Download presentation

Presentation is loading. Please wait.

Published byKatie Sinden Modified about 1 year ago

1
3-D Computer Vision CSc83020 / Ioannis Stamos Revisit filtering (Gaussian and Median) Introduction to edge detection 3-D Computater Vision CSc 83020

2
3-D Computer Vision CSc83020 / Ioannis Stamos Linear Filters Given an image In(x,y) generate a new image Out(x,y): For each pixel (x,y) Out(x,y) is a linear combination of pixels in the neighborhood of In(x,y) This algorithm is Linear in input intensity Shift invariant

3
3-D Computer Vision CSc83020 / Ioannis Stamos Discrete Convolution This is the discrete analogue of convolution The pattern of weights is called the “kernel” of the filter Will be useful in smoothing, edge detection

4
3-D Computer Vision CSc83020 / Ioannis Stamos Computing Convolutions What happens near edges of image? Ignore (Out is smaller than In) Pad with zeros (edges get dark) Replicate edge pixels Wrap around Reflect Change filter

5
3-D Computer Vision CSc83020 / Ioannis Stamos Example: Smoothing Original: Mandrill Smoothed with Gaussian kernel

6
3-D Computer Vision CSc83020 / Ioannis Stamos Gaussian Filters One-dimensional Gaussian Two-dimensional Gaussian

7
3-D Computer Vision CSc83020 / Ioannis Stamos Gaussian Filters

8
3-D Computer Vision CSc83020 / Ioannis Stamos Gaussian Filters

9
3-D Computer Vision CSc83020 / Ioannis Stamos Gaussian Filters Gaussians are used because: Smooth Decay to zero rapidly Simple analytic formula Limit of applying multiple filters is Gaussian (Central limit theorem) Separable: G 2 (x,y) = G 1 (x) G 1 (y)

10
3-D Computer Vision CSc83020 / Ioannis Stamos Size of the mask

11
3-D Computer Vision CSc83020 / Ioannis Stamos Edges & Edge Detection What are Edges? Theory of Edge Detection. Edge Operators (Convolution Masks) Edge Detection in the Brain? Edge Detection using Resolution Pyramids

12
3-D Computer Vision CSc83020 / Ioannis Stamos Edges

13
What are Edges? Rapid Changes of intensity in small region

14
3-D Computer Vision CSc83020 / Ioannis Stamos What are Edges? Surface-Normal discontinuity Depth discontinuity Surface-Reflectance Discontinuity Illumination Discontinuity Rapid Changes of intensity in small region

15
3-D Computer Vision CSc83020 / Ioannis Stamos Local Edge Detection

16
3-D Computer Vision CSc83020 / Ioannis Stamos What is an Edge? Edge easy to find

17
3-D Computer Vision CSc83020 / Ioannis Stamos What is an Edge? Where is edge? Single pixel wide or multiple pixels?

18
3-D Computer Vision CSc83020 / Ioannis Stamos What is an Edge? Noise: have to distinguish noise from actual edge

19
3-D Computer Vision CSc83020 / Ioannis Stamos What is an Edge? Is this one edge or two?

20
3-D Computer Vision CSc83020 / Ioannis Stamos What is an Edge? Texture discontinuity

21
3-D Computer Vision CSc83020 / Ioannis Stamos Local Edge Detection

22
Edge Types Ideal Step Edges Ideal Ridge Edges Ideal Roof Edges

23
3-D Computer Vision CSc83020 / Ioannis Stamos Real Edges I x Problems: Noisy Images Discrete Images

24
3-D Computer Vision CSc83020 / Ioannis Stamos Real Edges We want an Edge Operator that produces: Edge Magnitude (strength) Edge direction Edge normal Edge position/center High detection rate & good localization

25
3-D Computer Vision CSc83020 / Ioannis Stamos The 3 steps of Edge Detection Noise smoothing Edge Enhancement Edge Localization Nonmaximum suppression Thresholding

26
3-D Computer Vision CSc83020 / Ioannis Stamos Theory of Edge Detection x yB1,L(x,y)>0 B2,L(x,y)<0 t Unit Step Function:

27
3-D Computer Vision CSc83020 / Ioannis Stamos Theory of Edge Detection x yB1,L(x,y)>0 B2,L(x,y)<0 t Unit Step Function: Ideal Edge: Image Intensity (Brightness):

28
3-D Computer Vision CSc83020 / Ioannis Stamos Theory of Edge Detection x yB1,L(x,y)>0 B2,L(x,y)<0 t Partial Derivatives: Directional!

29
3-D Computer Vision CSc83020 / Ioannis Stamos Theory of Edge Detection x yB1,L(x,y)>0 B2,L(x,y)<0 t Rotationally Symmetric, Non-Linear Edge Magnitude Edge Orientation Squared Gradient:

30
Theory of Edge Detection x yB1,L(x,y)>0 B2,L(x,y)<0 t Laplacian: (Rotationally Symmetric & Linear) I xx Zero Crossing

31
3-D Computer Vision CSc83020 / Ioannis Stamos Difference Operators Ii,j+1Ii+1,j+1 Ii,jIi+1,j ε Finite Difference Approximations

32
3-D Computer Vision CSc83020 / Ioannis Stamos Squared Gradient x y

33
3-D Computer Vision CSc83020 / Ioannis Stamos Squared Gradient ifthreshold then we have an edge [Roberts ’65]

34
3-D Computer Vision CSc83020 / Ioannis Stamos Squared Gradient – Sobel Mean filter convolved with first derivative filter

35
3-D Computer Vision CSc83020 / Ioannis Stamos Examples First derivative Sobel operator

36
3-D Computer Vision CSc83020 / Ioannis Stamos Second Derivative Edge occurs at the zero-crossing of the second derivative

37
3-D Computer Vision CSc83020 / Ioannis Stamos Laplacian Rotationally symmetric Linear computation (convolution)

38
3-D Computer Vision CSc83020 / Ioannis Stamos Discrete Laplacian Ii,j+1Ii+1, j+1 Ii,jIi+1,j Finite Difference Approximations Ii+1,j-1Ii,j-1Ii-1,j-1 Ii-1,j Ii-1,j+1

39
3-D Computer Vision CSc83020 / Ioannis Stamos Discrete Laplacian Rotationally symmetric Linear computation (convolution) More accurate

40
3-D Computer Vision CSc83020 / Ioannis Stamos Discrete Laplacian Laplacian of an image

41
3-D Computer Vision CSc83020 / Ioannis Stamos Discrete Laplacian Laplacian is sensitive to noise First smooth image with Gaussian

42
3-D Computer Vision CSc83020 / Ioannis Stamos From Forsyth & Ponce.

43
3-D Computer Vision CSc83020 / Ioannis Stamos From Shree Nayar’s notes.

44
3-D Computer Vision CSc83020 / Ioannis Stamos Discrete Laplacian w/ Smoothing

45
3-D Computer Vision CSc83020 / Ioannis Stamos From Shree Nayar’s notes.

46
3-D Computer Vision CSc83020 / Ioannis Stamos Difference Operators – Second Derivative

47
3-D Computer Vision CSc83020 / Ioannis Stamos From Forsyth & Ponce.

48
3-D Computer Vision CSc83020 / Ioannis Stamos Edge Detection – Human Vision LoG convolution in the brain – biological evidence! LoGFlipped LoG

49
Image Resolution Pyramids Can save computations. Consolidation: Average pixels at one level to find value at higher level. Template Matching: Find match in COARSE resolution. Then move to FINER resolution.

50
3-D Computer Vision CSc83020 / Ioannis Stamos From Forsyth & Ponce.

Similar presentations

© 2016 SlidePlayer.com Inc.

All rights reserved.

Ads by Google