  Differentiable render is widely used in optimization-based 3D reconstruction
which requires gradients from differentiable operations for gradient-based
optimization. The existing differentiable renderers obtain the gradients of
rendering via numerical technique which is of low accuracy and efficiency.
Motivated by this fact, a differentiable mesh renderer with analytical
gradients is proposed. The main obstacle of rasterization based rendering being
differentiable is the discrete sampling operation. To make the rasterization
differentiable, the pixel intensity is defined as a double integral over the
pixel area and the integral is approximated by anti-aliasing with an average
filter. Then the analytical gradients with respect to the vertices coordinates
can be derived from the continuous definition of pixel intensity. To
demonstrate the effectiveness and efficiency of the proposed differentiable
renderer, experiments of 3D pose estimation by only multi-viewpoint silhouettes
were conducted. The experimental results show that 3D pose estimation without
3D and 2D joints supervision is capable of producing competitive results both
qualitatively and quantitatively. The experimental results also show that the
proposed differentiable renderer is of higher accuracy and efficiency compared
with previous method of differentiable renderer.
