Orthogonal filter banks with region Log-TiedRank covariance matrices for face recognition

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Abstract

With the capability of fusing varying features from a specific image region, the Region Covariance Matrices (RCM) image descriptor has been evidenced plausible in face recognition. However, a systematic study for RCM, regarding which features to be fused in particular, remains absent. This paper therefore explores several features derived from the orthogonal filter ensembles, i.e., Identity Transform, Discrete Haar Transform, Discrete Cosine Transform, and Karhunen-Loève Transform, for feature encoding in RCM. Aside from that, we also outline a RCM variant, dubbed Region Log-TiedRank Covariance Matrices (RLTCM) in this paper. The RLTCM descriptor, on average, exhibits dramatic performance gain over RCM as well as state-of-the-art descriptors, especially when probe sets far deviated from the face gallery. Furthermore, we discern that the RLTCM descriptor defined based on Identity Transform, i.e., the simplest form of orthogonal filters, and other learning-free orthogonal filters yield impressive performance on par with the learning-based counterparts.

Introduction

For face representation, the holistic and the local structural appearance emerge as two prominent approaches in literature. The longstanding holistic approaches, including the principal component analysis (PCA) [1], the linear discriminant analysis (LDA) [2], and other relevant variants [72], [73], [74], projects the entire face image, or a sub-block, into a feature subspace for a compact and discriminative representation. In comparison to PCA and LDA, the local appearance approaches that capture the local structures is often shown to be relatively superior. A prevalent local appearance instance is the Local Binary Pattern (LBP) [3], originally proposed by Ojala et al. [4] as a local texture descriptor. It encodes the local neighborhood differences with respect to the center pixel as histogram features, and it has been demonstrated to be robust to the illumination variation. Another distinguished local appearance instance is the Gabor-based descriptor in [5], which extracts multi-orientation, multi-scale local structures. Recently, a number of learning-based local appearance approaches have been proposed. The PCA network (PCANet) [6], proposed by Chan et al., is an unsupervised convolutional neural network leveraging PCA to learn a multilayer filter bank. The 2-layer PCA not only performs well in the object classification tasks, including face. The binarized statistical image features (BSIF) [7], on the contrary, learns statistically independent component analysis (ICA) filters for feature extraction. The BSIF descriptor shows remarkable performance on the challenging labelled faces in the wild (LFW) dataset [8,9].

In this work, we focus on a less well-known but powerful local appearance descriptor for face recognition i.e., region covariance matrices (RCM) [10]. RCM, in general, encodes the local regional features with covariance matrices. This permits the correlated image cues, e.g., pixel location, pixel intensity, and filter responses, to be fused with the spatial information. Despite of being low in dimensionality, it has showed favorable performance on object detection and tracking tasks [10], [11], [12]. Aside from that, Pang et al. [13] adopted Gabor filters as mapping function for RCM in face recognition, coined as GRCM. The promising performance has motivated various GRCM variants in the biometric-related domain, e.g., kernel GRCM, weighted GRCM, etc. [14], [15], [16], [17]. However, the RCM beyond Gabor filters as a means of face descriptor remains unexplored.

Section snippets

Related works

In this section, we review the most traditional Region Covariance Matrices (RCM) [10], followed by its extension, specifically, Gabor-based RCM (GRCM) [13] for face recognition.

Preliminary

In this section, we provide a brief on Tensor manifold where a covariance matrix resides, followed by Spearman’s rank correlation coefficient.

Orthogonal filter banks

In this section, the four pre-selected orthogonal filter banks and their respective basis selection schemes are detailed.

RLTCM descriptor

This section elaborates the RLTCM descriptor derivation based on the filer responses of IT, DHT, DCT and KLT. As reported earlier in [21], the generic RLTCM pipeline is schematically portrayed in Fig. 82. Unlike the handcrafted IT, DHT, and DCT

Experiments and discussions

This section analyses the RLTCM descriptor in face recognition, and compare its performance to that of RCM and the state of the art descriptors, followed by a concluding discussion.

Conclusion

This paper examines four orthogonal filter banks of varying properties (i.e., IT, DHT, DCT, and KLT) as Regional Covariance Matrix (RCM) mapping functions, along with the proposed Region Log-TiedRank Covariance Matrices (RLTCM). Apart from the superior performance gain for RLTCM over RCM on all evaluating orthogonal filters, we observe that KLT and DCT (which de-correlate filter responses) prevails over IT (where the filter responses are of highly correlated) with the RCM-derived descriptors

Acknowledgement

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NO. 2016R1A2B4011656).

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    This paper has been recommended for acceptance by Yicong Zhou.

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