Automated detection of visually salient regions is an active area of research in computer vision. Salient regions can serve as inputs for object detectors as well as inputs for region-based registration algorithms. In this paper, we consider the problem of speeding up computationally intensive bottom-up salient region detection in 3D medical volumes. The method uses the Kadir-Brady formulation of saliency. We show that in the vicinity of a salient region, entropy is amonotonically increasing function of the degree of overlap of a candidate window with the salient region. This allows us to initialize a sparse seed point grid as the set of tentative salient region centers and iteratively converge to the local entropy maxima, thereby reducing the computation complexity compared to the Kadir-Brady approach of performing this computation at every point in the image. We propose two different approaches for achieving this. The first approach involves evaluating entropy in the four quadrants around the seed point and iteratively moving in the direction that increases entropy. The second approach we propose makes use of mean shift tracking framework to affect entropy maximizing moves. Specifically, we propose the use of uniform pmf as the target distribution to seek high entropy regions.We demonstrate the use of our algorithm on medical volumes for left ventricle detection in PET images and tumor localization in brain MR sequences.