Efficient segmentation of globally optimal surfaces in volumetric images is a central problem in many medical image analysis applications. Intra-class variance has been successfully utilized, for instance, in the Chan-Vese model especially for images without prominent edges. In this paper, we study the optimization problem of detecting a region (volume) between two coupled smooth surfaces by minimizing the intra-class variance using an efficient polynomial-time algorithm. Our algorithm is based on the shape probing technique in computational geometry and computes a sequence of minimum-cost closed sets in a derived parametric graph. The method has been validated on computer-synthetic volumetric images and in X-ray CTscanned datasets of plexiglas tubes of known sizes. Its applicability to clinical data sets was demonstrated in human CT image data. The achieved results were highly accurate with mean signed surface positioning errors of the inner and outer walls of the tubes of +0.013mm a...