Asymmetric power distribution model of wavelet subbands for texture classification

Bayesian parameter estimation for asymmetric power distributions

“…The shape of the APD distribution is adjusted by the parameter λ > 0 controlling the tail decay whereas α ∈ (0, 1) characterizes the degree of asymmetry and γ > 0 is a scale parameter. Some related APD definitions that are equivalent up to an appropriate change of variables can also be found in [1,2,4].…”

“…The proposed distribution defined by (1) has two main advantages (for our purpose) with respect to APDs of [1] or [4]: the asymmetric parameter is constrained to belong to a finite length interval (0, 1) and the presence of a scale parameter makes it more flexible for practical applications.…”

“…Note that this distribution is easy to sample. This easy generation is mainly due to the form of APD introduced in (1), which differs from the definition of [2,4].…”

“…Since this conditional distribution is not easy to sample directly, we have used an MH acceptance rule based on a uniform proposal in the interval (0, 1). Again, the simple form of APD introduced in (1) makes this generation easier since α ∈ (0, 1) contrary to the APDs defined in [4] where α ∈ IR + .…”

“…However, in some other applications such as econometrics [1,2] or image processing, asymmetry has been observed in the distribution of the data. In particular, image processing applications involving asymmetric distributions include segmentation of magnetic resonance images (MRI) [3] or texture classification using wavelet coefficients [4]. This paper studies asymmetric power distributions (APDs) that have been introduced in [1,2].…”