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Generalized Hough Transforms

CS 510 Lecture #19 April 1, 2015

Preamble to Generalized Hough

•  Like correlation matching, when your problem admits to these techniques, use them!

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“Those  who  cannot  remember  the  past  are  condemned  to  repeat  it”  Jorge  AgusEn  Nicolás  Ruiz  de  Santayana  y  Borrás  

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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

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Generalized Hough Transform

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•  Proposed by Dana Ballard -1981 •  Consider edges from an arbitrary 2D curve:

Can  we  use  a  Hough  space  to  determine  if  the  curve  is  in  another  image?  

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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

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×

Generalized Hough (III)

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•  For every model edge, there is a vector from the edge to the reference point:

×

 Store  this  set  of  vectors  

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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!)

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In  this  example:        13    Model  Edges        11    Data  (image)  Edges    141    Votes  

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.

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Visualizing the Transformation

x

y

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Agreement  

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

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Rotate

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x

y

… 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

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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

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Clark  F.  Olson,  and  Daniel  P.  Huaenlocher,  Automa3c  Target  Recogni3on  by  Matching  Oriented  Edge  Pixels,  IEEE  Transac3ons  on  Image  Processing,  6(1):  103-­‐113,  January  1997  

FLIR  Image   Edges   Template  

True  Match   False  Match  

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Using  the  Circular  Hough  Transform  to  Find  Tropical  

Cyclone  Centers  Robert  DeMaria  CS  612  Project  

Fall  2013  

Next Topic - RANSAC •  When overwhelmed with possible votes?

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