Fractal indexing with the joint statistical properties and its application in texture image retrieval

Fractal image coding is a block-based scheme that exploits the self-similarity hiding within an image. Fractal parameters generated by the block-based scheme are quantitative measurements of self-similarity, and therefore they can be used to construct image signatures. By combining fractal parameters and collage error, a set of new statistical fractal signatures, such as histogram of collage error (HE), joint histogram of contrast scaling and collage error (JHSE), and joint histogram of range block mean and contrast scaling and collage error (JHMSE) is proposed. These fractal signatures effectively extract and reflect the statistical properties intrinsic in texture images. Hence, they provide new statistical features for use in texture image retrieval and identification. Furthermore, in order to reduce computational complexity of the JHMSE signature, the JHMSE signature is simplified to HM (histogram of range block mean) +JHSE and HM+HS (histogram of contrast scaling) +HE, based on the independence and distance equivalence. Mathematical analysis of the simplification scheme is also carried out. The proposed fractal signatures are compared with the existing fractal signatures. Experimental results show that the proposed signatures, HM+JHSE and HM+HS+HE, achieve a higher retrieval rate with a lower computational complexity.