Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

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.

Typology: Slides

2011/2012
On special offer
30 Points
Discount

Limited-time offer

Uploaded on 03/02/2012

cristelle
cristelle 🇺🇸

4.5

(53)

374 documents

1 / 11

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
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
pf3
pf4
pf5
pf8
pf9
pfa
Discount

On special offer

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!

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

0

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

Hough transform (example 5 continued)