Invite you to consult the lecture content "Fitting" below. Contents of lectures introduce to you the content ''Problem with vertical least squares, total least squares, least squares as likelihood maximization, least squares for general curves". Hopefully document content to meet the needs of learning, work effectively. | Fitting Fitting: Motivation We’ve learned how to detect edges, corners, blobs. Now what? We would like to form a higher-level, more compact representation of the features in the image by grouping multiple features according to a simple model 9300 Harris Corners Pkwy, Charlotte, NC Source: K. Grauman Fitting Choose a parametric model to represent a set of features simple model: lines simple model: circles complicated model: car Fitting Choose a parametric model to represent a set of features Line, ellipse, spline, etc. Three main questions: What model represents this set of features best? Which of several model instances gets which feature? How many model instances are there? Computational complexity is important It is infeasible to examine every possible set of parameters and every possible combination of features Fitting: Issues Noise in the measured feature locations Extraneous data: clutter (outliers), multiple lines Missing data: occlusions Case study: Line detection Fitting: Issues If we know which points belong to the line, how do we find the “optimal” line parameters? Least squares What if there are outliers? Robust fitting, RANSAC What if there are many lines? Voting methods: RANSAC, Hough transform What if we’re not even sure it’s a line? Model selection Least squares line fitting Data: (x1, y1), , (xn, yn) Line equation: yi = m xi + b Find (m, b) to minimize (xi, yi) y=mx+b Least squares line fitting Data: (x1, y1), , (xn, yn) Line equation: yi = m xi + b Find (m, b) to minimize Normal equations: least squares solution to XB=Y (xi, yi) y=mx+b Problem with “vertical” least squares Not rotation-invariant Fails completely for vertical lines Total least squares Distance between point (xi, yi) and line ax+by=d (a2+b2=1): |axi + byi – d| (xi, yi) ax+by=d Unit normal: N=(a, b) Total least squares Distance between point (xi, yi) and line ax+by=d (a2+b2=1): |axi + byi – d| Find (a, b, d) to minimize the sum of squared | Fitting Fitting: Motivation We’ve learned how to detect edges, corners, blobs. Now what? We would like to form a higher-level, more compact representation of the features in the image by grouping multiple features according to a simple model 9300 Harris Corners Pkwy, Charlotte, NC Source: K. Grauman Fitting Choose a parametric model to represent a set of features simple model: lines simple model: circles complicated model: car Fitting Choose a parametric model to represent a set of features Line, ellipse, spline, etc. Three main questions: What model represents this set of features best? Which of several model instances gets which feature? How many model instances are there? Computational complexity is important It is infeasible to examine every possible set of parameters and every possible combination of features Fitting: Issues Noise in the measured feature locations Extraneous data: clutter (outliers), multiple lines Missing data: occlusions Case study: Line .
