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Building Rome with Convex Optimization
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Building Rome with Convex Optimization
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Global bundle adjustment is made easy by depth prediction and convex optimization. We (i) propose a scaled bundle adjustment (SBA) formulation that lifts 2D keypoint measurements to 3D with learned depth, (ii) design an empirically tight convex semidfinite program (SDP) relaxation that solves SBA to certfiable global optimality, (iii) solve the SDP relaxations at extreme scale with Burer-Monteiro factorization and a CUDA-based trust-region Riemannian optimizer (dubbed XM), (iv) build a structure from motion (SfM) pipeline with XM as the optimization engine and show that XM-SfM compares favorably with existing pipelines in terms of reconstruction quality while being significantly faster, more scalable, and initialization-free.
Forward citations
Cited by 4 Pith papers
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Local Linear Convergence of the Alternating Direction Method of Multipliers for Semidefinite Programming under Strict Complementarity
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LieIPM applies a structure-preserving interior point optimizer to rigid-body trajectory planning on Lie groups using variational integrators and closed-form intrinsic derivatives.
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InstantSfM: Towards GPU-Native SfM for the Deep Learning Era
A fully GPU-native, PyTorch-based global Structure-from-Motion pipeline using sparse-aware Levenberg-Marquardt with optional metric depth priors reports ~8-40× speedups over COLMAP at comparable accuracy on several be...
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ProBA: Probabilistic Bundle Adjustment with the Bhattacharyya Coefficient
ProBA replaces rigid point tracks with a probabilistic pose graph and 3D Gaussian landmarks, optimizing via negative log-likelihood with the Bhattacharyya coefficient to expand the basin of attraction in prior-free SfM.
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