In this paper, we introduce a new method for depth perception from a 2D natural scene using scale variation of patterns. As the surface from a 2D scene gets farther away from us, the texture appears finer and smoother. Texture gradient is one of the monocular depth cues which can be represented by gradual scale variations of textured patterns. To extract feature vectors from textured patterns, higher order local autocorrelation functions are utilized at each scale step. The hierarchical linear discriminant analysis is employed to classify the scale rate of the feature vector which can be divided into subspaces by recursively grouping the overlapped classes. In the experiment, relative depth perception of 2D natural scenes is performed on the proposed method and it is expected to play an important role in natural scene analysis.

As a representative of the linear discriminant analysis, the Fisher method is most widely used in practice and it is very effective in two-class classification. However, when it is expanded to a multi-class classification problem, the precision of its discrimination may become worse. A main reason is an occurrence of overlapped distributions on the discriminant space built by Fisher criterion. In order to take such overlaps among classes into consideration, our approach builds a new discriminant space by hierarchically classifying the overlapped classes. In this paper, we propose a new hierarchical discriminant analysis for texture classification. We divide the discriminant space into subspaces by recursively grouping the overlapped classes. In the experiment, texture images from many classes are classified based on the proposed method. We show the outstanding result compared with the conventional Fisher method.