> ## Documentation Index
> Fetch the complete documentation index at: https://aegean.ai/llms.txt
> Use this file to discover all available pages before exploring further.

# Recovering 3D Structure from Images

> Projective geometry, single-view metrology, stereo, and visual motion, the tools that turn images into 3D structure.

A camera flattens a 3D scene onto a 2D image. This chapter works that projection
backward. You start with the projective geometry of points, lines and homographies.
You then measure a scene from one image using vanishing points, and recover depth from
two images with stereo and epipolar geometry. The chapter ends with how motion in 3D shows
up as motion in the image. Structure from motion and bundle adjustment, which recover
camera poses from many images, are still to come.

These tools produce the posed images that 3D Gaussian splatting needs in the
[Sim-to-Real Transfer](/aiml-common/lectures/sim2real/index) chapter.

<CardGroup cols={2}>
  <Card title="Representing Images and Geometry" icon="vector-square" href="/aiml-common/lectures/3d-reconstruction/images-and-geometry/index">
    Homogeneous coordinates, 2D transformations as matrices, point and line duality, and forward and backward warping.
  </Card>

  <Card title="Homographies and Robust Estimation" icon="object-ungroup" href="/aiml-common/lectures/3d-reconstruction/homographies/index">
    Estimate a plane-to-plane mapping with normalized DLT, reject outliers with RANSAC, and rectify a plane.
  </Card>

  <Card title="Measuring a Scene from One Image" icon="ruler-combined" href="/aiml-common/lectures/3d-reconstruction/single-view-metrology/index">
    Vanishing points, the cross-ratio, and camera calibration from one image of a room.
  </Card>

  <Card title="Depth from Two Views" icon="eye" href="/aiml-common/lectures/3d-reconstruction/stereo-vision/index">
    Disparity and depth, cost volumes and block matching, failure cases, and epipolar geometry.
  </Card>

  <Card title="Estimating Motion by Patch Matching" icon="arrows-up-down-left-right" href="/aiml-common/lectures/3d-reconstruction/motion-estimation/index">
    Recover image motion between two frames by local patch matching, and measure its error.
  </Card>

  <Card title="3D Motion and Its 2D Projection" icon="wind" href="/aiml-common/lectures/3d-reconstruction/3d-motion-projection/index">
    How the 3D motion of points and cameras projects to motion in the image.
  </Card>
</CardGroup>

***

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