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Finding region boundaries

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Finding region boundaries

Stockman MSU/CSE Fall 2009

- How to detect?
- How to represent?
- Problems relative to region/area segmentation

Stockman MSU/CSE Fall 2009

- 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

- Detection weakens at boundary corners
- Topology of result is imperfect

Stockman MSU/CSE Fall 2009

- Aggregating chains of boundary pixels
- Line and curve fitting
- Angles, sides, vertices
- Ribbons
- Imperfect graphs

Stockman MSU/CSE Fall 2009

- Detect, then follow high gradient boundary pixels
- Track along a “thin” edge
- Bridge across weaker contrast

Stockman MSU/CSE Fall 2009

Stockman MSU/CSE Fall 2009

Stockman MSU/CSE Fall 2009

- 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

Stockman MSU/CSE Fall 2009

Stockman MSU/CSE Fall 2009

- 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

Canny algorithm does some of these.

Stockman MSU/CSE Fall 2009

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

Stockman MSU/CSE Fall 2009

Y

Detected set of edge points

d

Textbook coordinate system vs Cartesian system

Θ

X

Stockman MSU/CSE Fall 2009

Row-column system

Cartesian coordinate system

d = x cos Θ + y sin Θ

Stockman MSU/CSE Fall 2009

Stockman MSU/CSE Fall 2009

Stockman MSU/CSE Fall 2009

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

Stockman MSU/CSE Fall 2009

- 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

- 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

- 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

- Plastic slides from Stockman
- Plastic slides from Kasturi

Stockman MSU/CSE Fall 2009

Stockman MSU/CSE Fall 2009

There are 3 parameters for a circle

Stockman MSU/CSE Fall 2009

Stockman MSU/CSE Fall 2009

- 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.

Stockman MSU/CSE Fall 2009

Stockman MSU/CSE Fall 2009

Stockman MSU/CSE Fall 2009

Stockman MSU/CSE Fall 2009

Stockman MSU/CSE Fall 2009

Stockman MSU/CSE Fall 2009

Stockman MSU/CSE Fall 2009

Stockman MSU/CSE Fall 2009

Stockman MSU/CSE Fall 2009

Stockman MSU/CSE Fall 2009

Stockman MSU/CSE Fall 2009

- 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