FACE REPRESENTATION WITH GRADIENT ORIENTATIONS AND EULER MAPPING: APPLICATION TO FACE RECOGNITION

This paper proposes a simple, yet very powerful local face representation, called the Gradient Orientations and Euler Mapping (GOEM). GOEM consists of two stages: gradient orientations and Euler mapping. In the first stage, we calculate gradient orientations of a central pixel and get the corresponding orientation representations by performing convolution operator. These representation results display spatial locality and orientation properties. To encompass different spatial localities and orientations, we concatenate all these representation results and derive a concatenated orientation feature vector. In the second stage, we define an explicit Euler mapping which maps the space of the concatenated orientation into a complex space. For a mapping image, we find that the imaginary part and the real part characterize the high frequency and the low frequency components, respectively. To encompass different frequencies, we concatenate the imaginary part and the real part and derive a concatenated mapping feature vector. For a given image, we use the two stages to construct a GOEM image and derive an augmented feature vector which resides in a space of very high dimensionality. In order to derive low-dimensional feature vector, we present a class of GOEM-based kernel subspace learning methods for face recognition. These methods, which are robust to changes in occlusion and illumination, apply the kernel subspace learning model with explicit Euler mapping to an augmented feature vector derived from the GOEM representation of face images. Experimental results show that our methods significantly outperform popular methods and achieve state-of-the-art performance for difficult problems such as illumination and occlusion-robust face recognition.