Metric Regression Forests for Human Pose Estimation

Traditionally, human pose estimation algorithms could be classified into generative [2] and discriminative [4] approaches. Generative approaches model the likelihood of the observations given a pose estimate, however, they are susceptible to local minima and thus require good initial pose estimates. Discriminative approaches learn a direct mapping from image features to pose space from training data, however, they struggle to generalize to unseen poses. Building on previous work [3], Taylor et al. [5] bypass some of these limitations using a hybrid-approach that discriminatively predicts, for each pixel in a depth image, a corresponding point on the surface of a humanoid mesh model. This mesh model is then robustly fit to the resulting set of correspondences using local optimization. Surprisingly though, these correspondences are actually inferred using a random forest whose structure was trained using a classification objective that arbitrarily equates target model points belonging to the same predefined body part [3]. In this paper, we address Taylor et al.’s use of this proxy classification objective by proposing Metric Space Information Gain (MSIG), a replacement objective function for training a random forest to directly minimize the uncertainty over the target model points, naturally encoding the correlation between these points as a function of the geodesic distance. To this end, we view the surface of the model U as a metric space (U,dU) defined by the geodesic distance metric dU (see first panel of Figure 1). The natural objective function to minimize the uncertainty in the resulting true distributions that result from a split function s in such a space, is the information gain I(s) [1]. This is generally approximated using an empirical distribution Q = {ui} ⊆U drawn from the true unsplit distribution pU as I(s)≈ I(s;Q) = Ĥ(Q)− ∑ i∈{L,R} |Qi| |Q| Ĥ(Qi), (1)