Computing gradients of visibility with respect to scene parameters is a long-standing challenge in differentiable rendering. Existing approaches either approximate the rendering process to make it differentiable, or rely on auxiliary data structures that add complexity. We present Rasterized Edge Gradients (REG), a method that computes accurate gradients at visibility discontinuities directly within a standard rasterization pipeline. Our key idea is to introduce micro-edges — infinitesimal edge segments along silhouette boundaries — that allow us to treat the rasterized image as the outcome of a differentiable, continuous process while remaining fully compatible with discrete-pixel rasterization. REG requires no modifications to the forward rendering pass and is applicable to masks, depth, normals, and color images.

Differentiable rendering has become a cornerstone of modern computer vision and graphics, enabling inverse rendering, 3D reconstruction from images, neural radiance fields, and physics-based material estimation. The fundamental requirement is to compute gradients of the rendered image with respect to scene parameters such as vertex positions, camera parameters, and material properties. While gradients at smooth, continuous regions of the image are straightforward to compute, the challenge lies at visibility discontinuities — silhouette edges where objects occlude each other. At these boundaries, small changes in scene parameters cause discrete pixel ownership changes, creating step-function discontinuities where standard differentiation fails.

Existing approaches to differentiable rendering can be broadly categorized into two families. The first family modifies the forward rendering process by blurring or softening visibility, effectively replacing the hard visibility function with a smooth approximation. While this makes gradients available everywhere, it introduces artifacts in the rendered images and biased gradients. The second family uses edge-sampling techniques that explicitly identify silhouette edges and compute gradients along them. These methods produce accurate gradients but require additional data structures, ray casting, or multi-pass rendering, significantly increasing complexity and computational cost. Our approach, REG, combines the simplicity of rasterization-based methods with the accuracy of edge-based gradient computation.

The core idea of REG is to decompose the gradient computation at visibility discontinuities into a sum of contributions from micro-edges. Consider a silhouette edge in the rendered image where a foreground triangle occludes a background triangle. As the silhouette edge moves by an infinitesimal amount, some pixels transition from showing the background to showing the foreground (or vice versa). The gradient contribution from each such pixel transition can be computed as the product of the pixel's value difference (foreground minus background) and the rate at which the edge sweeps across the pixel. By aggregating these contributions along the entire edge, we obtain the correct visibility gradient.

We introduce the concept of micro-edges to make this idea practical. A micro-edge is a small segment of a silhouette edge that passes through a single pixel. For each pixel that lies on a silhouette boundary, we identify the micro-edge passing through it and compute: (1) the local edge direction, which determines the axis of the gradient; (2) the foreground and background values at that pixel from the two adjacent triangles; and (3) the edge's sensitivity to each scene parameter, obtained from the screen-space projection of the mesh edge. The final gradient for each parameter is the sum of all micro-edge contributions across all silhouette pixels.

A critical advantage of the micro-edge formulation is that it works entirely within the rasterization framework. All information needed — silhouette pixel locations, foreground/background values, and edge directions — can be extracted from a standard rasterization pass with an additional silhouette detection step. Unlike ray-tracing-based methods, REG does not require shooting additional rays or maintaining acceleration structures. Furthermore, REG handles geometry intersections correctly, which many existing methods struggle with, by treating intersection edges as additional silhouette edges with their own micro-edge decomposition.

We evaluate REG on dynamic human head scene reconstruction, a challenging application that requires accurate gradients for both camera images and segmentation masks. Our method successfully reconstructs fine geometric details including hair strands, ear geometry, and facial wrinkles by leveraging accurate silhouette gradients. Compared to SoftRas (soft rasterization approach), our method produces sharper reconstructions with fewer artifacts. Compared to Nvdiffrast (an edge-sampling baseline), REG achieves comparable accuracy while being simpler to implement and requiring no auxiliary ray casting. Quantitatively, REG achieves a mean vertex error of 0.83mm on our benchmark, compared to 1.12mm for SoftRas and 0.87mm for Nvdiffrast.

We have presented Rasterized Edge Gradients (REG), a novel approach to computing visibility gradients in differentiable rendering that combines the simplicity and efficiency of rasterization with accurate edge-based gradient computation. Through the introduction of micro-edges, our method requires no modifications to the forward rendering pass and supports gradients for arbitrary image quantities including masks, depth, normals, and color. Our method correctly handles geometry intersections and achieves state-of-the-art reconstruction quality on dynamic human head scenes. We believe REG provides a practical and principled foundation for differentiable rendering in production pipelines.