Edge Enhancement

1
Edge Enhancement
Now we will go deeper to operators that enhance
edges and thus images
2
Image Enhancement

• Brightness control
• Contrast enhancement
• noise reduction
• Edge enhancement

?
?
?
3
Objectives

• What are edges?
• What are the properties of an edge?
• What is edge enhancement?
• How is edge enhancement performed?
• edge enhancement from first principles
• Neighbourhood operators
• laplacian
• unsharp masking

4
What are edges ?

• Change, or discontinuity, in image brightness
  between two reasonably smooth regions.
• Fundamentally important primitive image
  characteristics.
• Only information in most black and white images.

5
What are edges?

• Ideal edge
• It is usually ramped because of sensor processing
  during capture
• Noisy edge
• Line

A(x)
x
A(x)
x
A(x)
x
A(x)
x
6
Edge Properties

• Edge has two properties
• how steep it is
• direction, ie, is it pointing towards the left or
  right?

A(x)
x
A(x)
x
7
Edge Properties-gradient

• Consider a 1-d continuous image of an edge,
  denoted by A(x)
• Edge properties can be obtained from the gradient
  ?A / ? x
• gradientdA/dx as ? x?0.

A(x)
??A
??x
8
Edge Properties

• Gradient has two properties
• magnitude
• direction
• Magnitude, or steepness, given by dA/dx
• Direction, left or right, given by sign of dA/d x

9
Edge Properties-gradient

• Gradient given by first derivative dA /d x.
• Second derivative, d2A/d x2,generates two
  peaks at beginning and end of edge.
• Called ringing.

10
Edge Properties-discrete gradient
B-1 1
B1 -2 1
11
Neighbourhood Operators

• First derivative can be calculated by convolving
  with mask B-1 1.
• Second derivative can be calculated by convolving
  with mask B 1 -2 1.

12
Edges in 2-D Images

• Edge properties are provided by gradient of image
  brightness A(x,y)
• 1-d case the gradient direction is either ? or?
• 2-d gradient has a magnitude and orientation

13
Edges in 2-D Images

• Direction of gradient at any point is the
  direction of maximum change.

14
2-d Gradient Operator
15
Discrete 2-d gradient operator
Neighbour hood operators
16
Contour plot and gradient
17
Gradient Operators for Images

• Second-order gradient denoted by ?2A.
• Highlights discontinuties in an image.
• Scalar.

18
Neighbourhood Operators
19
Neighbourhood Operators
20
Laplacian Image
21
What is Edge-enhancement?

• Physcophysical experiments indicate that an image
  with accentuated or crispened edges is often more
  subjectively pleasing than the original image.

22
How do you enhance edges?

• What is a measure of the strength of an edge?
• How steep it is.

A(x)
x
23
Edge enhancement

• Laplacian
• Unsharp masking

24
Laplacian

• Add Laplacian to original.
• A(x)L
• Overshoot below and above edge.

25
Laplacian
A(x)
x
26
Neighbourhood Operations
laplacian
We will call it mask B
27
Original image enhanced with laplacian
Original image
28
(No Transcript)
29
Human Visual System

• Eye performs edge enhancement.
• Cells in retina implement Laplacian.
• Use approximately the same mask weights B.

30
(No Transcript)
31
Unsharp Masking

1. Originally a photographic sharpening technique
2. Superimpose a fraction of the blurred negative
3. Edge enhancement amplifies noise
4. Tradeoff between edge enhancement and noise
   enhancement
5. Equivalent to adding on a fraction of Laplacian

32
Unsharp Mask (1)
33
Neighbourhood Operations
34
(No Transcript)
35
(No Transcript)
36
Unsharp Mask (2)
Input Image
Lowpass Filter
Histogram Shrink
Subtract images
Histogram Stretch
Result
37
Summary
Conclusion

• Properties of edges
• What is edge enhancement?
• edge enhancement
• first principles
• Neighbourhood
• laplacian
• unsharp masking

• Gradient of an edge has magnitude and direction.
• Adding Laplacian to an image results in edge
  undershoot and overshoot.
• k factor tunes the degree of edge enhancement