Problems in differentiable rendering often involve optimizing scene parameters that cause motion in image space. The gradients for such parameters tend to be sparse, leading to poor convergence. While existing methods address this sparsity through proxy gradients such as topological derivatives or lagrangian derivatives, they make simplifying assumptions about rendering. Multi-resolution image pyramids offer an alternative approach but prove unreliable in practice. We introduce a method that uses locally orderless images, where each pixel maps to a histogram of intensities that preserves local variations in appearance. Using an inverse rendering objective that minimizes histogram distance, our method extends support for sparsely defined image gradients and recovers optimal parameters. We validate our method on various inverse problems using both synthetic and real data.

翻译：可微分渲染中的问题通常涉及优化导致图像空间运动的场景参数。此类参数的梯度往往稀疏，导致收敛性不佳。现有方法通过拓扑导数或拉格朗日导数等代理梯度解决稀疏性问题，但它们对渲染过程做出了简化假设。多分辨率图像金字塔提供了替代方案，但在实践中被证明不可靠。我们提出一种利用局部无序图像的方法，其中每个像素映射到保持局部外观变化的强度直方图。通过最小化直方图距离的反向渲染目标函数，我们的方法扩展了对稀疏定义图像梯度的支持，并恢复了最优参数。我们在合成数据和真实数据上通过多种反向问题验证了该方法的有效性。