Differentiable renderer is widely used in optimization-based 3D reconstruction which requires gradients for optimization. The existing differentiable renderers obtain gradients via numerical techniques. However, these methods are inaccurate and inefficient. Motivated by this fact, we propose a differentiable renderer with analytical gradients. The main obstacle of traditional renderer being differentiable is the discrete sampling operation of rasterization. To obtain a differentiable rasterization renderer, we define pixel intensity as a double integral over the pixel grid, and then derive the analytical gradients with respect to vertices. 3D pose estimation by multi-viewpoint silhouettes is conducted to reveal the effectiveness and efficiency of the proposed method. Experimental results show that 3D pose estimation without 3D and 2D joint supervision can produce competitive results. The findings also indicate that the proposed method has higher accuracy and efficiency than previous differentiable renderers.

可微分渲染器广泛用于需要优化梯度的基于优化的3D重建中。现有的微分渲染器通过数值技术获得渐变。但是，这些方法不准确且效率低下。基于这一事实，我们提出了一种具有解析梯度的可微分渲染器。传统渲染器可区分的主要障碍是光栅化的离散采样操作。为了获得可微分的光栅化渲染器，我们将像素强度定义为像素网格上的双整数，然后导出相对于顶点的解析梯度。通过多视点轮廓进行3D姿态估计，以揭示所提方法的有效性和效率。实验结果表明，在没有3D和2D联合监督的情况下进行3D姿态估计可以产生有竞争力的结果。研究结果还表明，所提出的方法比以前的可区分渲染器具有更高的准确性和效率。