6. Show that Laplacian 2f=fxx+fyy is also given by 2f=f+fn, where f is defined as second derivative of f in the direction , and fn is the second derivative in the direction perpendicular to . 7. Consider a bi-cubic polynomial defined in equation 2.13. (a) Derive equations 2.14 and 2.15. (b) Apply the substitution of variables x=sin,y=cos in equation 2.13 to change f(x,y) into f(), and show that f() is given by equation 2.18. 8. Consider a second order polynomial: f(x,y)=k1+k2x+k3y+k4x2+k5y2+k6xy. CHAPTER 2. EDGE DETECTION Compute masks for k1,k2,k3,k4,k5,k6 using least squares fit. You can use a 33 window around each pixel in the image. 9. Show that gradient magnitude is rotation invariant. Let that gradient at point (x,y) is given by (fx,fy). Assume that the object is rotated around Z axis, the point (x,y) moves to point (x,y). fx2+fy2=fx2+fy2 10. What is the computational complexity of Canny's edge detector and Laplacian of Gaussian edge detector. First identify main steps in each edge detector, then compute the complexity for each individual step