Generalized Hough Transforms

Transcription

1 Generalized Hough Transforms CS 510 Lecture #19 April 1, 2015 Preamble to Generalized Hough Those who cannot remember the past are condemned to repeat it Jorge AgusEn Nicolás Ruiz de Santayana y Borrás Like correlation matching, when your problem admits to these techniques, use them! 3/30/15 CS 510, Image Computa3on, Ross Beveridge & Bruce Draper 2 1

2 Hough Transform : Overview General idea fit features to parameterized models via parameter voting Avoid combinatorial process Requirements Small parameter space Finite parameters Features constrain parameters 3/30/15 CS 510, Image Computa3on, Ross Beveridge & Bruce Draper 3 Generalized Hough Transform Proposed by Dana Ballard Consider edges from an arbitrary 2D curve: Can we use a Hough space to determine if the curve is in another image? 3/30/15 CS 510, Image Computa3on, Ross Beveridge & Bruce Draper 4 2

3 Generalized Hough (cont.) Match under unknown translation Then select a reference point Can be center of mass, doesn t have to be Hough parameters are the position of this point 3/30/15 CS 510, Image Computa3on, Ross Beveridge & Bruce Draper 5 Generalized Hough (III) For every model edge, there is a vector from the edge to the reference point: Store this set of vectors 3/30/15 CS 510, Image Computa3on, Ross Beveridge & Bruce Draper 6 3

4 Generalized Hough (IV) Now consider the edges in your test data: Edge to model part pairing implies placement. The offset from the edge to the reference point must be one of the stored vectors! (vote often!) In this example: 13 Model Edges 11 Data (image) Edges 141 Votes 3/30/15 CS 510, Image Computa3on, Ross Beveridge & Bruce Draper 7 Generalized Hough (V) Create a Hough space of (x,y) reference point positions If there are n points in the model curve, then each edge votes n times An edge votes for the (x,y) positions that can be reached by adding one of the stored vectors to it. The peak in this Hough space is the reference point with the most supporting edges, i.e. votes. 3/30/15 CS 510, Image Computa3on, Ross Beveridge & Bruce Draper 8 4

5 Visualizing the Transformation Agreement x y 3/30/15 CS 510, Image Computa3on, Ross Beveridge & Bruce Draper 9 Making it Still More General... What if one curve might be rotated relative to another? You know the orientation of the model edge So you know the relative orientation of the displacement vector and the edge Rotate the displacement vector prior to voting This is easiest if you store displacement vectors as angle/length The result is rotation and translation invariant 2D curve matching 3/30/15 CS 510, Image Computa3on, Ross Beveridge & Bruce Draper 10 5

6 Rotate x y 3/30/15 CS 510, Image Computa3on, Ross Beveridge & Bruce Draper 11 and Even More General What if the curve might vary in scale, as well as rotation and translation? Two options The length of the displacement vectors is unknown; each edge point votes for a set of lines in Hough space See next slide Extend parameterization to (x,y,scale); each edge votes for a line in this 3D Hough space Larger Hough space slower Fewer accidental intersections more robust 3/30/15 CS 510, Image Computa3on, Ross Beveridge & Bruce Draper 12 6

7 Pose Clustering George Stockman 1987 Similar notion to generalized Hough Key distinction Small sets of features suggest object pose Each set votes by created a vote A vote is a point in the object pose space. To find objects, look for clusters of votes Complexity dominated # of votes, Rather than the dimensionality of pose 3/30/15 CS 510, Image Computa3on, Ross Beveridge & Bruce Draper 13 FLIR Image Edges Template True Match False Match Clark F. Olson, and Daniel P. Huaenlocher, Automa3c Target Recogni3on by Matching Oriented Edge Pixels, IEEE Transac3ons on Image Processing, 6(1): , January /30/15 CS 510, Image Computa3on, Ross Beveridge & Bruce Draper 14 7

8 Using the Circular Hough Transform to Find Tropical Cyclone Centers Robert DeMaria CS 612 Project Fall /30/15 CS 510, Image Computa3on, Ross Beveridge & Bruce Draper 15 Next Topic - RANSAC When overwhelmed with possible votes? 3/30/15 CS 510, Image Computa3on, Ross Beveridge & Bruce Draper 16 8