This paper presents an analysis method for ultrasound images based on modeling the speckle noise with a Rayleigh distribution. This distribution is parametrized by the parameter sigma, related to the characteristics of the biological tissue. Since some parameters of the Rayleigh distribution are proportional to the value of sigma, the local estimation of such statistics allows the identification of regions corresponding to different tissue types. This property can be employed to improve the automatic analysis of ultrasound images. We have considered the segmentation of the hip joint from ultrasound images for the automatic diagnosis of Developmental Dysplasia of the Hip, a difficult problem that requires an accurate segmentation of different anatomical structures from the ultrasound image.