CS 332 (Mini) Assignment 8 Due: Wednesday, December 8

Note: This assignment can be submitted late, up until the last day of finals (Friday, December 16), without penalty.

Recognition by a Linear Combination of Views (50 points)

Part a: Write up your solutions to the exercise given in class, in which you used the linear combination of views method to determine whether an unknown face is Harry or Henry. Show all of the work that led to the final recognition of the face image as Harry or Henry.

Part b: In practice, the predicted view that is derived from a linear combination of the known model views will probably not match perfectly with the actual image view to be recognized. Describe two different (and reasonable) ways to measure how well the predicted and actual image views match (be specific). Compare and contrast your two measures. Will they always produce the same results (i.e., if Model #1 fits better than Model #2 using one measure, will it necessarily fit better using the second measure)? Try to construct an example with a small number of points that would yield different results for your two different measures.

Part c: Is it possible that the linear equations used to solve for α and β will not have a solution? If so, when can this situation occur?

Part d: If the model and novel views of an object are related by rotation around a single axis, the transformation between the views can be determined using the positions of only two points. Suppose you know that the views are related by a single axis rotation, but there is error in the computed feature positions that could lead to error in the computation of α and β. To get a better estimate of these parameters, you could use the positions of more than two points and find a transformation (α and β) that best fits the positions of a larger number of points. Describe a method for doing this. Hint: consider other problems in which this issue arose, such as the computation of 2-D velocity from perpendicular components of motion, or computation of the focus of expansion in the case of observer motion.