雙靈活度量自適應(yīng)加權(quán)2DPCA在水下光學(xué)圖像識別中的應(yīng)用
doi: 10.11999/JEIT240359
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1.
南京信息工程大學(xué)人工智能學(xué)院 南京 210044
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內(nèi)河航運技術(shù)湖北省重點實驗室 武漢 430063
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3.
哈爾濱工程大學(xué)智能科學(xué)與工程學(xué)院 哈爾濱 150006
基金項目: 國家自然科學(xué)基金(5217110032)，江蘇省基礎(chǔ)研究計劃基金(BK20220452)，內(nèi)河航運技術(shù)湖北省重點實驗室基金(NHHY2022004)，江蘇省研究生實踐創(chuàng)新計劃項目(SJCX24_0479)
Underwater Optical Image Recognition Based on Dual Flexible Metric Adaptive Weighted 2DPCA
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School of Artificial Intelligence, Nanjing University of Information Science and Technology, Nanjing 210044, China
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Hubei Key Laboratory of Inland Shipping Technology, Wuhan University of Technology, Wuhan 430063, China
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3.
School of Intelligent Systems Science and Engineering, Harbin Engineering University, Harbin 150006, China
Funds: The National Natural Science Foundation of China (5217110032), The Natural Science Basic Research Plan in Jiangsu Province of China (BK20220452), Hubei Key Laboratory of Inland Shipping Technology (NHHY2022004), Jiangsu Province Graduate Student Practice Innovation Program Project (SJCX24_0479)
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摘要: 受觀測條件和采集場景等因素影響，水下光學(xué)圖像通常呈現(xiàn)出高維小樣本特性且易伴隨著噪聲信息干擾，導(dǎo)致許多降維方法對其識別過程中的魯棒表現(xiàn)力不足。為解決上述問題，該文提出一種新穎的雙靈活度量自適應(yīng)加權(quán)2維主成分分析方法(DFMAW-2DPCA)應(yīng)用于水下圖像識別。該方法不僅在建立重構(gòu)誤差和方差之間雙層關(guān)系中同時使用了靈活的魯棒距離度量機制，而且能夠根據(jù)每個樣本實際狀態(tài)自適應(yīng)學(xué)習(xí)到與之相匹配的權(quán)重，有效增強了模型在水下噪聲干擾環(huán)境下的魯棒性并實現(xiàn)識別精度的提升。與此同時，該文設(shè)計了一個快速非貪婪算法用于最優(yōu)解的獲取，其具有良好的收斂性。通過3個水下圖像數(shù)據(jù)庫中進行大量實驗的結(jié)果表明，DFMAW-2DPCA在同類方法中具有更為杰出的整體性能。
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關(guān)鍵詞:
- 模式識別 /
- 魯棒距離度量 /
- 自適應(yīng)加權(quán) /
- 水下光學(xué)圖像 /
- 2維主成分分析
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. -
1 DFMAW-2DPCA優(yōu)化求解算法
輸入：樣本增廣矩陣$ {\boldsymbol{A}} \in {R ^{mN \times n}} $，特征維度$ k $和$ p \in \left( {0,2} \right) $，其中樣本數(shù)據(jù)$ {{\boldsymbol{A}}_i} $已完成數(shù)據(jù)中心化處理。 初始化：$ {{\boldsymbol{V}}^{\left( {t - 1} \right)}} \in {{{R}}^{n \times k}} $，其滿足$ {{\boldsymbol{V}}^{\mathrm{T}}}{\boldsymbol{V}} = {{\boldsymbol{I}}_k} $，$ t = 1 $，$ \delta = 0.01 $。 當(dāng) 不收斂時 執(zhí)行 1：分別利用式(7)、式(10)和式(11)計算對角矩陣$ {{\boldsymbol{D}}^{\left( {t - 1} \right)}} $，$ {{\boldsymbol{S}}^{\left( {t - 1} \right)}} $和$ {{\boldsymbol{G}}^{\left( {t - 1} \right)}} $的對角元素$ \alpha _{ij}^{\left( {t - 1} \right)} $，$ s_{ij}^{\left( {t - 1} \right)} $和$ g_{ij}^{\left( {t - 1} \right)} $。 2：利用式(16)計算$ l_{ij}^{\left( {t - 1} \right)} $，并同時構(gòu)建由對角元素$ {1 \mathord{\left/ {\vphantom {1 {l_{ij}^{\left( {t - 1} \right)}}}} \right. } {l_{ij}^{\left( {t - 1} \right)}}} $所組成的對角矩陣$ {{\boldsymbol{L}}^{\left( {t - 1} \right)}} $。 3：計算對角矩陣$ {{\boldsymbol{U}}^{\left( {t - 1} \right)}} $的對角元素$ 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) $。 4：計算加權(quán)協(xié)方差矩陣$ {{\boldsymbol{A}}^{\mathrm{T}}}{{\boldsymbol{U}}^{\left( {t - 1} \right)}}{\boldsymbol{A}} $。 5：求解目標(biāo)函數(shù)式(8)的最優(yōu)投影矩陣$ {{\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 $個最大特征值所對應(yīng)特征向量組成。 6：檢驗收斂條件$ J({{\boldsymbol{V}}^{\left( t \right)}}) - J({{\boldsymbol{V}}^{\left( {t - 1} \right)}}) \le \delta $滿足；如果滿足，結(jié)束循環(huán)；否則執(zhí)行步驟7。 7：通過獲取到的$ {{\boldsymbol{V}}^{\left( t \right)}} $完成對角矩陣$ {{\boldsymbol{D}}^{\left( t \right)}} $，$ {{\boldsymbol{S}}^{\left( t \right)}} $和$ {{\boldsymbol{G}}^{\left( t \right)}} $中的每個對角元素$ \alpha _{ij}^{\left( t \right)} $，$ s_{ij}^{\left( t \right)} $和$ g_{ij}^{\left( t \right)} $的計算。 8：根據(jù)$ {{\boldsymbol{V}}^{\left( t \right)}} $，$ \alpha _{ij}^{\left( t \right)} $，$ s_{ij}^{\left( t \right)} $和$ g_{ij}^{\left( t \right)} $執(zhí)行對于對角矩陣$ {{\boldsymbol{L}}^{\left( t \right)}} $中每個對角元素$ {1 \mathord{\left/ {\vphantom {1 {l_{ij}^{\left( t \right)}}}} \right. } {l_{ij}^{\left( t \right)}}} $的計算。 9：完成對角矩陣$ {{\boldsymbol{U}}^{\left( t \right)}} $中每個對角元素$ u_{ij}^{\left( t \right)} $的計算。 10：$ t \leftarrow t + 1 $。 結(jié)束循環(huán) 輸出：$ {{\boldsymbol{V}}^{\left( t \right)}} \in {{{R}}^{n \times k}} $。 
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表 1 NF數(shù)據(jù)庫中每種方法的平均最優(yōu)識別準(zhǔn)確率(%)和平均最小重構(gòu)誤差及其所對應(yīng)的標(biāo)準(zhǔn)差
2DPCA-L1 F-2DPCA Angle-2DPCA GC-2DPCA Cos-2DPCA 2DPCA-2-LP DFMAW-2DPCA p =0.5 p = 1 p =1.5 識別精度 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 重構(gòu)誤差 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數(shù)據(jù)庫中每種方法的平均最優(yōu)識別準(zhǔn)確率(%)和平均最小重構(gòu)誤差及其所對應(yīng)的標(biāo)準(zhǔn)差
2DPCA-L1 F-2DPCA Angle-2DPCA GC-2DPCA Cos-2DPCA 2DPCA-2-LP DFMAW-2DPCA p =0.5 p = 1 p =1.5 識別精度 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 重構(gòu)誤差 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數(shù)據(jù)庫中每種方法的平均最優(yōu)識別準(zhǔn)確率(%)和平均最小重構(gòu)誤差及其所對應(yīng)的標(biāo)準(zhǔn)差
2DPCA-L1 F-2DPCA Angle-2DPCA GC-2DPCA Cos-2DPCA 2DPCA-2-LP DFMAW-2DPCA p =0.5 p = 1 p =1.5 識別精度 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 重構(gòu)誤差 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個水下圖像數(shù)據(jù)庫中每種方法的平均運行時間與對應(yīng)的標(biāo)準(zhǔn)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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