {{\boldsymbol{G}}^{\left( {t - 1} \right)}} $的对角元素$ \alpha _{ij}^{\left( {t - 1} \right)} $，$ s_{ij}^{\left( {t - 1} \right)} $和$ g_{ij}^{\left( {t - 1} \right)} $。 2：利用式(16)计算$ l_{ij}^{\left( {t - 1} \right)} $，并同时构建由对角元素$ {1 \mathord{\left/ {\vphantom {1 {l_{ij}^{\left( {t - 1} \right)}}}} \right. } {l_{ij}^{\left( {t - 1} \right)}}} $所组成的对角矩阵$ {{\boldsymbol{L}}^{\left( {t - 1} \right)}} $。 3：计算对角矩阵$ {{\boldsymbol{U}}^{\left( {t - 1} \right)}} $的对角元素$ u_{ij}^{\left( {t - 1} \right)} $，其中$ u_{ij}^{\left( {t - 1} \right)} = {1 \mathord{\left/ {\vphantom {1 {l_{ij}^{\left( {t - 1} \right)}}}} \right. } {l_{ij}^{\left( {t - 1} \right)}}}\left( {s_{ij}^{\left( {t - 1} \right)} + \alpha _{ij}^{\left( {t - 1} \right)}g_{ij}^{\left( {t - 1} \right)}} \right) $。 4：计算加权协方差矩阵$ {{\boldsymbol{A}}^{\mathrm{T}}}{{\boldsymbol{U}}^{\left( {t - 1} \right)}}{\boldsymbol{A}} $。 5：求解目标函数式(8)的最优投影矩阵$ {{\boldsymbol{V}}^{\left( t \right)}} $，$ {{\boldsymbol{V}}^{\left( t \right)}} $是由$ {{\boldsymbol{A}}^{\mathrm{T}}}{{\boldsymbol{U}}^{\left( {t - 1} \right)}}{\boldsymbol{A}} $的前$ k $个最大特征值所对应特征向量组成。 6：检验收敛条件$ J({{\boldsymbol{V}}^{\left( t \right)}}) - J({{\boldsymbol{V}}^{\left( {t - 1} \right)}}) \le \delta $满足；如果满足，结束循环；否则执行步骤7。 7：通过获取到的$ {{\boldsymbol{V}}^{\left( t \right)}} $完成对角矩阵$ {{\boldsymbol{D}}^{\left( t \right)}} $，$ {{\boldsymbol{S}}^{\left( t \right)}} $和$ {{\boldsymbol{G}}^{\left( t \right)}} $中的每个对角元素$ \alpha _{ij}^{\left( t \right)} $，$ s_{ij}^{\left( t \right)} $和$ g_{ij}^{\left( t \right)} $的计算。 8：根据$ {{\boldsymbol{V}}^{\left( t \right)}} $，$ \alpha _{ij}^{\left( t \right)} $，$ s_{ij}^{\left( t \right)} $和$ g_{ij}^{\left( t \right)} $执行对于对角矩阵$ {{\boldsymbol{L}}^{\left( t \right)}} $中每个对角元素$ {1 \mathord{\left/ {\vphantom {1 {l_{ij}^{\left( t \right)}}}} \right. } {l_{ij}^{\left( t \right)}}} $的计算。 9：完成对角矩阵$ {{\boldsymbol{U}}^{\left( t \right)}} $中每个对角元素$ u_{ij}^{\left( t \right)} $的计算。 10：$ t \leftarrow t + 1 $。 结束循环 输出：$ {{\boldsymbol{V}}^{\left( t \right)}} \in {{{R}}^{n \times k}} $。 
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表 1 NF数据库中每种方法的平均最优识别准确率(%)和平均最小重构误差及其所对应的标准差
2DPCA-L1 F-2DPCA Angle-2DPCA GC-2DPCA Cos-2DPCA 2DPCA-2-LP DFMAW-2DPCA p =0.5 p = 1 p =1.5 识别精度 80.25±0.76 85.77±0.69 87.16±0.82 87.50±0.85 88.27±0.66 88.64±0.65 89.85±0.60 88.42±0.68 89.38±0.64 重构误差 462.47±2.14 415.86±1.92 391.25±2.01 382.04±1.97 364.59±1.88 356.78±1.90 326.14±1.81 357.51±1.92 338.92±1.86
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表 2 JEDI数据库中每种方法的平均最优识别准确率(%)和平均最小重构误差及其所对应的标准差
2DPCA-L1 F-2DPCA Angle-2DPCA GC-2DPCA Cos-2DPCA 2DPCA-2-LP DFMAW-2DPCA p =0.5 p = 1 p =1.5 识别精度 68.70±0.64 73.15±0.72 73.77±0.73 74.29±0.67 75.06±0.58 75.63±0.61 76.67±0.56 75.30±0.58 76.07±0.53 重构误差 226.59±1.75 210.36±1.68 193.42±1.84 178.90±1.65 155.81±1.60 146.04±1.57 121.53±1.62 149.64±1.67 133.42±1.63
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表 3 EPIDHEU数据库中每种方法的平均最优识别准确率(%)和平均最小重构误差及其所对应的标准差
2DPCA-L1 F-2DPCA Angle-2DPCA GC-2DPCA Cos-2DPCA 2DPCA-2-LP DFMAW-2DPCA p =0.5 p = 1 p =1.5 识别精度 77.38±1.57 82.79±1.81 83.71±1.73 84.25±1.59 84.96±1.55 85.50±1.52 86.04±1.54 85.25±1.50 86.54±1.56 重构误差 300.47±3.21 279.80±3.08 268.92±3.03 261.76±3.10 245.28±2.93 236.04±2.97 232.42±2.90 240.53±2.89 227.34±2.92
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表 5 3个水下图像数据库中每种方法的平均运行时间与对应的标准差(s)
2DPCA-L1 F-2DPCA Angle-2DPCA GC-2DPCA Cos-2DPCA 2DPCA-2-LP DFMAW-2DPCA NF 11.26±0.58 2.13±0.15 5.60±0.44 4.79±0.37 3.08±0.30 3.15±0.34 3.19±0.25 JEDI 7.53±0.46 1.84±0.12 3.37±0.49 2.68±0.34 2.26±0.32 2.31±0.28 2.37±0.21 EPIDHEU 6.24±0.77 1.52±0.18 2.64±0.61 2.21±0.40 1.80±0.39 1.83±0.36 1.88±0.32
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