6760, Math 21a, Fall 2009
Week 6 Problems E, Math 21a, Multivariable Calculus
Corner Detection
Course head: Oliver Knill
Office: SciCtr 434
Problem E: Corner detection

In this exercise we derive and discuss a formula for the curvature of a level curve f(x,y) = c at a point (x0,y0). It is used in computer vision.

a) (4 points) Verify that the curvature of the level curve f(x,y) = c is the absolute value of the directional derivative of
g(x,y) = arctan(fy/fx) 
in the direction
v= ( -fy,fx ) (fx2+fy2)(-1/2) 
b) (4 points) Find an expression for the directional derivative
 Dv g(x,y)   . 
This problem is hard to solve without the help of the problem sessions. Not the MQC but the problem sessions will provide more help with this problem. c) (2 points) Use this formula to compute the curvature of the curve x4+2 y4=3 at (1,1)

Questions and comments to knill@math.harvard.edu
Math21b | Math 21a | Fall 2009 | Department of Mathematics | Faculty of Art and Sciences | Harvard University