minimizing vector is a solution of the normal equation The solution of the system of linear equations is given in terms of the matrix , called the pseudoinverse of A, by which minimizes the sum of the squares of the distances from the projected model locations to the corresponding image locations. Outlier detection Outliers can now be removed by checking for agreement between each image feature and the model, given the parameter solution. Given the linear least squares solution, each match is required to agree within half the error range that was used for the parameters in the Hough transform bins. As outliers are discarded, the linear least squares solution is re-solved with the remaining points, and the process iterated. If fewer than 3 points remain after discarding outliers, then the match is rejected. In addition, a top-down matching phase is used to add any further matches that agree with the projected model position, which may have been missed from the Hough transform bin due to the similarity transform approximation or other errors. The final decision to accept or reject a model hypothesis is based on a detailed probabilistic model. This method first computes the expected number of false matches to the model pose, given the projected size of the model, the number of features within the region, and the accuracy of the fit. A Bayesian probability analysis then gives the probability that the object is present based on the actual number of matching features found. A model is accepted if the final probability for a correct interpretation is greater than 0.98. Lowe's SIFT based object recognition gives excellent results except under wide illumination variations and under non-rigid transformations. Algorithm Scale-space extrema detection We begin by detecting points of interest, which are termed keypoints in the SIFT framework. The image is convolved with Gaussian filters at different scales, and then the difference of successive Gaussian-blurred images are taken. Keypoints are then taken as maxima/minima of the Difference of Gaussians (DoG) that occur at multiple scales. Specifically, a DoG image is given by , where is the convolution of the original image with the Gaussian blur at scale , i.e., Hence a DoG image between scales and is just the difference of the Gaussian-blurred images at scales and . For scale space extrema detection in the SIFT algorithm, the image is first convolved with Gaussian-blurs at different scales. The convolved images