  The prevalence of accessible depth sensing and 3D laser scanning techniques
has enabled the convenient acquisition of 3D dynamic point clouds, which
provide efficient representation of arbitrarily-shaped objects in motion.
Nevertheless, dynamic point clouds are often perturbed by noise due to
hardware, software or other causes. While a plethora of methods have been
proposed for static point cloud denoising, few efforts are made for the
denoising of dynamic point clouds with varying number of irregularly-sampled
points in each frame. In this paper, we represent dynamic point clouds
naturally on graphs and address the denoising problem by inferring the
underlying graph via spatio-temporal graph learning, exploiting both the
intra-frame similarity and inter-frame consistency. Firstly, assuming the
availability of a relevant feature vector per node, we pose spatial-temporal
graph learning as optimizing a Mahalanobis distance metric $\mathbf{M}$, which
is formulated as the minimization of graph Laplacian regularizer. Secondly, to
ease the optimization of the symmetric and positive definite metric matrix
$\mathbf{M}$, we decompose it into $\mathbf{M}=\mathbf{R}^{\top}\mathbf{R}$ and
solve $\mathbf{R}$ instead via proximal gradient. Finally, based on the
spatial-temporal graph learning, we formulate dynamic point cloud denoising as
the joint optimization of the desired point cloud and underlying
spatio-temporal graph, which leverages both intra-frame affinities and
inter-frame consistency and is solved via alternating minimization.
Experimental results show that the proposed method significantly outperforms
independent denoising of each frame from state-of-the-art static point cloud
denoising approaches.
