ECE 661 Computer Vision : HW 5 Dae

In the last homework, the DLT algorithm was used to find the homography which minimized an algebraic cost function. In this homework, we wish to find the homography H which minimizes the geometric cost function given by Equation 4.6 in the textbook (pg. 94) (1) where d() is Euclidean distance. Equation (1) can be rewritten as a nonlinear least squares problem with the form C(p) = X − F (p) 2 (2) where X is a set of data points and F (p) is a nonlinear function with parameters p. Note that the minimization is carried out only over the parameters p; the data points and nonlinear function are fixed. The first part of the problem is to determine what X, F (p), and p should be in Equation (2) in order to give the same cost as Equation (1). Once the cost function is in the form of Equation (2), there are several iterative methods available to minimize it. In this homework you will try 2 standard methods, gradient descent and Gauss-Newton, as well as two hybrid methods, Levenberg-Marquardt and dog leg.