Vonn distribution of relative phase for statistical image modeling in complex wavelet domain

With the assumptions of Gaussian as well as Gaussian scale mixture models for images in wavelet domain, marginal and joint distributions for phases of complex wavelet coefficients are studied in detail. From these hypotheses, we then derive a relative phase probability density function, which is called Vonn distribution, in complex wavelet domain. The maximum-likelihood method is proposed to estimate two Vonn distribution parameters. We demonstrate that the Vonn distribution fits well with behaviors of relative phases from various real images including texture images as well as standard images. The Vonn distribution is compared with other standard circular distributions including von Mises and wrapped Cauchy. The simulation results, in which images are decomposed by various complex wavelet transforms, show that the Vonn distribution is more accurate than other conventional distributions. Moreover, the Vonn model is applied to texture image retrieval application and improves retrieval accuracy.