  In this work we introduce a differential rendering module which allows neural
networks to efficiently process cluttered data. The module is composed of
continuous piecewise differentiable functions defined as a sensor array of
cells embedded in 3D space. Our module is learnable and can be easily
integrated into neural networks allowing to optimize data rendering towards
specific learning tasks using gradient based methods in an end-to-end fashion.
Essentially, the module's sensor cells are allowed to transform independently
and locally focus and sense different parts of the 3D data. Thus, through their
optimization process, cells learn to focus on important parts of the data,
bypassing occlusions, clutter and noise. Since sensor cells originally lie on a
grid, this equals to a highly non-linear rendering of the scene into a 2D
image. Our module performs especially well in presence of clutter and
occlusions. Similarly, it deals well with non-linear deformations and improves
classification accuracy through proper rendering of the data. In our
experiments, we apply our module to demonstrate efficient localization and
classification tasks in cluttered data both 2D and 3D.
