I. Introduction
Texture classification, unlike other forms of classifications where the objects being categorized have a definite structure, most textures have large stochastic variations which make them difficult to model [1]. Therefore, local statistical representation is a long lasting approach for texture representation. In order to obtain the statistical representation, each local structure should be labeled distinctively. Specifically, two fundamental problems to label the local structures are:
How to generate local feature vectors to describe local structures with higher distinguishing ability, lower redundancy and imaging conditions invariance.
How to quantize the local feature vectors distinctively to preserve more structure information.
For the first item, the joint distribution of intensity values over compact neighborhoods is often used as local feature vectors to describe the local structures. The joint distribution is mostly the gradient of neighborhoods, the responses of filter banks or even the intensity values themselves. The imaging conditions include illumination (brightness and contrast), rotation and scale variation. Sometimes the local feature vectors are normalized to achieve some degree of robustness to illumination variation. The selection of dominant orientation, combination of histogram bins or other techniques are used to achieve rotation invariance, and the multi-scale analysis is used to make the representation more robust to different scales. The second item is about the vector quantization method which is important for the labeling step. The local binary pattern (LBP) operator used binary coding to generate a decimal number to label each local structure [2]. Similar to the vector quantization approach used in data compression, the texton dictionary-based methods used nearest texton in the texton dictionary to label the local structure [3]–[6]. In this paper, we propose normalized local oriented energies to generate local feature vectors which are invariant to the imaging conditions to some extent. Motivated by LBP operation using binary coding for quantization, we propose to use N-nary coding which reduces the quantization loss and thus preserves more local structure information.