Computer Vision

CSE 252A, Winter 2004

David Kriegman

 

Assignment 2

Photometry & Cameras

(Due date: 2/12/2004)

1.      Problem 1.5 in Forsyth & Ponce

2.      Problem 2.7 in Forsyth & Ponce

3.      Consider a pinhole camera with center at the origin, unit focal length, and optical axis pointing in the positive z direction (i.e., the image plane is at z=1.

    1. Consider a moving point that at time t=0 is at the position (1,0,3).  The point travels in the x direction at a speed of one unit of distance per unit of time.  For example, at time t=1, the point is at (2,0,3).  Suppose this point is being imaged using the perspective camera.  Write an equation that gives the x coordinate of the image of the point as a function of time.
    2. Now, suppose instead that the point travels in the z direction at the same speed.  For example, at time t = 1, the point is at (1,0,4).  Write an equation that gives the x coordinate of the image of the point as a function of time.
    3. As t ® ¥, what do the image coordinates in the two cases approach?

4.      Assume that the sky has constant radiance L over the entire upper hemisphere (it is a perfectly cloudy day).

A.     Show that a constant radiance hemispherical source would contribute irradiance E = π L to a point on the ground.

B.     Suppose at some point on the terrain the ground plane is tilted by an angle θ with the respect to the horizon. These means a angular wedge of the hemispherical sky will not be visible at that point because parts of the sky are below the local horizon of the surface. What is the irradiance E at this point?

 

 

  1. Consider a square light source with constant radiance L and vertices (-1,-1,1), (-1,1,1), (1,1,1), and (1,-1,1).  What is the irradiance E at the point (0,0,0), assuming that the surface at (0,0,0) has a normal vector of (0,0,1) [i.e., it points straight towards the center of the square]?