So today, we're going to talk about Nonlinear Least Square estimation. Recall, we have used the least square methods, quite often in this class. And there are two type of least square problem that we've seen, all on the forum of AX, on the left side, the first type of AX equaled the b, on the right, the second one is AX equal to zero on the right. And the solution to both can be computer efficiently. For example, for the type one of least squares, we construct the matrix Ax- b, and typically the matrix a, has a set of rows corresponding to point correspondence of points in the space. And the columns of A are typically associated with the dimension of unknowns. To the case of a line, where have three unknown variables correspond to the lying equations, in the case of a homogeneous, in the case of a fundamental matrix, we have a total of nine columns. Again take the non linear least square, we can go to the set of simple [INAUDIBLE], and obtain a quadratic functions in terms of X, and this matrix Q is allowing us to compute a solution to this problem quickly, the matrix Q is constressed a transpose A. And as such, it has it's own eigen values, all positive, or greater than, or equal to zero. Which means, the energy function, the cost of the square problem, looks like this parabolic curve in a one dimensional space, and has a unique minima. So, there's many solution to this problem. But, the properties that, the global solution exists, and the solution is unique. And typically, we have SVD, as a solution to this problem, and they can be computed efficiently, and because of this, the initialization is not a major factor to us, any initialization will get to the same solution. So that's, why we prefer the square. Life is not always simple, not all the functions we need to look at it, has a linear formations. This function f of x, where x for example is the camera post, might not be linear. And this is what we'll see, how to solve this particular problem where we have a non-linear function f, on the function x, and x typically in our case is the location, and translation of our cameras, equals some unknown variable, b. And this function we'll see has multiple local minimums. But will have a good estimate, what the initial solution should be. And this solution allows, us to tighten up the solution space much better.