Several studies dealt with medical ultrasound registration. Their similarity metrics relied on pixel-to-pixel intensity comparisons. Hence, they are not well suited to the case of speckled images. To better handle the speckle noise, our previous work proposed an information-theoretic feature detector-based registration approach. This work aims to extend it to the cases where the image speckle model is Rayleigh or normalized Fisher-Tippett distributed. Using speckle modeling based on these distributions, a speckle-specific information-theoretic feature detector is constructed and applied to provide feature images. Those feature images are then registered using differential equations, the solution of which provides a transformation to bring the images into alignment. Compared to standard gradient-based techniques, the experimental results demonstrate the effectiveness of our method, particularly for low contrast ultrasound images.