基于圖像協(xié)方差無關(guān)的增量特征提取方法研究
doi: 10.11999/JEIT181138
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天津理工大學天津市先進機電系統(tǒng)設(shè)計與智能控制重點實驗室 ??天津 ??300384
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天津理工大學機電工程國家級實驗教學示范中心 ??天津 ??300384
基金項目: 國家重點研發(fā)計劃(2017YFB1303304)，天津市科技計劃重大專項(17ZXZNGX00110)，天津市自然科學重點基金(16JCZDJC30400)
An Incremental Feature Extraction Method without Estimating Image Covariance Matrix
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Tianjin Key Laboratory for Advanced Mechatronical System Design and Intelligent Control, Tianjin University of Technology, Tianjin 300384, China
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National Experimental Teaching Demonstration Center of Electromechanical Engineering, Tianjin University of Technology, Tianjin 300384, China
Funds: The National Key R & D Plan of China (2017YFB1303304), The Tianjin Science and Technology Planed Key Project (17ZXZNGX00110), The Tianjin Natural Science Key Foundation (16JCZDJC30400)
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摘要: 針對2維主成分分析(2DPCA)算法無法實現(xiàn)在線特征提取及無法體現(xiàn)完整數(shù)據(jù)結(jié)構(gòu)信息等問題，該文提出一種基于圖像協(xié)方差無關(guān)的增量式2DPCA(I2DPCA)算法。該算法無需對圖像協(xié)方差矩陣進行特征值分解奇異值分解，復雜度將大為降低，提高了特征提取速度。針對I2DPCA僅提取了橫向特征的問題，又提出一種增量式行列順序2DPCA(IRC2DPCA)算法，該算法對I2DPCA的特征矩陣再次進行縱向特征提取，保留了圖像的橫向與縱向結(jié)構(gòu)信息，實現(xiàn)了行列兩個方向上的特征提取與數(shù)據(jù)降維。最后，以自建的物塊數(shù)據(jù)集、通用的ORL和Yale人臉數(shù)據(jù)集分別進行對比實驗，結(jié)果表明，該文算法在收斂率、分類率及復雜度等性能方面均得到了顯著提高，其收斂率達到99%以上，分類率可達97.6%，平均處理速度為29 幀/s，能夠滿足增量特征提取的實時處理需求。
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關(guān)鍵詞:
- 模式識別 /
- 協(xié)方差無關(guān) /
- 特征提取 /
- 增量學習 /
- 2維主成分分析
Abstract: To solve the problems that Two-Dimensional Principal Component Analysis (2DPCA) can not implement the on-line feature extraction and can not represent the complete structure information, an Incremental 2DPCA (I2DPCA) without estimating covariance matrices is presented by an iterative estimation method, not to deal with the image covariance matrices by the eigenvalue decomposition or the singular value decomposition. The complexity will be greatly reduced and the on-line feature extraction speed can be improved. The proposed I2DPCA can only extract the horizontal features, and thus another Incremental Row-Column 2DPCA (IRC2DPCA) is proposed to incrementally extract the longitudinal ones from the feature matrices of the I2DPCA. The IRC2DPCA can preserve the horizontal and longitudinal features and implement the dimensionality reduction in both row and column directions. Finally, a series of experiments are carried out with the self-built block dataset, ORL and Yale face datasets, respectively. The results show that the proposed algorithms have significantly improved the performances of the convergence rate, the classification rate and the complexity. The convergence rate is over 99%, the classification rate can reach 97.6% and the average processing speed is about 29 frames per second, and it can meet the on-line feature extraction requirements for incremental learning. -
表 1 不同數(shù)據(jù)集下特征向量收斂率的均值及標準差
數(shù)據(jù)集 輸入次數(shù) I2DPCA(均值/標準差) IRC2DPCA(均值/標準差) 前4個特征向量 后4個特征向量 前4個特征向量 后4個特征向量 物塊 $m = 2$ 0.99442/0.00361 0.86836/0.17826 0.98964/0.00573 0.96564/0.01135 $m = 5$ 0.99924/0.00041 0.95478/0.15818 0.99824/0.00101 0.97302/0.01020 $m = 10$ 0.99981/0.00010 0.98453/0.02225 0.99950/0.00030 0.99495/0.00322 ORL $m = 2$ 0.99991/0.00004 0.89400/0.06763 0.99753/0.00203 0.98175/0.01027 $m = 5$ 0.99997/0.00002 0.91620/0.05154 0.99951/0.00037 0.99441/0.00231 $m = 10$ 0.99998/0.00001 0.92833/0.05163 0.99986/0.00010 0.99755/0.00074 Yale $m = 2$ 0.93732/0.07244 0.96069/0.03026 0.99602/0.00441 0.98308/0.00659 $m = 5$ 0.96001/0.04678 0.98261/0.01609 0.99924/0.00074 0.99528/0.00140 $m = 10$ 0.97283/0.03180 0.99041/0.00970 0.99975/0.00024 0.99793/0.00088 
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表 2 物塊數(shù)據(jù)集的最佳分類率
每類訓練
樣本數(shù)2DPCA
(120×4)[8]RC2DPCA
(8×8)[11]Angle-2DPCA
(120×4)[12]BA2DPCA
(8×8)[13]BDPCA
(8×8)[10]IBDPCA
(8×8)[17]I2DPCA
(120×4)IRC2DPCA
(8×8)L=10 0.933 0.927 0.922 0.931 0.930 0.930 0.926 0.922 L=25 0.957 0.960 0.958 0.961 0.959 0.959 0.962 0.968 L=50 0.959 0.961 0.961 0.961 0.961 0.967 0.962 0.972 L=75 0.954 0.957 0.954 0.957 0.958 0.956 0.955 0.958 L=100 0.966 0.963 0.966 0.964 0.963 0.973 0.971 0.976
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表 3 ORL數(shù)據(jù)集的最佳分類率
每類訓練
樣本數(shù)2DPCA
(112×4)[8]RC2DPCA
(8×8)[11]Angle-2DPCA
(112×4)[12]BA2DPCA
(8×8)[13]BDPCA
(8×8)[10]IBDPCA
(8×8)[17]I2DPCA
(112×4)IRC2DPCA
(8×8)L=1 0.744 0.728 0.742 0.725 0.728 0.708 0.736 0.717 L=2 0.850 0.844 0.850 0.847 0.847 0.844 0.847 0.841 L=3 0.868 0.857 0.868 0.861 0.861 0.846 0.864 0.857 L=4 0.888 0.896 0.888 0.892 0.904 0.904 0.883 0.900 L=5 0.905 0.905 0.905 0.905 0.915 0.915 0.905 0.925
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表 4 Yale數(shù)據(jù)集的最佳分類率
每類訓練
樣本數(shù)2DPCA
(100×4)[8]RC2DPCA
(8×8)[11]Angle-2DPCA
(100×4)[12]BA2DPCA
(8×8)[13]BDPCA
(8×8)[10]IBDPCA
(8×8)[17]I2DPCA
(100×4)IRC2DPCA
(8×8)L=1 0.560 0.560 0.560 0.560 0.560 0.553 0.573 0.560 L=2 0.719 0.733 0.719 0.733 0.741 0.741 0.726 0.726 L=3 0.800 0.808 0.792 0.800 0.817 0.825 0.792 0.825 L=4 0.857 0.876 0.857 0.876 0.876 0.876 0.857 0.867 L=5 0.856 0.889 0.856 0.889 0.889 0.889 0.856 0.889
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表 5 物塊數(shù)據(jù)集處理的所需時間對比(s)
算法 L=10 L=25 L=50 L=75 L=100 特征提取 分類識別 特征提取 分類識別 特征提取 分類識別 特征提取 分類識別 特征提取 分類識別 2DPCA(120×4)[8] 2.152 5.279 9.568 6.561 32.745 7.990 69.065 9.015 123.779 10.319 RC2DPCA(8×8)[11] 2.029 0.941 9.208 1.140 32.630 1.362 66.446 1.335 115.344 1.554 Angle-2DPCA(120×4)[12] 4.991 1.097 15.604 1.174 93.28 1.296 67.788 1.471 57.624 1.545 BA2DPCA(8×8)[13] 13.117 1.179 14.261 1.190 46.107 1.203 65.105 1.250 48.089 1.233 BDPCA(8×8)[10] 2.356 0.933 9.456 0.966 32.988 1.248 67.501 1.414 127.39 1.556 IBDPCA(8×8)[17] 11.826 0.868 29.074 1.055 56.778 1.221 86.120 1.408 114.845 1.604 I2DPCA(120×4) 3.103 5.361 7.381 6.225 14.693 7.778 21.938 8.963 29.039 11.181 IRC2DPCA(8×8) 7.159 0.846 17.047 1.043 34.413 1.266 51.577 1.443 65.510 1.669
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表 6 物塊數(shù)據(jù)集處理的所需內(nèi)存對比(kB)
算法 L=10 L=25 L=50 L=75 L=100 特征提取 分類識別 特征提取 分類識別 特征提取 分類識別 特征提取 分類識別 特征提取 分類識別 2DPCA(120×4)[8] 16.658 70.889 37.588 69.935 72.753 68.149 107.941 66.383 143.179 64.622 RC2DPCA(8×8)[11] 16.736 11.354 38.199 11.423 73.977 11.227 109.867 10.805 145.764 10.612 Angle-2DPCA(120×4)[12] 16.096 48.774 16.096 48.118 16.080 46.768 16.080 45.596 16.080 44.440 BA2DPCA(8×8)[13] 16.080 21.642 16.088 21.142 16.104 20.57 16.12 20.504 16.096 20.036 BDPCA(8×8)[10] 16.379 11.345 37.040 11.427 71.663 11.243 106.438 10.768 141.160 10.620 IBDPCA(8×8)[17] 8.830 11.382 8.499 11.403 8.482 11.218 8.478 10.780 8.486 10.612 I2DPCA(120×4) 8.847 70.897 8.503 69.935 8.486 68.141 8.486 66.301 8.503 64.602 IRC2DPCA(8×8) 8.511 11.350 8.507 11.419 8.486 11.243 8.536 10.797 8.511 10.604
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