EE 4780 Edge Detection Bahadir K Gunturk Detection
EE 4780 Edge Detection Bahadir K. Gunturk
Detection of Discontinuities n Matched Filter Example >> a=[0 0 1 2 3 0 0 2 2 2 0 0 1 2 -2 -1 0 0]; >> figure; plot(a); >> h 1 = [-1 -2 2 1]/10; >> b 1 = conv(a, h 1); figure; plot(b 1); Bahadir K. Gunturk 2
Detection of Discontinuities n Point Detection Example: q q Apply a high-pass filter. A point is detected if the response is larger than a positive threshold. Threshold q The idea is that the gray level of an isolated point will be quite different from the gray level of its neighbors. Bahadir K. Gunturk 3
Detection of Discontinuities n Point Detection Detected point Bahadir K. Gunturk 4
Detection of Discontinuities n Line Detection Example: Bahadir K. Gunturk 5
Detection of Discontinuities n Line Detection Example: Bahadir K. Gunturk 6
Detection of Discontinuities n Edge Detection: q q q An edge is the boundary between two regions with relatively distinct gray levels. Edge detection is by far the most common approach for detecting meaningful discontinuities in gray level. The reason is that isolated points and thin lines are not frequent occurrences in most practical applications. The idea underlying most edge detection techniques is the computation of a local derivative operator. Bahadir K. Gunturk 7
Origin of Edges surface normal discontinuity depth discontinuity surface color discontinuity illumination discontinuity n Edges are caused by a variety of factors Bahadir K. Gunturk 8
Profiles of image intensity edges Bahadir K. Gunturk 9
Image gradient n The gradient of an image: n The gradient points in the direction of most rapid change in intensity n The gradient direction is given by: n The edge strength is given by the gradient magnitude Bahadir K. Gunturk 10
The discrete gradient n How can we differentiate a digital image f[x, y]? q q Option 1: reconstruct a continuous image, then take gradient Option 2: take discrete derivative (finite difference) Bahadir K. Gunturk 11
Effects of noise n Consider a single row or column of the image q Plotting intensity as a function of position gives a signal Bahadir K. Gunturk 12
Solution: smooth first Bahadir K. Gunturk Look for peaks in 13
Derivative theorem of convolution n This saves us one operation: Bahadir K. Gunturk 14
Laplacian of Gaussian n Consider Laplacian of Gaussian operator Bahadir K. Gunturk Zero-crossings of bottom graph 15
2 D edge detection filters Laplacian of Gaussian n derivative of Gaussian is the Laplacian operator: Bahadir K. Gunturk 16
Edge Detection Possible filters to find gradients along vertical and horizontal directions: Averaging provides noise suppression This gives more importance to the center point. Bahadir K. Gunturk 17
Edge Detection Bahadir K. Gunturk 18
Edge Detection Bahadir K. Gunturk 19
Edge Detection n The Laplacian of an image f(x, y) is a second-order derivative defined as Digital approximations: Bahadir K. Gunturk 20
Edge Detection One simple method to find zerocrossings is black/white thresholding: 1. Set all positive values to white 2. Set all negative values to black 3. Determine the black/white transitions. Compare (b) and (g): • Edges in the zero-crossings image is thinner than the gradient edges. • Edges determined by zero-crossings have formed many closed loops. Bahadir K. Gunturk 21
Edge Detection n The Laplacian of a Gaussian filter A digital approximation: Bahadir K. Gunturk 0 0 1 0 0 0 1 2 1 0 1 2 -16 2 1 0 1 2 1 0 0 0 1 0 0 22
The Canny edge detector n Bahadir K. Gunturk original image (Lena) 23
The Canny edge detector n Bahadir K. Gunturk norm of the gradient 24
The Canny edge detector n Bahadir K. Gunturk thresholding 25
The Canny edge detector n Bahadir K. Gunturk n thinning (non-maximum suppression) 26
Edge detection by subtraction Bahadir K. Gunturk original 27
Edge detection by subtraction Bahadir K. Gunturk smoothed (5 x 5 Gaussian) 28
Edge detection by subtraction Why does this work? Bahadir K. Gunturk smoothed – original 29
Gaussian - image filter Gaussian Bahadir K. Gunturk delta function 30 Laplacian of Gaussian
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