3D Human shape tracking consists in fitting a template model to temporal sequences of visual observations. It usually comprises an association step, that finds correspondences between the model and the input data, and a deformation step, that fits the model to the observations given correspondences. Most current approaches follow the Iterative-Closest-Point (ICP) paradigm, where the association step is carried out by searching for the nearest neighbors. It fails when large deformations occur and errors in the association tend to propagate over time. In this paper, we propose a discriminative alternative for the association, that leverages random forests to infer correspondences in one shot. Regardless the choice of shape parameterizations, being surface or volumetric meshes, we convert 3D shapes to volumetric distance fields and thereby design features to train the forest. We investigate two ways to draw volumetric samples: voxels of regular grids and cells from Centroidal Voronoi Tessellation (CVT). While the former consumes considerable memory and in turn limits us to learn only subject-specific correspondences, the latter yields much less memory footprint by compactly tessellating the interior space of a shape with optimal discretization. This facilitates the use of larger cross-subject training databases, generalizes to different human subjects and hence results in less overfitting and better detection. The discriminative correspondences are successfully integrated to both surface and volumetric deformation frameworks that recover human shape poses, which we refer to as ‘tracking-bydetection of 3D human shapes.’ It allows for large deformations and prevents tracking errors from being accumulated. When combined with ICP for refinement, it proves to yield better accuracy in registration and more stability when tracking over time. Evaluations on existing datasets demonstrate the benefits with respect to the state-of-the-art.