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Move beyond stereo to reconstruct 3D scenes from arbitrary collections of images. Learn the Structure from Motion pipeline that powers Google Maps 3D, feature matching strategies, bundle adjustment for global optimization, and practical tools like COLMAP that bring theory to life.
Multi-view geometry extends the principles of two-view (stereo) geometry to an arbitrary number of images. While stereo vision works with a calibrated pair, multi-view methods can reconstruct 3D scenes from dozens, hundreds, or even thousands of uncalibrated photographs. This is the technology behind Google Earth's 3D cities, photogrammetric survey, and visual SLAM systems that build maps while navigating.
What is this chapter about? We develop the theory and practice of 3D reconstruction from multiple images. Starting with the trifocal tensor (the three-view generalization of the fundamental matrix), we build up the complete Structure from Motion (SfM) pipeline: feature detection, matching, incremental reconstruction, and bundle adjustment. We then explore practical SfM tools and compare incremental versus global approaches.
Why does this matter? Most real-world 3D reconstruction tasks have far more than two views. A drone surveying a building captures hundreds of images. A tourist photographing a monument takes shots from many angles. Multi-view geometry enables us to extract the full 3D structure and all camera poses from these unordered image collections---automatically, without calibration targets, and with high precision.
How the topics connect: We begin with N-view geometry to generalize two-view constraints. The SfM pipeline shows how to chain these constraints into a full reconstruction system. Feature matching solves the correspondence problem across many images. Bundle adjustment jointly optimizes everything. COLMAP demonstrates a production-quality implementation. Finally, we compare incremental vs global SfM approaches.
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The trifocal tensor, multi-view triangulation, and projective reconstruction beyond stereo.
Pipeline and correspondence
The incremental reconstruction loop — initial pair, register cameras, triangulate, repeat.
SIFT, SuperPoint, LoFTR — finding correspondences across many views.
Joint optimization of all cameras and points — minimizing total reprojection error.
Production systems
The standard open-source SfM tool — from images to dense 3D reconstruction.
Trade-offs between growing reconstructions incrementally and solving everything at once.
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