1. Design of PCA and SVM based face recognition system for intelligent robots
Department of Electrical Engineering, Southern Taiwan University, Tainan County, Taiwan, R.O.C.
Ming-Yuan Shieh, Kuo-Yang Wang, Juing-Shian Chiou,
Yu-Chia Hu, Chung-Chieh Lien and Shih-Wen Cheng
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2. Outline Abstract Introduction Face recognition system
Principal Component Analysis
SVM for recognition
Experimental results
Conclusion
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3. Abstract
This paper proposed the image recognition system that integrates principal component analysis (PCA) and support vector machine (SVM) for intelligent robots.
The integrated scheme aims to apply the SVM method to improve the validity of PCA based image recognition system on dynamic robotic visual perception. Experimental results show that the proposed method simplifies features effectively and obtains more accurate classification.
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4. Introduction
The proposed scheme is applied to the visual perception system of the intelligent robot – Fairy robot for facial recognition. From several experiments, the results show the integrated scheme really benefits the human-robot interaction.
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5. Face recognition system
The procedures of the face detection and recognition system are shown in Figure 1.
Fig. 1. The system flowchart of face detection and recognition.
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6. Principal Component Analysis(1/4)
Suppose there are M samples of normalized facial images, where each one is denoted by an array. By rearranging each array into a vector, the M samples can be as M vectors, denoted as To average them, we get the average vector as .
Assume the covariance matrix of all facial samples C will be
(1)
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7. Principal Component Analysis(2/4)
One can determine the eigenvalues and eigenvectors of C by
One can compute the eigenvalues and the eigenvectors of the matrix , as shown in next equation, firstly because its dimension is only
To multiply both sides of upper equation by the matrix A, we have
(2)
(3)
(4)
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8. Principal Component Analysis(3/4)
In comparison with (2) and (4), while
One can determine the eigenvalues and the eigenvectors of C from (3). The eigenvector ui denotes the eigenface of ith sample face as shown in (6).
(5)
(6)
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9. Principal Component Analysis(4/4)
If we sort the eigenvalues of all samples and then arrange the relative eigenvectors into an eigenspace. Determine the weighting matrix W of the eigenspace as (7)
The vectors in the matrix W can be regarded as trained image data of a sample. Each sample image has a relative matrix W. While finish the computation of W for all samples, it means the training of the face image database has been accomplished.
(7)
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10. SVM for recognition(1/3)
When we use the PCA to identify target feature weight will be followed by the results using SVM recognition. First we define the training sample:
In order to find the division of the hyperplane, we had to resolve the question of quadratic optimization. The constraints were
(8)
(9)
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11. SVM for recognition(2/3)
We also had to determine the minimum value of So, we used the Lagrange multiplier to resolve the question of quadratic optimization with linear constraints. We obtained
After performing the substitution, we were left with the new equation
(10)
(11)
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12. SVM for recognition(3/3)
After the optimal solution to the dual question had been identified, each Lagrange modulus was expected to map onto each trained data. The following equation is the final function
(12)
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13. Fig. 2. The screen of the proposed system interface
Experimental results
Figure 2 shows the processed images which consist of the ones after skin color segmentation, Sobel edge detection, elliptic detection or face recognition.
Fig. 2. The screen of the proposed system interface
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14. Conclusion
The PCA and SVM based image recognition system is proposed for solving face detection and recognition problems on human-robot interaction. The captured face images are preprocessing by the PCA. Then, these data will be analyzed by the SVM. It results in more accuracy on distinguishing facial features for face recognition. The experimental results demonstrate the feasibility of the proposed method.
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15. Thanks for your attention!
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