This article develops a geometric framework for detecting targets, in the form of regions of interest, from certain sonar imagery. The main idea is to extract level sets from voxel images and compute local geometric features of the resulting surfaces. Examples include Gaussian and principal curvatures, radial distances, patch areas etc. These features are then compressed into histograms, or estimated probability density functions (pdfs), and compared using the Fisher-Rao (FR) metric. Specifically, the square roots of pdfs are elements of a unit Hilbert sphere and the F-R metric is precisely the arc-length on this sphere. This combination of geometric representations and F-R metric allows one to perform detection tasks using any machine learning technique. This approach is demonstrated on imagery with and without noise and objects. The imagery used here is generated using a simulated ultra-wideband sonar system that insonifies a computer generated environment.