Local  $N$ -Ary Pattern and Its Extension for Texture Classification
Texture image classification is important in computer vision research. To effectively capture texture patterns, a distinctive feature such as a local binary pattern (LBP) is needed. An LBP is robust against monotonic and gray-scale variations and it computes quickly. Its robustness and speed advantage have made it popular in various texture analysis applications. However, an LBP is sensitive to noise, particularly smooth weak illumination gradients in near-uniform regions. To mitigate the effect of noise and increase distinctiveness, a local ternary pattern (LTP) is proposed. Compared with a binary coding LBP, an LTP adopts ternary coding. As a result, an LTP can better tolerate noise and is significantly more distinctive. These advantages of an LTP effectively improve its classification accuracy. However, the potential of ternary coding is not fully explored in LTPs because a ternary pattern is split into a pair of binary patterns. In this paper, to fully explore the distinctiveness in the local pattern, the feature extraction process is formulated as an integer decomposition problem, which is a generalized version of the Bachet de Meziriac weight problem (BMWP). Following this generalization, a local n-ary pattern (LNP) is proposed, for which the LBP is a special case parametrized under n = 2. The LTP is not a special case of the LNP. Both LBP and LTP are used as benchmark methods to evaluate LNPs performance due to their well-recognized success. In addition, a rotation-invariant and uniform LNP is also proposed and compared with a rotation-invariant and uniform LBP. The proposed LNP achieves significantly improved texture classification accuracy compared with the LBP and also demonstrates considerable improvement over the LTP.