Download presentation

Presentation is loading. Please wait.

Published byKatie Sinden Modified over 2 years 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

OK

Edge detection Goal: Identify sudden changes (discontinuities) in an image Intuitively, most semantic and shape information from the image can be encoded.

Edge detection Goal: Identify sudden changes (discontinuities) in an image Intuitively, most semantic and shape information from the image can be encoded.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on email etiquettes presentation folder Free ppt on germination of seeds Ppt on question tags rules Free ppt on physical features of india Ppt on domestic robots Ppt on content development definition Ppt on articles of association texas Ppt on self development Ppt on eisenmenger syndrome vsd Forms of energy for kids ppt on batteries