Directional Hartley transform and content based image retrieval

This paper proposes directional Hartley transform (DirHT) in the Hartley domain by partitioning the two dimensional Hartley plane. Two different approaches, wrapping based directional Hartley transform (WDirHT) and overlapping based directional Hartley transform (ODirHT) have been proposed. WDirHT uses the Fourier integral operator (FIO) tiling scheme and ODirHT uses the ridgelet tiling scheme. WDirHT takes less computation time as compared to ODirHT, however, ODirHT has less redundancy factor as compared to WDirHT. The computational complexity of both WDirHT and ODirHT is O(N2log2N)O(N2log2N) for N×NN×N image. The two dimensional Hartley plane is neither symmetric nor antisymmetric, hence, each Hartley directional subband coefficient in the two dimensional Hartley plane is unique. As a result, features obtained from the Hartley domain are unique. These features are exploited for content based image retrieval (CBIR) application. The proposed CBIR algorithm using WDirHT and ODirHT is applied on AT&T face and Brodatz textures databases. Results show that retrieval rate of both WDirHT and ODirHT is better as compared to several other methods. Among WDirHT and ODirHT, WDirHT gives better retrieval rate.