An Orientation-Selective Orthogonal Lapped Transform

A novel critically sampled orientation-selective orthogonal lapped transform called the lapped Hartley transform (LHT) is derived. In a first step, overlapping basis functions are generated by modulating basis functions of a 2-D block Hartley transform by a cosine wave. To achieve invertibility and orthogonality, an iterative filter is applied as prefilter in the analysis and as postfilter in the synthesis operation, respectively. Alternatively, filtering can be restricted to analysis or synthesis, ending up with a biorthogonal transform (LHT-PR, LHT-PO). A statistical analysis based on a 4000-image data base shows that the LHT and LHT-PO have better redundancy removal properties than other block or lapped transforms. Finally, image compression and noise removal examples are given, showing the advantages of the LHT especially in images containing oriented textures. - Reference

Texture Analysis and Classification With Linear Regression Model Based on Wavelet Transform

The wavelet transform as an important multiresolution analysis tool has already been commonly applied to texture analysis and classification. Nevertheless, it ignores the structural information while capturing the spectral information of the texture image at different scales. In this paper, we propose a texture analysis and classification approach with the linear regression model based on the wavelet transform. This method is motivated by the observation that there exists a distinctive correlation between the sample images, belonging to the same kind of texture, at different frequency regions obtained by 2-D wavelet packet transform. Experimentally, it was observed that this correlation varies from texture to texture. The linear regression model is employed to analyze this correlation and extract texture features that characterize the samples. Therefore, our method considers not only the frequency regions but also the correlation between these regions. In contrast, the pyramid-structured wavelet transform (PSWT) and the tree-structured wavelet transform (TSWT) do not consider the correlation between different frequency regions. Experiments show that our method significantly improves the texture classification rate in comparison with the multiresolution methods, including PSWT, TSWT, the Gabor transform, and some recently proposed methods derived from these. - Reference