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. 2014 Oct 21;9(10):e110318.
doi: 10.1371/journal.pone.0110318. eCollection 2014.

Low-rank and eigenface based sparse representation for face recognition

Yi-Fu Hou  1 , Zhan-Li Sun  1 , Yan-Wen Chong  2 , Chun-Hou Zheng  1
Affiliations

Low-rank and eigenface based sparse representation for face recognition

Yi-Fu Hou et al. PLoS One. .

Erratum in

Abstract

In this paper, based on low-rank representation and eigenface extraction, we present an improvement to the well known Sparse Representation based Classification (SRC). Firstly, the low-rank images of the face images of each individual in training subset are extracted by the Robust Principal Component Analysis (Robust PCA) to alleviate the influence of noises (e.g., illumination difference and occlusions). Secondly, Singular Value Decomposition (SVD) is applied to extract the eigenfaces from these low-rank and approximate images. Finally, we utilize these eigenfaces to construct a compact and discriminative dictionary for sparse representation. We evaluate our method on five popular databases. Experimental results demonstrate the effectiveness and robustness of our method.

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Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.

Figures

Figure 1
Figure 1. The relation between face matrix and eigenface matrix.
Each column of matrix formula image represents a eigenface, and each sample (column) in face matrix formula image can be represented by eigenfaces in eigenface matrix formula image with eigenface expression pattern (column in matrix formula image) of the corresponding sample.
Figure 2
Figure 2. Overview of our method.
Figure 3
Figure 3. The relation between recognition rates and the corresponding parameter .
Figure 4
Figure 4. Accuracy rate of different number of eigenfaces.
The number of eigenfaces 1, 2, 3, 4, 6, 8, 10, 12, 14 correspond to 25.95%, 74.59%, 90.30%, 96.46%, 98.31%, 98.89%, 99.47%, 99.30%, 99.47%.
Figure 5
Figure 5. An example of Robust PCA algorithm on the Extended Yale B Face Database.
First row is the original images with vary illumination and expression changes. Second row shows the low rank and approximate images of (a). Third row is the sparse error images of (a) which is the difference of (a) and (b).
Figure 6
Figure 6. The relation between ranks of face matrices and number of iterations.
Top-left represents the relation between the rank of first class face matrix and the number of iterations on Yale B Face Database with 40 training samples. Top-right, bottom-left and bottom-right represent that of second, third and forth class face matrices, respectively.
Figure 7
Figure 7. Some examples from the CMU-PIE Face Database with variation in illumination, expression.
Figure 8
Figure 8. Classification errors under different number of weak classifier.
Figure 9
Figure 9. An example from the AR Database with 30% pixels corruptions.
The top row is the original images. The middle row shows corrupted images of (a) with 30% pixels replaced by random noises. The noise values are random selected from [0, 255] and the locations are unknown. The below row is the recovered low-rank images of (b) by Robust PCA algorithm.
Figure 10
Figure 10. Recognition accuracy on the AR Database with different percentage of pixels corruptions.
Figure 11
Figure 11. The separate effect of these two sub-processes of ESRC_LR algorithm on the AR Database with increasing corrupted pixels.
Figure 12
Figure 12. An example of images from UMIST Face Database with random block occlusions ().
Figure 13
Figure 13. Recognition rates on UMIST Face Database with different level of block occlusions.
See this image and copyright information in PMC

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