Recovering 3D geometry from 2D images is a foundational problem in computer vision. Part of the common pipeline in the field has depended on the 45-year-old Random Sample Consensus (RANSAC) algorithm, which relies on minimal subset sampling—effectively ignoring the bulk of the data during model generation. I will present a robust, global, and complementary alternative: the Subspace-constrained Tyler’s Estimator (STE). I will analyze the success of STE by assuming a generalized weak inlier-outlier model, pushing the outlier fraction beyond the threshold where the problem is traditionally proven to be computationally hard. I will show that in this setting, provided the initialization satisfies a specific condition, STE can recover the underlying subspace with high probability. I will also review additional mathematical ideas to infer global camera poses from relative ones—specifically the recent Cycle-Sync method—and outline future directions for robust geometric perception.