1. Stanford CS223B Computer Vision, Winter 2005 Lecture 3 Filters and Features (with Matlab)
Sebastian Thrun, Stanford
Rick Szeliski, Microsoft
Hendrik Dahlkamp, Stanford
[with slides by D Forsyth, D. Lowe, M. Polleyfeys, C. Rasmussen, G. Loy, D. Jacobs, J. Rehg, A, Hanson, G. Bradski,…]

2. Assignment 1 FAQ Compiling projects Taking the images
cxcored.dll is the debug version of cxcore.dll, can be compiled from cxcore.dsp
Use template cvsample.dsp to get paths right
Taking the images
Assignment change: out-of-focus images no longer needed
Don’t print a border around the chessboard

3. Assignment 1 FAQ Corner finding How to verify results
Supply correct parameters e.g. corner_count<>0
Visualize corner ordering
How to verify results
Backproject scene corners into image
Use common sense: etc

4. Stanford CS223B Computer Vision, Winter 2005 Lecture 3 Filters and Features (with Matlab)
Sebastian Thrun, Stanford
Rick Szeliski, Microsoft
Hendrik Dahlkamp, Stanford
[with slides by D Forsyth, D. Lowe, M. Polleyfeys, C. Rasmussen, G. Loy, D. Jacobs, J. Rehg, A, Hanson, G. Bradski,…]

5. Today’s Goals Features 101 Linear Filters and Edge Detection
Canny Edge Detector

6. Today’s Question What is a feature? What is an image filter?
How can we find corners?
How can we find edges?

7. What is a Feature?
Local, meaningful, detectable parts of the image

8. Features in Computer Vision
What is a feature?
Location of sudden change
Why use features?
Information content high
Invariant to change of view point, illumination
Reduces computational burden

9. (One Type of) Computer Vision
Feature 1
Feature 2 :
Feature N
Image 2
Image 1
Feature 1
Feature 2 :
Feature N
Computer
Vision
Algorithm

10. Where Features Are Used
Calibration
Image Segmentation
Correspondence in multiple images (stereo, structure from motion)
Object detection, classification

11. What Makes For Good Features?
Invariance
View point (scale, orientation, translation)
Lighting condition
Object deformations
Partial occlusion
Other Characteristics
Uniqueness
Sufficiently many
Tuned to the task

12. Today’s Goals Features 101 Linear Filters and Edge Detection
Canny Edge Detector

13. What Causes an Edge? Depth discontinuity
Surface orientation discontinuity
Reflectance discontinuity (i.e., change in surface material properties)
Illumination discontinuity (e.g., shadow)
Slide credit: Christopher Rasmussen

14. Quiz: How Can We Find Edges?

15. Edge Finding 101 im = imread('bridge.jpg'); image(im); figure(2);
bw = double(rgb2gray(im));
image(bw);
gradkernel = [-1 1];
dx = abs(conv2(bw, gradkernel, 'same'));
image(dx);
colorbar; colormap gray
[dx,dy] = gradient(bw);
gradmag = sqrt(dx.^2 + dy.^2);
image(gradmag);
matlab
colorbar
colormap(gray(255))
colormap(default)

16. Edge Finding 101
Example of a linear Filter

17. What is Image Filtering?
Modify the pixels in an image based on some function of a local neighborhood of the pixels 10 5 3 4 1 7 7
Some function

18. Linear Filtering Linear case is simplest and most useful
Replace each pixel with a linear combination of its neighbors.
The prescription for the linear combination is called the convolution kernel. 10 5 3 4 1 7
0.5
1.0 7
kernel

19. Linear Filter = Convolution
g11
g11 I(i-1,j-1)
I(.)
g12
+ g12 I(i-1,j)
I(.)
g13
+ g13 I(i-1,j+1) +
I(.)
g21
g21 I(i,j-1)
g22
+ g22 I(i,j)
I(.)
I(.)
g23
+ g23 I(i,j+1) +
I(.)
g31
g31 I(i+1,j-1)
I(.)
g32
+ g32 I(i+1,j)
I(.)
g33
+ g33 I(i+1,j+1)
f (i,j) =

20. Linear Filter = Convolution

21. Filtering Examples

22. Filtering Examples

23. Filtering Examples

24. Image Smoothing With Gaussian
figure(3);
sigma = 3;
width = 3 * sigma;
support = -width : width;
gauss2D = exp( - (support / sigma).^2 / 2);
gauss2D = gauss2D / sum(gauss2D);
smooth = conv2(conv2(bw, gauss2D, 'same'), gauss2D', 'same');
image(smooth);
colormap(gray(255));
gauss3D = gauss2D' * gauss2D;
tic ; smooth = conv2(bw,gauss3D, 'same'); toc

25. Smoothing With Gaussian
Averaging
Gaussian
Slide credit: Marc Pollefeys

26. Smoothing Reduces Noise
The effects of smoothing
Each row shows smoothing
with gaussians of different
width; each column shows
different realizations of
an image of gaussian noise.
Slide credit: Marc Pollefeys

27. Example of Blurring
Image
Blurred Image - =

28. Edge Detection With Smoothed Images
figure(4);
[dx,dy] = gradient(smooth);
gradmag = sqrt(dx.^2 + dy.^2);
gmax = max(max(gradmag));
imshow(gradmag);
colormap(gray(gmax));

29. Scale Increased smoothing: Eliminates noise edges.
Makes edges smoother and thicker.
Removes fine detail.

30. The Edge Normal

31. Displaying the Edge Normal
figure(5);
hold on;
image(smooth);
colormap(gray(255));
[m,n] = size(gradmag);
edges = (gradmag > 0.3 * gmax);
inds = find(edges);
[posx,posy] = meshgrid(1:n,1:m); posx2=posx(inds); posy2=posy(inds);
gm2= gradmag(inds);
sintheta = dx(inds) ./ gm2;
costheta = - dy(inds) ./ gm2;
quiver(posx2,posy2, gm2 .* sintheta / 10, -gm2 .* costheta / 10,0);
hold off;

32. Separable Kernels

33. Combining Kernels / Convolutions

34. Effect of Smoothing Radius
1 pixel
3 pixels
7 pixels

35. Robert’s Cross Operator
1 0
0 -1
0 1
-1 0 +
S =
[ I(x, y) - I(x+1, y+1) ]2 + [ I(x, y+1) - I(x+1, y) ]2 or
S =
| I(x, y) - I(x+1, y+1) | + | I(x, y+1) - I(x+1, y) |

36. Sobel Operator -1 -2 -1 0 0 0 1 2 1 -1 0 1 -2 0 2 S1= S2 =
S1=
S2 =
Edge Magnitude =
Edge Direction =
S1 + S1 2
tan-1 S1 S2

37. The Sobel Kernel, Explained
Sobel kernel is separable!
Averaging done parallel to edge

38. Sobel Edge Detector
figure(6)
edge(bw, 'sobel')

39. Robinson Compass Masks

40. Claim Your Own Kernel!
Frei & Chen

41. Comparison (by Allan Hanson)
Analysis based on a step edge inclined at an angle q (relative to y-axis) through center of window.
Robinson/Sobel: true edge contrast less than 1.6% different from that computed by the operator.
Error in edge direction
Robinson/Sobel: less than 1.5 degrees error
Prewitt: less than 7.5 degrees error
Summary
Typically, 3 x 3 gradient operators perform better than 2 x 2.
Prewitt2 and Sobel perform better than any of the other 3x3 gradient estimation operators.
In low signal to noise ratio situations, gradient estimation operators of size larger than 3 x 3 have improved performance.
In large masks, weighting by distance from the central pixel is beneficial.

42. Today’s Goals Features 101 Linear Filters and Edge Detection
Canny Edge Detector

43. Canny Edge Detector
figure(7)
edge(bw, 'canny')

44. Canny Edge Detection Steps: Apply derivative of Gaussian
Non-maximum suppression
Thin multi-pixel wide “ridges” down to single pixel width
Linking and thresholding
Low, high edge-strength thresholds
Accept all edges over low threshold that are connected to edge over high threshold

45. Non-Maximum Supression
Non-maximum suppression:
Select the single maximum point across the width of an edge.

46. Linking to the Next Edge Point
Assume the marked point is an edge point.
Take the normal to the gradient at that point and use this to predict continuation points (either r or s).

47. Edge Hysteresis Hysteresis: A lag or momentum factor
Idea: Maintain two thresholds khigh and klow
Use khigh to find strong edges to start edge chain
Use klow to find weak edges which continue edge chain
Typical ratio of thresholds is roughly
khigh / klow = 2

48. Canny Edge Detection (Example)
gap is gone
Strong +
connected
weak edges
Original
image
Strong
edges
only
Weak
edges
courtesy of G. Loy

49. Canny Edge Detection (Example)
Using Matlab with default thresholds

50. Application: Road Finding
(add roadrunner video here)

51. Corner Effects

52. Today’s Goals Features 101 Linear Filters and Edge Detection
Canny Edge Detector