EE 4780 Introduction to Computer Vision Discontinuity Detection

EE 4780: Introduction to Computer Vision Discontinuity 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 12

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 13

Solution: smooth first Bahadir K. Gunturk Look for peaks in 14

Derivative theorem of convolution n This saves us one operation: Bahadir K. Gunturk 15

Laplacian (2 nd order derivative) of Gaussian n Consider Laplacian of Gaussian operator Bahadir K. Gunturk Zero-crossings of bottom graph 16

Edge Detection Bahadir K. Gunturk 17

Edge Detection Bahadir K. Gunturk 18

Edge Detection Bahadir K. Gunturk 19

Edge Detection Bahadir K. Gunturk 20

Edge Detection Bahadir K. Gunturk 21

Edge Detection n The Laplacian of an image f(x, y) is a second-order derivative defined as Bahadir K. Gunturk 22

Edge Detection Bahadir K. Gunturk 23