Presentation is loading. Please wait.

Presentation is loading. Please wait.

Chapter 10 Image Segmentation

Similar presentations


Presentation on theme: "Chapter 10 Image Segmentation"— Presentation transcript:

1 Chapter 10 Image Segmentation
智能视觉理解 实验室

2 10.1 Fundamentals Boundary Region of Constant Intensity
Result of Segmentation Result of Segmentation Textured Region Result of Edge Computation

3 Horizontal Intensity Profile through the Center
10.2 Point Line and Edge Detection Horizontal Intensity Profile through the Center 𝝏𝒇 𝝏𝒙 = 𝒇 ′ 𝒙 =𝒇 𝒙+𝟏 −𝒇 𝒙 𝝏 𝟐 𝒇 𝝏 𝒙 𝟐 = 𝒇 ′′ 𝒙 =𝒇 𝒙+𝟏 +𝒇(𝒙−𝟏)−𝟐𝒇 𝒙

4 A General Spatial Filter Mask
10.2 Point Line and Edge Detection A General Spatial Filter Mask 𝑹= 𝒊=𝟏 𝟗 𝒘 𝒊 𝒛 𝒊

5 Point Detection (Laplacian) Mask Result of Convolving the Mask
Detection of Isolated Points Point Detection (Laplacian) Mask Result of Convolving the Mask 𝒈 𝒙,𝒚 = 𝟏 𝐢𝐟 𝑹 𝒙,𝒚 ≥𝑻 𝟎 𝐨𝐭𝐡𝐞𝐫𝐰𝐢𝐬𝐞 X-ray Image

6 Absolute Value of the Laplacian Positive Value of the Laplacian
Line Detection Original Image Laplacian Image Absolute Value of the Laplacian Positive Value of the Laplacian

7 Line Detection Line Detection Masks 𝐋𝐢𝐧𝐞 𝒊: 𝑹 𝒊 ≥| 𝑹 𝒋 |

8 10.2.3 Line Detection Wire-bond Template Result of +45 Line Detector
Zoomed View of the Top Left Zoomed View of the Bottom Right All Points Whose Value Satisfied 𝒈≥𝑻 All Negative Value set to Zero

9 Ideal Representations
Edge Models Ideal Representations Step Edge Ramp Edge Roof Edge

10 Edge Models A 1508×1970 image showing (zoomed) actual ramp (bottom, left), step (top, right), and roof edge profiles.

11 Horizontal Intensity Profile Separated by an Ideal Vertical Ramp Edge
Edge Models Detail Near the Edge Horizontal Intensity Profile Separated by an Ideal Vertical Ramp Edge

12 Ramp Edge Corrupted by Gaussian Noise
First-derivative Second-derivative 𝑵(𝟎,𝟎) Ramp Edge Corrupted by Gaussian Noise 𝑵(𝟎,𝟎.𝟏) 𝑵(𝟎,𝟏) 𝑵(𝟎,𝟏𝟎)

13 Gradient Operators 10.2.5 Basic Edge Detection
𝛁𝒇= 𝒈 𝒙 𝒈 𝒚 = 𝝏𝒇 𝝏𝒙 𝝏𝒇 𝝏𝒚 𝛁𝐟 = 𝝏𝒇 𝝏𝒙 𝟐 + 𝝏𝒇 𝝏𝒚 𝟐 𝟏 𝟐 ∞ 𝝏𝒇 𝝏𝒙 + 𝝏𝒇 𝝏𝒚 𝜶 𝒙,𝒚 =𝐭𝐚 𝐧 −𝟏 𝒈 𝒚 𝒈 𝒙

14 Basic Edge Detection Using the gradient to determine edge strength and direction at a point.

15 One-dimensional Masks
Basic Edge Detection One-dimensional Masks 𝒈 𝒙 = 𝝏𝒇(𝒙,𝒚) 𝝏𝒙 =𝒇 𝒙+𝟏,𝒚 −𝒇(𝒙,𝒚) 𝒈 𝒚 = 𝝏𝒇(𝒙,𝒚) 𝝏𝒚 =𝒇 𝒙,𝒚+𝟏 −𝒇(𝒙,𝒚)

16 Roberts Cross Gradients
Basic Edge Detection Roberts Cross Gradients 𝒈 𝒙 = 𝒛 𝟗 − 𝒛 𝟓 𝒈 𝒚 = 𝒛 𝟖 − 𝒛 𝟔 𝛁𝒇 ≈ 𝒛 𝟗 − 𝒛 𝟓 𝟐 + 𝒛 𝟖 − 𝒛 𝟔 𝟐 𝟏 𝟐 𝛁𝒇 ≈ 𝒛 𝟗 − 𝒛 𝟓 +| 𝒛 𝟖 − 𝒛 𝟔 | Prewitt Operators 𝒈 𝒙 = 𝒛 𝟕 + 𝒛 𝟖 + 𝒛 𝟗 −( 𝒛 𝟏 + 𝒛 𝟐 + 𝒛 𝟑 ) 𝒈 𝒚 = 𝒛 𝟑 + 𝒛 𝟔 + 𝒛 𝟗 −( 𝒛 𝟏 + 𝒛 𝟒 + 𝒛 𝟕 ) 𝒗𝒂𝒓𝒊𝒂𝒕𝒊𝒐𝒏 𝒈 𝒙 = 𝒛 𝟕 + 𝟐𝒛 𝟖 + 𝒛 𝟗 −( 𝒛 𝟏 + 𝟐𝒛 𝟐 + 𝒛 𝟑 ) 𝒈 𝒚 = 𝒛 𝟑 + 𝟐𝒛 𝟔 + 𝒛 𝟗 −( 𝒛 𝟏 + 𝟐𝒛 𝟒 + 𝒛 𝟕 )

17 Y-Direction X-Direction

18 Basic Edge Detection Diagonal Edge 45-Direction -45-Direction

19 Basic Edge Detection Using the Sobel Mask Original Image | 𝒈 𝒙 | | 𝒈 𝒚 | 𝒈 𝒙 +| 𝒈 𝒚 |

20 Gradient Angle Image 10.2.5 Basic Edge Detection
𝜶 𝒙,𝒚 =𝐭𝐚 𝐧 −𝟏 𝒈 𝒚 𝒈 𝒙

21 Smoothed using a 5×5 averaging filter
Basic Edge Detection Smoothed using a 5×5 averaging filter Original Image | 𝒈 𝒙 | | 𝒈 𝒚 | 𝒈 𝒙 +| 𝒈 𝒚 |

22 Diagonal Edge Detection
Basic Edge Detection Diagonal Edge Detection Sobel 45 Sobel -45

23 Laplacian Masks 10.2.5 Basic Edge Detection
𝛁 𝟐 𝒇= 𝝏 𝟐 𝒇 𝝏 𝒙 𝟐 + 𝝏 𝟐 𝒇 𝝏 𝒚 𝟐 𝟒 𝑵 ′ 𝒔: 𝛁 𝟐 𝒇=𝟒 𝒛 𝟓 − 𝒛 𝟐 + 𝒛 𝟒 + 𝒛 𝟔 + 𝒛 𝟖 𝟖 𝑵 ′ 𝒔: 𝛁 𝟐 𝒇=𝟒 𝒛 𝟓 −( 𝒛 𝟏 + 𝒛 𝟐 + 𝒛 𝟑 + 𝒛 𝟒 + 𝒛 𝟓 + 𝒛 𝟔 + 𝒛 𝟕 + 𝒛 𝟖 + 𝒛 𝟗 )

24 Negative of the LoG 10.2.6 Marr-Hildreth Edge Detector
𝑮 𝒙,𝒚 = 𝒆 − 𝒙 𝟐 + 𝒚 𝟐 𝟐 𝝈 𝟐 𝛁 𝟐 𝑮 𝒙,𝒚 = 𝒙 𝟐 + 𝒚 𝟐 −𝟐 𝝈 𝟐 𝝈 𝟒 𝒆 − 𝒙 𝟐 + 𝒚 𝟐 𝟐 𝝈 𝟐

25 10.2.6 Marr-Hildreth Edge Detector
Original Image 𝝈=𝟒, 𝒏=𝟐𝟓 Threshold: 0 Threshold: 4

26 Gaussian Smoothing Function
Marr-Hildreth Edge Detector Original Image Sobel Gradient Gaussian Smoothing Function Laplacian Mask LoG Threshold LoG Zero Crossings

27 Negatives of the LoG (solid) and DoG (dotted)
Marr-Hildreth Edge Detector Negatives of the LoG (solid) and DoG (dotted) Ratio: 1.75:1 Ratio: 1.6:1

28 Canny Edge Detector Range of values (in gray) of 𝜶 Two possible orientation of a horizontal edge The angle ranges of the edge normals for the four types of edge directions in a neighborhood.

29 10.2.6 Canny Edge Detector Original Image Thresholded Gradient
Marr-Hildreth Canny

30 10.2.6 Canny Edge Detector Original Image Thresholded Gradient
Marr-Hildreth Canny

31 10.2.7 Edge Linking and Boundary Detection
𝑴 𝒔,𝒕 −𝑴 𝒙,𝒚 ≤𝑬 𝜶 𝒔,𝒕 −𝜶 𝒙,𝒚 ≤𝑨 Original Image Gradient magnitude |𝑮 𝒙 | Morphological thinning |𝑮 𝒚 | 𝐋𝐨𝐠𝐢𝐜𝐚𝐥 𝐎𝐑

32 10.2.7 Edge Linking and Boundary Detection
Illustration of the iterative polygonal fit algorithm

33 10.2.7 Edge Linking and Boundary Detection
Edge linking using a polygonal approximation

34 Morphological Shrinking Morphological cleaning
Gradient Image Majority Filter Morphological Shrinking Morphological cleaning Spur Reduction Skeleton T = 3 T = 6 T = 12 Smoothed Smoothed

35 ( 𝒙 𝒊 , 𝒚 𝒊 ) & 𝒚=𝒂𝒙+𝒃⇒ 𝒚 𝒊 =𝒂 𝒙 𝒊 +𝒃
Edge Linking and Boundary Detection Global processing using the Hough transform ( 𝒙 𝒊 , 𝒚 𝒊 ) & 𝒚=𝒂𝒙+𝒃⇒ 𝒚 𝒊 =𝒂 𝒙 𝒊 +𝒃 𝒃=− 𝒙 𝒊 𝒂+ 𝒚 𝒊 All ( 𝒙 𝒊 , 𝒚 𝒊 )’s on a line intersect each other at (𝒂,𝒃 )

36 10.2.7 Edge Linking and Boundary Detection
Subdivision of the parameter plane for use in the Hough transform

37 10.2.7 Edge Linking and Boundary Detection
Geometrical interpretation of the parameters 𝒙 𝒊 𝒄𝒐𝒔𝜽+ 𝒚 𝒊 𝒔𝒊𝒏𝜽=𝝆 xy-plane 𝝆𝜽-plane Accumulator cells

38 Image containing five points
Edge Linking and Boundary Detection Image containing five points Parameter space

39 10.2.7 Edge Linking and Boundary Detection
Canny Hough parameter space Lines superimposed

40 10.3 Thresholding Original H-T Thr-Grad Linked

41 𝑭 𝒙,𝒚 >𝑻 𝐭𝐡𝐞𝐧 𝒙,𝒚 𝐢𝐬 𝐛𝐞𝐥𝐨𝐧𝐠 𝐭𝐨 𝐨𝐛𝐣𝐞𝐜𝐭,
10.3 Thresholding 𝑭 𝒙,𝒚 >𝑻 𝐭𝐡𝐞𝐧 𝒙,𝒚 𝐢𝐬 𝐛𝐞𝐥𝐨𝐧𝐠 𝐭𝐨 𝐨𝐛𝐣𝐞𝐜𝐭, 𝐞𝐥𝐬𝐞 𝒙,𝒚 𝐢𝐬 𝐛𝐞𝐨𝐧𝐠 𝐭𝐨 𝐛𝐚𝐜𝐤𝐠𝐫𝐨𝐮𝐧𝐝 Bi-level (T) Multi-level ( 𝐓 𝟏 , 𝐓 𝟐 ,…, 𝐓 𝐧 ) Threshold image: 𝒈 𝒙,𝒚 = 𝟏 𝒇 𝒙,𝒚 >𝑻 𝟎 𝒇 𝒙,𝒚 ≤𝑻

42 10.3 Thresholding Thresholds

43 10.3 Thresholding Noiseless 𝝁=𝟎 𝝈=𝟏𝟎 𝝁=𝟎 𝝈=𝟓𝟎

44 10.3 Thresholding Noised Image Ramp in [0.2, 0.6] Product

45 10.3.2 Basic Global Thresholding
A Heuristic Approach Initial estimate for T Segment image to 𝑮 𝟏 (>𝑻) and 𝑮 𝟐 (≤𝑻) Compute average value 𝒎 𝟏 and 𝒎 𝟐 in 𝑮 𝟏 and 𝑮 𝟐 𝑻= 𝟏 𝟐 𝒎 𝟏 + 𝒎 𝟐 Repeat 2-4 until small changed

46 10.3.2 Basic Global Thresholding
An example of segmentation based on a threshold 𝑻 𝟎 =𝟎 𝑪𝒐𝒏𝒗𝒆𝒓𝒈𝒆𝒏𝒄𝒆 𝑻 𝒇 =𝟏𝟐𝟓.𝟒

47 10.3.2 Basic Global Thresholding
Local Thr. Mosaic

48 10.3.2 Basic Global Thresholding
Good Subimage Bad Subimage Further block-ing

49 10.3.3 Optimum Global Thresholding Using Otsu’s Method
𝑷 𝟏 𝒌 = 𝒊=𝟎 𝒌 𝒑 𝒊 , 𝑷 𝟐 𝒌 = 𝒊=𝒌−𝟏 𝑳−𝟏 𝒑 𝒊 =𝟏− 𝑷 𝟏 𝒌 𝒑 𝒊 = 𝒏 𝒊 𝑴𝑵 Mean intensity value: 𝒎 𝟏 𝒌 = 𝟏 𝑷 𝟏 𝒌 𝒊=𝟎 𝒌 𝒊 𝒑 𝒊 , 𝒎 𝟐 𝒌 = 𝟏 𝑷 𝟐 (𝒌) 𝒊=𝒌+𝟏 𝑳−𝟏 𝒊 𝒑 𝒊 𝒎 𝒌 = 𝒊=𝟎 𝒌 𝒊 𝒑 𝒊 , 𝒎 𝑮 = 𝒊=𝟎 𝑳−𝟏 𝒊 𝒑 𝒊 Separability measure: 𝜼 𝒌 = 𝝈 𝑩 𝟐 𝒌 𝝈 𝑮 𝟐 , 𝝈 𝑮 𝟐 = 𝒊=𝟎 𝑳−𝟏 𝟏− 𝒎 𝑮 𝟐 𝒑 𝒊 , 𝝈 𝑩 𝟐 𝒌 = 𝒎 𝑮 𝑷 𝟏 𝒌 −𝒎 𝒌 𝟐 𝑷 𝟏 𝒌 𝟏− 𝑷 𝟏 𝒌

50 Basic Global Algorithm
Optimum Global Thresholding Using Otsu’s Method Input Histogram Basic Global Algorithm Ostu’s Method

51 10.3.4 Using Image Smoothing to Improve Global Thresholding
Noised Image Ostu’s Method 55 Averaging Mask Ostu’s Method

52 10.3.4 Using Image Smoothing to Improve Global Thresholding
Noised Image Ostu’s Method 55 Averaging Mask Ostu’s Method Failed in both cases

53 10.3.5 Using Edges to Improve Global Thresholding
Noisy Image Gradient Magnitude Product Ostu’s Method

54 Threshold Absolute Laplacian
Using Edges to Improve Global Thresholding Ostu’s Method Threshold Absolute Laplacian Ostu’s Method

55 Lower Value to Threshold the Absolute Laplacian
Using Edges to Improve Global Thresholding Lower Value to Threshold the Absolute Laplacian

56 10.3.6 Multiple Thresholds Between-class variance:
𝝈 𝑩 𝟐 = 𝒌=𝟏 𝑲 𝑷 𝒌 𝒎 𝒌 − 𝒎 𝑮 𝟐 , 𝑷 𝒌 = 𝒊∈ 𝑪 𝒌 𝒑 𝒊 , 𝒎 𝒌 = 𝟏 𝑷 𝒌 𝒊∈ 𝑪 𝒌 𝒊 𝒑 𝒊 Separability measure: 𝜼 𝒌 𝟏 ∗ , 𝒌 𝟐 ∗ = 𝝈 𝑩 𝟐 𝒌 𝟏 ∗ , 𝒌 𝟐 ∗ 𝝈 𝑮 𝟐 , 𝝈 𝑮 𝟐 𝒌 𝟏 ∗ , 𝒌 𝟐 ∗ = max 𝟎< 𝒌 𝟏 < 𝒌 𝟐 <𝑳−𝟏 𝝈 𝑩 𝟐 ( 𝒌 𝟏 , 𝒌 𝟐 ) Threshold image: 𝒈(𝒙,𝒚)= 𝒂 𝐢𝐟 𝒇 𝒙,𝒚 ≤ 𝒌 𝟏 ∗ 𝒃 𝐢𝐟 𝒌 𝟏 ∗ <𝒇 𝒙,𝒚 ≤ 𝒌 𝟐 ∗ 𝒄 𝐢𝐟 𝒇 𝒙,𝒚 > 𝒌 𝟐 ∗

57 Multiple Thresholds Image Segmented into Three Regions Using Dual Ostu Thresholds

58 Iterative Global Algorithm
Variable Thresholds Noisy, Shaded Image Iterative Global Algorithm Ostu’s Method Subdivided Ostu’s Method

59 Variable Thresholds Histograms of the Six Subimages

60 Variable Thresholding Based on Local Image Properties
Variable Thresholds Variable Thresholding Based on Local Image Properties 𝑻 𝒙𝒚 =𝒂 𝝈 𝒙𝒚 +𝒃 𝒎 𝒙𝒚 𝑻 𝒙𝒚 =𝒂 𝝈 𝒙𝒚 +𝒃 𝒎 𝑮 Segmented image 𝒈 𝒙,𝒚 = 𝟏 𝐢𝐟 𝒇 𝒙,𝒚 > 𝑻 𝒙𝒚 𝟎 𝐢𝐟 𝒇 𝒙,𝒚 ≤ 𝑻 𝒙𝒚 Predicts based on the parameters: 𝒈 𝒙,𝒚 = 𝟏 𝐢𝐟 𝑸 𝐥𝐨𝐜𝐚𝐥 𝐩𝐚𝐫𝐚𝐦𝐞𝐭𝐞𝐫𝐬 𝐢𝐬 𝐭𝐫𝐮𝐞 𝟎 𝐢𝐟 𝑸 𝐥𝐨𝐜𝐚𝐥 𝐩𝐚𝐫𝐚𝐦𝐞𝐭𝐞𝐫𝐬 𝐢𝐬 𝐟𝐚𝐥𝐬𝐞 Q 𝝈 𝒙𝒚 , 𝒎 𝒙𝒚 = 𝐭𝐫𝐮𝐞 𝐢𝐟 𝒇 𝒙,𝒚 >𝒂 𝝈 𝒙𝒚 𝐀𝐍𝐃 𝒇 𝒙,𝒚 >𝒃 𝒎 𝒙𝒚 𝐟𝐚𝐥𝐬𝐞 𝐨𝐭𝐡𝐞𝐫𝐰𝐢𝐬𝐞

61 Dual Thresholding Approach Local Standard Deviations
Variable Thresholds Original Image Dual Thresholding Approach Local Standard Deviations Local Thresholding

62 Moving Average: 10.3.7 Variable Thresholds
𝒎 𝒌+𝟏 =𝒎 𝒌 + 𝟏 𝒏 ( 𝒛 𝒌+𝟏 − 𝒛 𝒌−𝒏 ) Ostu’s Method Moving Average

63 Variable Thresholds Original Image Ostu’s Method Moving Average

64 10.4 Region-Based Segmentation
𝒊=𝟏 𝒏 𝑹 𝒊 𝑹 𝒊 𝐚𝐫𝐞 𝐜𝐨𝐧𝐧𝐞𝐜𝐭𝐞𝐝 𝐫𝐞𝐠𝐢𝐨𝐧𝐬 𝐑 𝐢 𝑹 𝒋 =∅ , 𝒊≠𝒋 𝑷 𝑹 𝒊 =𝐓𝐑𝐔𝐄 𝑷 𝑹 𝒊 𝑹 𝒋 =𝐅𝐀𝐋𝐒𝐄

65 Smallest Dual Thresholds
Initial Seed Image Final Seed Image Difference Smallest Dual Thresholds Dual Thresholds Region Growing

66 10.4 Region-Based Segmentation
Split and Merging

67 Limit the Smallest Allowed Quadregion
10.4 Region-Based Segmentation Limit the Smallest Allowed Quadregion 3232 1616 88

68 10.5 Segmentation Using Morphological Watersheds
Flooding

69 10.5 Segmentation Using Morphological Watersheds
Further Flooding Merging Water Longer Dams Final Watershed

70 Dam Construction Stage n-1 Stage n Structuring Element Result

71 10.5.3 Water Segmentation Algorithm
Image Gradient Watershed Lines Superimposed on Input

72 The Use of Markers Apply the Watershed Segmentation to the Gradient Image

73 The Use of Markers Internal Markers and External Markers

74 10.6 The Use of Motion in Segmentation
Absolute ADIs Positive ADIs Negative ADIs

75 10.6 The Use of Motion in Segmentation
Two Frames in a Sequence Result

76 10.6 The Use of Motion in Segmentation
LANDSAT frame

77 10.6 The Use of Motion in Segmentation
Intensity plot of the image LANDSAT, with the target circle

78 10.6 The Use of Motion in Segmentation
Spectrum of Eq. (10.6-8) showing a peak at 𝑢 1 =3

79 10.6 The Use of Motion in Segmentation
Spectrum of Eq. (10.6-9) showing a peak at 𝑢 2 =4

80 智能视觉理解 实验室


Download ppt "Chapter 10 Image Segmentation"

Similar presentations


Ads by Google