1. MSU CSE 803 Stockman Perspective algebra: quick- and-dirty first look Geometry of similar triangles yields algebra for computing world-image transformation.

2. MSU CSE 803 Stockman Pin hole lens model ABC abc Light rays pass through pin hole to image World surface point reflects light through lens center to image plane Actual pin hole camera can take sharp pictures of static scene with long exposure time When a lens replaces the pin hole, light is collected over an entire cone enabling much faster imaging but suffering some optical effects.

3. MSU CSE 803 Stockman Actual lens model (more later) ABC abc World surface point reflects light through lens center to image plane When a lens replaces the pin hole, light is collected over an entire cone enabling much faster imaging but suffering some optical effects. real image is inverted Lens and not pinhole X c X i

4. MSU CSE 803 Stockman Camera looking down 90 deg

5. MSU CSE 803 Stockman General trans in 3D Camera coord sys 3D object point in camera coord sys Image point in camera coord sys

6. MSU CSE 803 Stockman notes Similar triangles mean mapping is from mm in world to mm in image Or inches in world to inches in image Can convert mm to pixels “nominal resolution” is patch of world that images to a pixel

7. MSU CSE 803 Stockman Perspective vs orthographic projection Perspective distortion gets worse toward the periphery of the image. Distance c-a is not equal to distance a-b in image Orthographic is often used in design and blueprints. True (scaled) dimensions can be taken from the image. Distance c-a = distance a-b. c a b

8. MSU CSE 803 Stockman Future work in Chs 12 and 13 Model 2 cameras to get stereo model Model camera and projector for structured light Use world coordinate system and relate camera model to it via rotation and translation