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# Class Note for EECS 841 with Professor Potetz at KU 4

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Date Created: 02/06/15

EECS 841 Computer Vision Brian Potetz Fall 2008 Lecture 9 Active Contours Suggested Reading Forsyth amp Ponce quotComputer Vision A Modern Approach Chapter 151 E R Davies quotMachine Vision Chapters 911 L G Shapiro G C Stockman quotComputer Vision Chapter 10 Reparameterization of Lines 50 740 A 720 E c D U E Q 0 2 0 gtlt 3 O L t 20 4o 60 5 Example Points Reparameterization of Lines Two Lines Finding Circles by Hough Transform Equation of Circle x agt2 y b2 r2 If radius is known 2D Hough Space Accumulator Array Aa 1 Question What is the advantage of this Hough transform over Convolution Red circles locus of the center of possible circles Finding Circles by Hough Transform Equation of Circle x a2 y b2 7392 If radius is unknown 3D Hough Space Accumulator Array Aa b Iquot What is he surface in the hough space a Red circles locus of the center of possible circles b W Finding Circles by Hough Transform Equation of Circle x agt2 y bgt2 r2 If radius is unknown 3D Hough Space AccumulatorArray Aabr Alterna ively use a 2D Accumulator array Aab and increment it for each radius in some range of possible radii Red circles locus of the center of possible circles Question Why wouldn t this falsely accept ellipses Generalized Hough Transform Find contours that match a xed template Template can be any shape Works just like Hough transform for circles of known size Modal Generalized Hough Transform I 39 quot quot 4 gt v EECS 841 Computer Vision Brian Potetz Fall 2008 Lecture 9 Active Contours Suggested Reading D H Ballard C M Brown quotComputer Vision Sect 45 A Approach L G Shapiro G C Stockman quotComputer Vision Section 143 Energy Model Kass Witkin Terzopoulos quotSnakes Active Contour Models IJCV 1988 Energy Model Following Edges Using Graph Searching 1 Use traditional techniques to nd edges in the image 2 Convert the edge image into a weighted directional graph 3 Find the path of least cost through the graph using the A search algorithm From Edges to Weighted Graphs One way to de ne a directed graph Directed graph Original image Gradient magnitude IVIxyl Let the cost of each arc be M VIxy where Xy is the point on the image corresponding to the destination node of the arc Finding the LeastCost Path The A algorithm 1 Initialize the queue with the path from the source vertex to itself 2 Until the rst path in the queue reaches the destination vertex i Remove the rst path from the queue For each neighbor of the last node in this path create a new path ii If a new path terminates in a node that has already been explored and no path in the queue terminates in that node delete that new path iii If a new path terminates in a node that has already been explored and there is a path in the queue that terminates in that node delete the path that has the greatest cost iv Sort the queue by the cost of the paths Properties of the A Algorithm As long as 1 The actual cost of all paths through the graph is the sum of the costs of each arc it traverses 2 And each arc has positive cost Then A will nd the globallyoptimum least cost path UserDefined Costs In addition weighing paths according to how closely they follow edges in the image we want our snake to respond to advice from the user Some additional costs to weight include Distance to the original estimate Allow the user to discourage or encourage particular regions of the image Limitations on curvature Improving Search Performance When performing A let the cost of each path be the sum of the weights of all arcs traversed plus the some lowerbound estimate of the cost of traversing the remaining distance to the destination node in fact the search algorithm is not called A unless it uses this technique minwj e gt 0 Cost12 acn w1gt2 w23 wgnil gn E 39 ibdestz nation Improving Search Performance When performing A let the cost of each path be the sum of the weights of all arcs traversed plus the some lowerbound estimate of the cost of traversing the remaining distance to the destination node in fact the search algorithm is not called A unless it uses this technique minwij a gt 0 Cost12 Jan w51gt2 tuna wgnil gn E 39 destz natz 0n Carefully choose your cost functions Flat terrains take more time to search Improving Search Performance Use the edge direction to eliminate arcs in your graph Improving Search Performance Use the edge direction to eliminate arcs in your graph egtlti Figure 519 Graph representation ofan edge image a Edge directions corresponding graph NatlonalINaval Ice Center Amery Sea Icebergs B17B B15K ENVISAT Image 05 June 2008 I 02432 Analyst A61 SW Heisler B175 6 093 4E 26NMX11NM National Naval Ice Center Weddell Sea Icebergs B15L c1gn ENVISAT Image 04 June 2008 03242 Analysl39 A61 SW Heisler

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