FastMap: Revisiting Dense and Scalable Structure from Motion

We propose FastMap, a new global structure from motion method focused on speed and simplicity. Previous methods like COLMAP and GLOMAP are able to estimate high-precision camera poses, but suffer from poor scalability when the number of matched keypoint pairs becomes large. We identify two key factors leading to this problem: poor parallelization and computationally expensive optimization steps. To overcome these issues, we design an SfM framework that relies entirely on GPU-friendly operations, making it easily parallelizable. Moreover, each optimization step runs in time linear to the number of image pairs, independent of keypoint pairs or 3D points. Through extensive experiments, we show that FastMap is one to two orders of magnitude faster than COLMAP and GLOMAP on large-scale scenes with comparable pose accuracy.

Score Distillation via Reparametrized DDIM

While 2D diffusion models generate realistic, high-detail images, 3D shape generation methods like Score Distillation Sampling (SDS) built on these 2D diffusion models produce cartoon-like, over-smoothed shapes. To help explain this discrepancy, we show that the image guidance used in Score Distillation can be understood as the velocity field of a 2D denoising generative process, up to the choice of a noise term. In particular, after a change of variables, SDS resembles a high-variance version of Denoising Diffusion Implicit Models (DDIM) with a differently-sampled noise term: SDS introduces noise i.i.d. randomly at each step, while DDIM infers it from the previous noise predictions. This excessive variance can lead to over-smoothing and unrealistic outputs. We show that a better noise approximation can be recovered by inverting DDIM in each SDS update step. This modification makes SDS's generative process for 2D images almost identical to DDIM. In 3D, it removes over-smoothing, preserves higher-frequency detail, and brings the generation quality closer to that of 2D samplers. Experimentally, our method achieves better or similar 3D generation quality compared to other state-of-the-art Score Distillation methods, all without training additional neural networks or multi-view supervision, and providing useful insights into relationship between 2D and 3D asset generation with diffusion models.