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 x 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 x

7. Consider a 1-d continuous image of an edge, denoted by A(x) Edge properties can be obtained from the gradient =  A /  x gradient=dA/dx as  x  0. Edge Properties- gradient  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. Gradient given by first derivative dA /d x. Second derivative, d 2 A/d x 2,generates two peaks at beginning and end of edge. Called ‘ringing’. Edge Properties- gradient

10. Edge Properties-discrete gradient B=[-1 1] B=[1 -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 j i dA/dx dA/dy

15. Discrete 2-d gradient operator Neighbour hood operators

16. Contour plot and gradient

17. Gradient Operators for Images Second-order gradient denoted by  2 A. Highlights discontinuties in an image. Scalar.

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

25. Laplacian A(x) x +L

26. Neighbourhood Operations laplacian B We will call it mask B

27. Original image Original image enhanced with laplacian

29. Human Visual System Eye performs edge enhancement. Cells in retina implement Laplacian. Use approximately the same mask weights B.

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

36. Unsharp Mask (2) Input ImageLowpass Filter Histogram Shrink Subtract images Histogram Stretch Result

37. Summary 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 Conclusion