Gaussian Splatting has emerged as a prominent model for constructing 3D representations from images across diverse domains. However, the efficiency of the 3D Gaussian Splatting rendering pipeline relies on several simplifications. Notably, reducing Gaussian to 2D splats with a single viewspace depth introduces popping and blending artifacts during view rotation. Addressing this issue requires accurate per-pixel depth computation, yet a full per-pixel sort proves excessively costly compared to a global sort operation. In this paper, we present a novel hierarchical rasterization approach that systematically resorts and culls splats with minimal processing overhead. Our software rasterizer effectively eliminates popping artifacts and view inconsistencies, as demonstrated through both quantitative and qualitative measurements. Simultaneously, our method mitigates the potential for cheating view-dependent effects with popping, ensuring a more authentic representation. Despite the elimination of cheating, our approach achieves comparable quantitative results for test images, while increasing the consistency for novel view synthesis in motion. Due to its design, our hierarchical approach is only 4% slower on average than the original Gaussian Splatting. Notably, enforcing consistency enables a reduction in the number of Gaussians by approximately half with nearly identical quality and view-consistency. Consequently, rendering performance is nearly doubled, making our approach 1.6x faster than the original Gaussian Splatting, with a 50% reduction in memory requirements. Our renderer is publicly available at https://github.com/r4dl/StopThePop.
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