TAILIEUCHUNG - Fitting: The hough transform

Voting schemes, hough transform, parameter space representation, algorithm outline, basic illustration,. As the main contents of the lecture "Fitting: The hough transform". Each of your content and references for additional lectures will serve the needs of learning and research. | Fitting: The Hough transform Voting schemes Let each feature vote for all the models that are compatible with it Hopefully the noise features will not vote consistently for any single model Missing data doesn’t matter as long as there are enough features remaining to agree on a good model Hough transform An early type of voting scheme General outline: Discretize parameter space into bins For each feature point in the image, put a vote in every bin in the parameter space that could have generated this point Find bins that have the most votes . Hough, Machine Analysis of Bubble Chamber Pictures, Proc. Int. Conf. High Energy Accelerators and Instrumentation, 1959 Image space Hough parameter space Parameter space representation A line in the image corresponds to a point in Hough space Image space Hough parameter space Source: S. Seitz Parameter space representation What does a point (x0, y0) in the image space map to in the Hough space? Image space Hough parameter space Parameter space representation What does a point (x0, y0) in the image space map to in the Hough space? Answer: the solutions of b = –x0m + y0 This is a line in Hough space Image space Hough parameter space Parameter space representation Where is the line that contains both (x0, y0) and (x1, y1)? Image space Hough parameter space (x0, y0) (x1, y1) b = –x1m + y1 Parameter space representation Where is the line that contains both (x0, y0) and (x1, y1)? It is the intersection of the lines b = –x0m + y0 and b = –x1m + y1 Image space Hough parameter space (x0, y0) (x1, y1) b = –x1m + y1 Problems with the (m,b) space: Unbounded parameter domain Vertical lines require infinite m Parameter space representation Problems with the (m,b) space: Unbounded parameter domain Vertical lines require infinite m Alternative: polar representation Parameter space representation Each point will add a sinusoid in the ( , ) parameter space Algorithm outline Initialize accumulator H

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