Finding region boundaries
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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

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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


Begin tracking only at high gradient points

Begin tracking only at high gradient points

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


Finding region boundaries

Binning evidence: note that original pixels [R, C] are saved in the bins.

Stockman MSU/CSE Fall 2009


Real world considerations

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

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

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

Additional material

  • 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

Stockman MSU/CSE Fall 2009


Circular hough transform

Circular Hough Transform

There are 3 parameters for a circle

Stockman MSU/CSE Fall 2009


Possible implementation1

Possible implementation

Stockman MSU/CSE Fall 2009


Some notes

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

Fitting models to edge data

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

Stockman MSU/CSE Fall 2009


Fitting curves

Fitting curves

Stockman MSU/CSE Fall 2009


An unlimited number of models

An unlimited number of models

Stockman MSU/CSE Fall 2009


Least squares fitting

Least squares fitting

Stockman MSU/CSE Fall 2009


Best fit minimizes sum of squared errors

Best fit minimizes sum of squared errors

Stockman MSU/CSE Fall 2009


Finding region boundaries

Stockman MSU/CSE Fall 2009


Axis of least inertia better

Axis of least inertia better?

Stockman MSU/CSE Fall 2009


Ramer s alg perimeter to polygon

Ramer’s alg: perimeter to polygon

Stockman MSU/CSE Fall 2009


Angles corners ribbons

Angles, corners, ribbons

Stockman MSU/CSE Fall 2009


The downspout as a ribbon

The downspout as a ribbon

Stockman MSU/CSE Fall 2009


Road and canal as ribbons

Road and canal as ribbons

Stockman MSU/CSE Fall 2009


More boundary detection later

More boundary detection later

  • 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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