  Learning and predicting the pose parameters of a 3D hand model given an
image, such as locations of hand joints, is challenging due to large viewpoint
changes and articulations, and severe self-occlusions exhibited particularly in
egocentric views. Both feature learning and prediction modeling have been
investigated to tackle the problem. Though effective, most existing
discriminative methods yield a single deterministic estimation of target poses.
Due to their single-value mapping intrinsic, they fail to adequately handle
self-occlusion problems, where occluded joints present multiple modes. In this
paper, we tackle the self-occlusion issue and provide a complete description of
observed poses given an input depth image by a novel method called hierarchical
mixture density networks (HMDN). The proposed method leverages the
state-of-the-art hand pose estimators based on Convolutional Neural Networks to
facilitate feature learning, while it models the multiple modes in a two-level
hierarchy to reconcile single-valued and multi-valued mapping in its output.
The whole framework with a mixture of two differentiable density functions is
naturally end-to-end trainable. In the experiments, HMDN produces interpretable
and diverse candidate samples, and significantly outperforms the
state-of-the-art methods on two benchmarks with occlusions, and performs
comparably on another benchmark free of occlusions.
