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Finding region boundaries. Object boundaries. How to detect? How to represent? Problems relative to region/area segmentation. advantages. Contrast often more reliable under varying lighting Boundaries give precise location Boundaries have useful shape information

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Finding region boundaries

Finding region boundaries

Stockman MSU/CSE Fall 2009


Object boundaries
Object boundaries

  • How to detect?

  • How to represent?

  • Problems relative to region/area segmentation

Stockman MSU/CSE Fall 2009


Advantages
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
problems

  • Detection weakens at boundary corners

  • Topology of result is imperfect

Stockman MSU/CSE Fall 2009


Topics
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
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


Canny algorithm data
Canny algorithm data

Stockman MSU/CSE Fall 2009


Overall canny algorithm
Overall Canny algorithm

Stockman MSU/CSE Fall 2009


Create thin edge response by suppressing weaker neighbors
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



Results with two spreads
Results with two spreads

Stockman MSU/CSE Fall 2009


Notes variations
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

Aggregating pixels into curves

Producing a discrete data structure with meaningful parts.

Stockman MSU/CSE Fall 2009


Tracking tasks
Tracking tasks

Canny algorithm does some of these.

Stockman MSU/CSE Fall 2009


Possible output from tracker
Possible output from tracker

Stockman MSU/CSE Fall 2009


The hough transform

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


Voting evidence in cluster space
Voting evidence in cluster space

Stockman MSU/CSE Fall 2009


Pixels with distinct r c coordinates map to same d
Pixels with distinct (r,c) coordinates map to same (d, Θ)

Y

Detected set of edge points

d

Textbook coordinate system vs Cartesian system

Θ

X

Stockman MSU/CSE Fall 2009


Mapping pixels r c to polar parmameters d
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


Simple algorithm overview
Simple algorithm overview

Stockman MSU/CSE Fall 2009


Possible implementation
Possible implementation

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
Real world considerations in the bins.

  • 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
Solutions in the bins.

  • 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
What is the space of d and in the bins.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
Additional material in the bins.

  • Plastic slides from Stockman

  • Plastic slides from Kasturi

Stockman MSU/CSE Fall 2009


Image to map work of kasturi
Image to map work of Kasturi in the bins.

Stockman MSU/CSE Fall 2009


Circular hough transform
Circular Hough Transform in the bins.

There are 3 parameters for a circle

Stockman MSU/CSE Fall 2009


Possible implementation1
Possible implementation in the bins.

Stockman MSU/CSE Fall 2009


Some notes
Some notes in the bins.

  • 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

Fitting models to edge data in the bins.

Can use straight line segments for data compression, or parametric curves for shape detection.

Stockman MSU/CSE Fall 2009


Fitting curves
Fitting curves in the bins.

Stockman MSU/CSE Fall 2009


An unlimited number of models
An unlimited number of models in the bins.

Stockman MSU/CSE Fall 2009


Least squares fitting
Least squares fitting in the bins.

Stockman MSU/CSE Fall 2009


Best fit minimizes sum of squared errors
Best fit minimizes sum of squared errors in the bins.

Stockman MSU/CSE Fall 2009



Axis of least inertia better
Axis of least inertia better? in the bins.

Stockman MSU/CSE Fall 2009


Ramer s alg perimeter to polygon
Ramer’s alg: perimeter to polygon in the bins.

Stockman MSU/CSE Fall 2009


Angles corners ribbons
Angles, corners, ribbons in the bins.

Stockman MSU/CSE Fall 2009


The downspout as a ribbon
The downspout as a ribbon in the bins.

Stockman MSU/CSE Fall 2009


Road and canal as ribbons
Road and canal as ribbons in the bins.

Stockman MSU/CSE Fall 2009


More boundary detection later
More boundary detection later in the bins.

  • Will investigate “physics-based models”

  • Can fit to 2D (snakes) or 3D data (balloons)

  • Models do not allow the object topology to break

  • Models enforce object smoothness

Stockman MSU/CSE Fall 2009


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