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Edge Linking-Digital Image Processing-Lecture 17 Slides Slides-Electrical and Computer Engineering, Slides of Digital Image Processing

University of Alabama (UA)Digital Image Processing

Edge Linking, Boundary Detection, Detection, Edge, Linking, Local Processing, Global Processing, Hough, Transform, Accumulator Cells, Matlab, Array, Digital Image Processing, Lecture Slides, Dr D J Jackson, Department of Electrical and Computer Engineering, University of Alabama, United States of America.

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Dr. D. J. Jackson Lecture 17-1Electrical & Computer Engineering

Computer Vision &

Digital Image Processing

Edge Linking and Boundary Detection

Dr. D. J. Jackson Lecture 17-2Electrical & Computer Engineering

Edge linking and boundary detection

•Ideally, edge detection techniques yield pixels lying

only on the boundaries between regions

•In practice, this pixel set seldom characterizes a

boundary completely because of

–noise

–breaks in the boundary due to non-uniform illumination

–other effects that introduce spurious discontinuities

•Thus, edge detection algorithms are usually

followed by linking and other boundary detection

procedures designed to assemble edge pixels into

meaningful boundaries

On special offer

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Download Edge Linking-Digital Image Processing-Lecture 17 Slides Slides-Electrical and Computer Engineering and more Slides Digital Image Processing in PDF only on Docsity!

Electrical & Computer Engineering Dr. D. J. Jackson Lecture 17-

Computer Vision &

Digital Image Processing

Edge Linking and Boundary Detection

Edge linking and boundary detection

Ideally, edge detection techniques yield pixels lying

only on the boundaries between regions

In practice, this pixel set seldom characterizes a

boundary completely because of

noise
breaks in the boundary due to non-uniform illumination
other effects that introduce spurious discontinuities
Thus, edge detection algorithms are usually

followed by linking and other boundary detection

procedures designed to assemble edge pixels into

meaningful boundaries

Electrical & Computer Engineering Dr. D. J. Jackson Lecture 17-

Edge linking: local processing

Basic idea:
- Analyze the characteristics of pixels in a small neighborhood (3x3,

5x5, etc) for every point (x,y) that has undergone edge detection

All points that are “similar” are linked, forming a boundary of pixels

that share some common property

Two principal properties for establishing similarity
- The strength of the response of the gradient operator used to produce

the edge pixels

The direction of the gradient

⎟⎟ ⎠

⎞ ⎜⎜ ⎝

⎛ = − x

y G

G α( x , y ) tan^1

Edge linking: local processing (cont.)

An edge pixel at (x’,y’) in the neighborhood centered at (x,y) is similar in magnitude to the pixel at (x,y) if
where T is a predetermined threshold
An edge pixel at (x’,y’) in the neighborhood centered at (x,y) is similar in angle to the pixel at (x,y) if
where A is a predetermined angle threshold
A point in the neighborhood of (x,y) is linked to (x,y) if both magnitude and angle criteria are satisfied

∇ f ( x , y )−∇ f ( x ', y ')≤ T

α( x , y )− α( x ', y ')≤ A

Electrical & Computer Engineering Dr. D. J. Jackson Lecture 17-

Hough transform: accumulator cells

The computational attractiveness of the Hough

transform arises from the subdivision of the

parameter space into accumulator cells

( a (^) min ,a (^) max ) and ( b (^) min ,b (^) max ) are expected ranges of

slope and intercept values

b (^) min 0 b (^) max

a (^) max

a (^) min

Hough transform: accumulator cells

The cell at coordinates (i,j), with cell value A(i,j), corresponds to the

square associated with parameter space coordinates (a i ,b j)

The collection of accumulator cells is commonly called the Hough matrix

(or Hough array) and are computed as

1. Set all cells to zero.

2. For every point (xk,yk) in the image plane, let a equal each of the allowed

subdivision values on the a axis and solve for b using b=-x ka+yk

3. The resulting b’s are rounded off to the nearest allowed value in the b axis

4. If a choice of ap results in solution b q, we let A(p,q)=A(p,q)+

5. At the end of the procedure, a value of M in A(i,j) corresponds to M points in

the xy plane lying on the line y=aix+bj

The accuracy of the collinearity of these points is determined by the

number of subdivisions in the ab plane

Electrical & Computer Engineering Dr. D. J. Jackson Lecture 17-

The Hough transform (continued)

• A problem with this representation is that the slope and

intercept approach infinity as the line approaches the vertical

• Solution: use the normal representation of a line given by

x cos θ + y sin θ = ρ

y

x

ρmin 0 ρmax

θmax

θmin

The Hough transform (continued)

• Instead of straight lines in the ab plane, we now have

sinusoidal curves in the ρθ plane

• M collinear points lying on the line

• yields M sinusoidal curves that intersect at (ρi,θj ) in the

parameter space

• The range of θ is ±90°, measured with respect to the x axis

A horizontal line has θ=0°, with ρ equal to the positive x intercept
A vertical line has θ=+90°, with ρ equal to the positive y intercept or

θ=-90°, with ρ equal to the negative y intercept

• The range of ρ is ±(2)½^ D. Where D is the distance between

corners in the image

x cos θ j + y sin θ j = ρ i

Electrical & Computer Engineering Dr. D. J. Jackson Lecture 17-

Hough transform (example 1 continued)

Hough transform (example 2)

image(a);colormap(gray( 6));
Original image matrix
- image(v);colormap(gray( ));
- Image of the Hough array

Electrical & Computer Engineering Dr. D. J. Jackson Lecture 17-

Hough transform (example 2 continued)

Hough transform (example 3)

image(a);colormap(gray(256));
Original image matrix
- image(v);colormap(gray(16));
- Image of the Hough array

Electrical & Computer Engineering Dr. D. J. Jackson Lecture 17-

Hough transform (example 4 continued)

Hough transform (example 5)

image(a);colormap(gray(256));
Original image matrix
- image(v);colormap(gray(16));
- Image of the Hough array

Edge Linking-Digital Image Processing-Lecture 17 Slides Slides-Electrical and Computer Engineering, Slides of Digital Image Processing

Related documents

Partial preview of the text

Download Edge Linking-Digital Image Processing-Lecture 17 Slides Slides-Electrical and Computer Engineering and more Slides Digital Image Processing in PDF only on Docsity!

Computer Vision &

Digital Image Processing

Edge Linking and Boundary Detection

Edge linking and boundary detection

only on the boundaries between regions

boundary completely because of

followed by linking and other boundary detection

procedures designed to assemble edge pixels into

meaningful boundaries

Edge linking: local processing

5x5, etc) for every point (x,y) that has undergone edge detection

that share some common property

the edge pixels

Edge linking: local processing (cont.)

α( x , y )− α( x ', y ')≤ A

Hough transform: accumulator cells

transform arises from the subdivision of the

parameter space into accumulator cells

slope and intercept values

Hough transform: accumulator cells

square associated with parameter space coordinates (a i ,b j)

(or Hough array) and are computed as

1. Set all cells to zero.

2. For every point (xk,yk) in the image plane, let a equal each of the allowed

subdivision values on the a axis and solve for b using b=-x ka+yk

3. The resulting b’s are rounded off to the nearest allowed value in the b axis

4. If a choice of ap results in solution b q, we let A(p,q)=A(p,q)+

5. At the end of the procedure, a value of M in A(i,j) corresponds to M points in

the xy plane lying on the line y=aix+bj

number of subdivisions in the ab plane

The Hough transform (continued)

• A problem with this representation is that the slope and

intercept approach infinity as the line approaches the vertical

• Solution: use the normal representation of a line given by

x cos θ + y sin θ = ρ

y

x

ρmin 0 ρmax

θmax

θmin

The Hough transform (continued)

• Instead of straight lines in the ab plane, we now have

sinusoidal curves in the ρθ plane

• M collinear points lying on the line

• yields M sinusoidal curves that intersect at (ρi,θj ) in the

parameter space

• The range of θ is ±90°, measured with respect to the x axis

θ=-90°, with ρ equal to the negative y intercept

• The range of ρ is ±(2)½^ D. Where D is the distance between

corners in the image

x cos θ j + y sin θ j = ρ i

Hough transform (example 1 continued)

Hough transform (example 2)

Hough transform (example 2 continued)

Hough transform (example 3)

Hough transform (example 4 continued)

Hough transform (example 5)

Hough transform (example 5 continued)