Structure from motion reconstructs 3D scenes and camera positions from a set of ordinary 2D photos — the classic pipeline behind photogrammetry, 3D mapping, and the initialization of visual SLAM and NeRFs.
Structure from motion takes a bunch of ordinary photos of a scene from different spots and works out both the 3D shape of the scene and where each photo was taken from — turning flat pictures into a 3D model.
Give a computer a pile of photos of a building taken from different angles, and it can reconstruct the building in 3D and figure out where every photo was taken from. That's structure from motion (SfM) — recovering 3D from moving 2D views.
What it recovers
SfM solves two intertwined unknowns at once from a set of overlapping images:
Structure — the 3D positions of scene points.
Motion — the camera's pose (position + orientation) for each image.
Neither is known in advance, yet the geometry of multiple views constrains both — so SfM untangles them jointly, turning flat pictures into a 3D point cloud and a set of camera positions.
Photos to 3D + camera poses
By matching the same points across images and exploiting the geometry between views, SfM recovers both the scene's 3D shape and where each camera was.
The pipeline
Detect and match features (SIFT/ORB) across the images to find the same points in multiple views.
Estimate two-view geometry using epipolar geometry (the essential/fundamental matrix) to get relative camera poses and initial 3D points (triangulation).
Grow incrementally — add images one by one, registering each camera and triangulating more points.
Bundle adjustment — jointly refine all cameras and points to minimize reprojection error, the accuracy step that makes the reconstruction crisp.
Tools like COLMAP implement this pipeline and are widely used.
Where it's used
Photogrammetry and 3D scanning — reconstructing objects, buildings, and terrain from photos or drone imagery (mapping, surveying, heritage).
Initializing modern methods — SfM computes the camera poses that NeRFs and 3D Gaussian splatting need as input.
Robotics mapping. Related to visual SLAM — SfM is typically the offline, batch cousin (process all images together for best accuracy), while SLAM is the online, real-time version.
SfM vs SLAM
SfM — offline, unordered image sets, maximum accuracy, no real-time constraint.
SLAM — online, sequential frames, real-time, for a live robot.
They share the same underlying multi-view geometry and bundle adjustment.
Why it matters
Structure from motion is the classical foundation of 3D reconstruction from images — the pipeline that turns ordinary photos into 3D models and camera trajectories. It underlies photogrammetry, feeds modern neural reconstruction methods, and is the batch counterpart to visual SLAM, making it a cornerstone of geometric computer vision.
