Corner Detection

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(f_y/f_x)

in the direction

v= ( -f_y,f_x ) (f_x²+f_y²)^(-1/2)

b) (4 points) Find an expression for the directional derivative

 D_v 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)