Analytical Derivatives for Differentiable Renderer: 3D Pose Estimation by Silhouette Consistency

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.

A Novel Self-Intersection Penalty Term for Statistical Body Shape Models and Its Applications in 3D Pose Estimation

Statistical body shape models are widely used in 3D pose estimation due to their low-dimensional parameters representation. However, it is difficult to avoid self-intersection between body parts accurately. Motivated by this fact, we proposed a novel self-intersection penalty term for statistical body shape models applied in 3D pose estimation. To avoid the trouble of computing self-intersection for complex surfaces like the body meshes, the gradient of our proposed self-intersection penalty term is manually derived from the perspective of geometry. First, the self-intersection penalty term is defined as the volume of the self-intersection region. To calculate the partial derivatives with respect to the coordinates of the vertices, we employed detection rays to divide vertices of statistical body shape models into different groups depending on whether the vertex is in the region of self-intersection. Second, the partial derivatives could be easily derived by the normal vectors of neighboring triangles of the vertices. Finally, this penalty term could be applied in gradient-based optimization algorithms to remove the self-intersection of triangular meshes without using any approximation. Qualitative and quantitative evaluations were conducted to demonstrate the effectiveness and generality of our proposed method compared with previous approaches. The experimental results show that our proposed penalty term can avoid self-intersection to exclude unreasonable predictions and improves the accuracy of 3D pose estimation indirectly. Further more, the proposed method could be employed universally in triangular mesh based 3D reconstruction.