Computer Vision:

• automatic understanding of images and video
  • computing properties of the 3D world from visual data(measurement)
  • Algorithms and representations to allow a machine to recognize objects, people, scenes, and activities (perception and interpretation)
  • Algorithms to mine, search, and interact with visual data(interaction)

Projective Geometry:

Q. What is lost? A: Length, Area, Angles

Q. What is preserved? A: Straight lines are still straight

Vanishing points and lines: parallel lines in the world intersect in the image at a “vanishing point”

Projection: world coordinates → image coordinates

Homogeneous Coordinates Conversion

Converting to homogeneous coordinates

Converting from homogeneous coordinates

Invariant to Scaling

Point in Cartesian is ray in Homogeneous

Projection Matrix

Intrinsic Assumptions