  A 3D point cloud is typically constructed from depth measurements acquired by
sensors at one or more viewpoints. The measurements suffer from both
quantization and noise corruption. To improve quality, previous works denoise a
point cloud \textit{a posteriori} after projecting the imperfect depth data
onto 3D space. Instead, we enhance depth measurements directly on the sensed
images \textit{a priori}, before synthesizing a 3D point cloud. By enhancing
near the physical sensing process, we tailor our optimization to our depth
formation model before subsequent processing steps that obscure measurement
errors.
  Specifically, we model depth formation as a combined process of
signal-dependent noise addition and non-uniform log-based quantization. The
designed model is validated (with parameters fitted) using collected empirical
data from a representative depth sensor. To enhance each pixel row in a depth
image, we first encode intra-view similarities between available row pixels as
edge weights via feature graph learning. We next establish inter-view
similarities with another rectified depth image via viewpoint mapping and
sparse linear interpolation. This leads to a maximum a posteriori (MAP) graph
filtering objective that is convex and differentiable. We minimize the
objective efficiently using accelerated gradient descent (AGD), where the
optimal step size is approximated via Gershgorin circle theorem (GCT).
Experiments show that our method significantly outperformed recent point cloud
denoising schemes and state-of-the-art image denoising schemes in two
established point cloud quality metrics.
