Stockman MSU/CSE Fall 2009 Finding region boundaries.
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Transcript of Stockman MSU/CSE Fall 2009 Finding region boundaries.
Stockman MSU/CSE Fall 2009
Object boundaries How to detect? How to represent? Problems relative to region/area
segmentation
Stockman MSU/CSE Fall 2009
advantages Contrast often more reliable under
varying lighting Boundaries give precise location Boundaries have useful shape
information Boundary representation is sparse Humans use edge information
Stockman MSU/CSE Fall 2009
problems Detection weakens at boundary
corners Topology of result is imperfect
Stockman MSU/CSE Fall 2009
topics Aggregating chains of boundary
pixels Line and curve fitting Angles, sides, vertices Ribbons Imperfect graphs
Stockman MSU/CSE Fall 2009
Canny edge detector/tracker Detect, then follow high gradient boundary
pixels Track along a “thin” edge Bridge across weaker contrast
Stockman MSU/CSE Fall 2009
Create thin edge response by suppressing weaker neighbors Find neighbors in direction of the gradient
(across the edge) If neighbor response is weaker, delete it. Recall thick edges from 5x5 Sobel or Prewitt
Stockman MSU/CSE Fall 2009
Notes/Variations Very few parameters needed Can use multiple spreads and correlate
the results in multiple edge images Can carefully manage the use of low
and high thresholds, perhaps depending on size and quality of the current track
Canny edge tracker is very popular
Stockman MSU/CSE Fall 2009
Aggregating pixels into curves
Producing a discrete data structure with meaningful
parts.
Stockman MSU/CSE Fall 2009
The Hough Transform
Detecting a straight line segment as a cluster in rho-
theta space. (Can do circles or ellipses
too.)
Stockman MSU/CSE Fall 2009
Pixels with distinct (r,c) coordinates map to same (d, Θ)
X
Y
Θ
d
Detected set of edge points
Textbook coordinate system vs Cartesian system
Stockman MSU/CSE Fall 2009
Mapping pixels (r, c) to polar parmameters (d, Θ)Row-column system
Cartesian coordinate system
d = x cos Θ + y sin Θ
Stockman MSU/CSE Fall 2009
Binning evidence: note that original pixels [R, C] are saved in the bins.
Stockman MSU/CSE Fall 2009
Real world considerations The gradient direction Θ is bound
to have error (due to what?) Since d is computed from Θ, d will
also have error Thus, evidence is spread in
parameter space and may frustrate binning methods (2D histogram)
Stockman MSU/CSE Fall 2009
Solutions Bins for (d, Θ) can be smoothed to
aggregate neighbors. Multiple evidence can be put into the
bins by adding deltas to Θ and computing variations of (d, Θ)
Clustering can be done in real space; e.g. do not use binning
Busy images should be handled using a grid of (overlapping) windows to avoid a cluttered transform space
Stockman MSU/CSE Fall 2009
What is the space of d and Θ ? Many apps range Θ from 0 to π only However, gradient direction can be
detected from 0 to 2 π. Imagine a checkerboard – there are 4
prominent directions, not 2. Using full range of direction requires
negative values of d – consider checkerboard with origin in the center.
Stockman MSU/CSE Fall 2009
Additional material
Plastic slides from Stockman Plastic slides from Kasturi
Stockman MSU/CSE Fall 2009
Some notes
Circular and elliptical Hough Transforms are interesting, but of dubious value by themselves
Smarter tracking methods, such as Snakes, balloons, etc. might be needed along with region features
There are weak publications that will not help in real applications.
Stockman MSU/CSE Fall 2009
Fitting models to edge data
Can use straight line segments for data
compression, or parametric curves for shape detection.