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by: Kathleen Cartwright


Kathleen Cartwright
GPA 3.73


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Class Notes
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This 37 page Class Notes was uploaded by Kathleen Cartwright on Monday September 28, 2015. The Class Notes belongs to CIS580 at University of Pennsylvania taught by Staff in Fall. Since its upload, it has received 20 views. For similar materials see /class/215387/cis580-university-of-pennsylvania in Computer Information Technology at University of Pennsylvania.

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Date Created: 09/28/15
Fitting Marc Pollefeys COMP 256 Some slides and illustrations from D Forsyth T Darrel A Zisserman Fitting Choose a parametric Three main objectsome objects questions to represent a set of what object tokens represents this set Most interesting case Of t0kens beSt is when criterion is WhiCh 0f SEVera39 not local objects gets which can t tell whether a tOken set of points lies on how many ObJeCtS a line by looking are there only at each point and the next you could read line for object here or circle or ellipse or Hough transform straight lines image y C b parameter space implementation 1 the parameter space is discretised 2 a counter is incremented at each cell where the lines pass 3 peaks are detected problem unbounded parameter domain vertical lines require infinite a alternative representation r Hough transform straight lines xCOSH ysin6 p X Each point will add a cosine function in the Ep parameter space vows Hough transform straight lines Square Circle Hough transform straight lines Mechanics of the Hough transform Construct an array representing 6 d For each point render the curve 6 d into this array adding one at each cell Difficulties how big should the cells be too big and we cannot distinguish between quite different lines too small and noise causes lines to be missed 0 How many lines count the peaks in the Hough array 0 Who belongs to which line tag the votes 0 Hardly ever satisfactory in practice because problems with noise and cell size defeat it wkens vows Maximum number of votes nn EU I I I I I I I I I 15 it 10 i 39339 3E 4E a as as 1E i 5 l l l I 1 J T i 39E 3919 0 001 002 003 004 005 005 007 006 009 01 Noise level Maximum number of votes I I I 40 50 30 103 133 140 163 130 Number of noise points 2C0 Who came from which line 0 Assume we know how many lines there are but which lines are they easy if we know who came from which line 0 Three strategies Incremental line fitting Kmeans Probabilistic later Algorithm 151 lncrementa Hne tting by wa kw ng a ong a cuNe tting a Hne to Ms of pixe s a ong me cuNe and breaking the Curve when the reswdua 5 too arge Put all points on curve 139 t in order alum the cum Emptv the hue paint List 39 List Um there are con few pumts on ch curve Transfer rst f w points on thn Cm39vn to the hm point list Fit line tu Linc point hst Vhile ttud Line is good man b no the Line paint list and re t the line Cm Trzmsfer last points back to cum R r us Attach line to line list cud Incremental line ttin Incremental line ttin Incremental line tting Incremental line tting Incremental line tting Algorithm 152 Krmeans Hue mm by aHocau ng points to me dosest hue and then re tting Hypothesize 1 Lines perhaps uujfmmly at random 5 to paints hen t hues using this assxgumeuc 0r Hypothesize a1 assignman of line ml Until convergence ocatc Cnch point to the closest line 39 as Re t 1m and Kmeans line tting Kmeans line tting Kmeans line tting Kmeans line tting Kmeans line tting Kmeans line tting Kmeans line tting Robustness 0 As we have seen squared error can be a source of bias in the presence of noise points One fix is EM we ll do this shortly Another is an M estimator 0 Square nearby threshold far away A third is RANSAC 0 Search for good points Mestimators 0 Generally minimize ZMnxi k where nee9 is the residual Robust Estimation A quadratic p function gives too much weight to outliers Instead use robust norm In uence function ddr of norm


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