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Epipolar Geometry Visualizer

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About This MicroSim

This MicroSim demonstrates epipolar geometry in stereo vision. See how the epipolar constraint restricts correspondence search to a line, and understand the relationship between disparity and depth.

How to Use

  1. Adjust Baseline: Change the distance between cameras
  2. Move Point: Adjust the 3D point's X and Z position
  3. Show Epipolar Plane: Visualize the plane through cameras and point
  4. Show Multiple Lines: See the pattern of epipolar lines
  5. Drag to Rotate: Change the 3D view angle

Key Concepts

Epipolar Constraint: For corresponding points p and p': \(\(\mathbf{p'}^T \mathbf{F} \mathbf{p} = 0\)\)

Depth from Disparity (rectified stereo): \(\(Z = \frac{f \cdot b}{d}\)\)

Term Symbol Meaning
Baseline b Distance between camera centers
Disparity d Horizontal shift between corresponding points
Epipole e Where baseline intersects image plane
Epipolar line l Line where epipolar plane intersects image

Learning Objectives

Students will be able to: - Understand the epipolar constraint and its geometric meaning - Relate disparity to depth in stereo vision - Identify epipoles and epipolar lines - Apply the fundamental matrix concept

Lesson Plan

Introduction (5 minutes)

Epipolar geometry constrains where corresponding points can appear. Instead of searching the entire image, we only search along a line.

Exploration (10 minutes)

  1. Move the 3D point and observe how projected points move
  2. Note that both points stay on the green epipolar line
  3. Increase baseline - disparity increases, depth estimation improves
  4. Move point closer (decrease Z) - disparity increases

Key Insight

Larger baseline improves depth resolution but makes stereo matching harder due to increased appearance change.

References