EGGN 512 - Lecture 23-1 Epipolar and Essential

Epipolar Geometry and the Essential Matrix

In this section, we will learn about epipolar geometry and the essential matrix. We will explore different methods to infer 3D information from 2D images.

Introduction to Epipolar Geometry

• Model-based pose estimation involves a single calibrated camera looking at a known model where we know the geometry of the model.

• Stereo vision involves two calibrated cameras taking a picture simultaneously of some arbitrary scene, and we know the relative pose between the cameras.

• Structure from motion is another method called structure and motion from a moving camera since you have a single camera that's moving, it's calibrated so we know its intrinsic parameters but don't know the relative pose between the cameras positions.

Epipolar Lines and Central Matrix

• The lecture talks about preliminary stuff like epipolar lines and central matrix.

• Epipolar lines are lines on an image plane corresponding to points in 3D space that intersect with a plane defined by two camera centers and one point in space.

• The intersection of this 3D plane with the 2D image plane for each camera is an epipolar line.

• Three vectors - P0, P1, T (translation vector between Camera0 & Camera1 origin)- are coplanar. This can be expressed as R * P1 + T = lambda * P0 where R is rotation matrix between Camera1 & Camera0.

Essential Matrix

• The essential matrix relates corresponding points in stereo images without requiring knowledge of depth or distance to scene points.

• It can be used to compute the relative position and orientation of two cameras.

• The essential matrix can be computed from point correspondences between stereo images.