Edge Detection

Computação Visual e Multimédia

10504: Mestrado em Engenharia Informática

Chap. 5 — Edge Detection

Chapter 5: Edge Detection

Outline

Chapter 5: Edge Detection Monochrome image ���segmentation algorithms

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Chapter 5: Edge Detection

Chapter 5: Edge Detection Isolated point detection ���(Laplacian-based)

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0 1 01 −4 10 1 0

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−1 −1 −1−1 8 −1−1 −1 −1

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Laplacian mask other typical mask

original image

masked image thresholded image

Chapter 5: Edge Detection Line detection���(Laplacian-based)

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original image Positive/negative double line effect of Laplacian

absolute value of the Laplacian

positive values of the Laplacian

Chapter 5: Edge Detection

Line detection

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binary wire-bond mask absolute value with a -45º line detector

Result of threshold image

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−1 −1 −12 2 2−1 −1 −1

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−1 −1 2−1 2 −12 −1 −1

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−1 2 −1−1 2 −1−1 2 −1

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2 −1 −1−1 2 −1−1 −1 2

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horizontal 45º vertical -45º

Chapter 5: Edge Detection

Edge models

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step edge ramp edge roof edge

intensity profiles for different types of edges

Chapter 5: Edge Detection

Edge models: derivatives

gray-scale profile

1st derivative

2nd derivative

Chapter 5: Edge Detection Edge models: derivatives���(cont’d)

5 7 6 4 152 148 149

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GX (4) = −12× 6 + 0 × 4 +

12×152

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LX (4) =1× 6 − 2 × 4 +1×152

Chapter 5: Edge Detection Basic edge detection ���(gradient-based)

Sobel filter provides a better noise supression than Prewitt filter

original image |GY| |GX| |GX|+|GY|

Chapter 5: Edge Detection

Advanced edge detection

Chapter 5: Edge Detection

LoG edge detection (Marr-Hildreth)

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1st derivative f ’

2nd derivative f ’’

function f

zero crossing

Chapter 5: Edge Detection

LoG edge detection (Marr-Hildreth)

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LoG =∇2G(x,y) =x 2 + y 2 − 2σ2

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−x 2 +y 2

2σ 2

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G(x,y) = e−x 2 +y 2

2σ 2

Since LoG filter is linear, the two constituent filters (Gaussian and Laplacian) can be applied separately, thus allowing us to use different sized filters for each of the actions.

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L(x,y)⊗G(x,y)⊗ f (x,y)

Chapter 5: Edge Detection LoG edge detection (Marr-Hildreth)���(1st alternative)

Chapter 5: Edge Detection LoG edge detection (Marr-Hildreth)���(2nd alternative)

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0 0 −1 0 00 −1 −2 −1 0−1 −2 16 −2 −10 −1 −2 −1 00 0 −1 0 0

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LoG mask = approximation to the shape of

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G(x,y) = e−x 2 +y 2

2σ 2

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LoG =∇2G(x,y) =x 2 + y 2 − 2σ2

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∇2G

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∇2G

- black is negative; - gray is the zero plane - white is positive

cross section showing zero crossings

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∇2G

Chapter 5: Edge Detection

Canny edge detection

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Chapter 5: Edge Detection Canny edge detection (1st step):���smooth image

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S(x,y) =Gσ (x,y)⊗ f (x,y)

Output: a smoothed/nonnoisy image S(x,y)

Chapter 5: Edge Detection Canny edge detection (2nd step):���compute gradient

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GX (x,y) ≈ S(x,y +1) − S(x,y) + S(x +1,y +1) − S(x +1,y)[ ] /2GY (x,y) ≈ S(x,y) − S(x +1,y) + S(x,y +1) − S(x +1,y +1)[ ] /2

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G(x,y) = GX2 (x,y) +GY

2 (x,y)

θ(x,y) = tan−1 GY2 (x,y)

GX2 (x,y)

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Output: 2 arrays of the same size as the image: - gradient magnitude array G(x,y) - gradient angle array θ(x,y)

Chapter 5: Edge Detection Canny edge detection (3rd step):���non-maxima suppression

Output: 1 array of the same size as the image: - non-maxima suppressed array N(x,y)

Chapter 5: Edge Detection Canny edge detection (4th step):���double thresholding (hysteresis thresholding)

Double thresholding = false edge point reduction + edge linking

Chapter 5: Edge Detection Canny edge detection (cont’d):���double thresholding

Double thresholding = false edge point reduction + edge linking

Chapter 5: Edge Detection Canny edge detection:���revisited

original image Step 2: G(x,y) with σ=2.0

Step 3 Step 4: TL=10 and TH=50

Chapter 5: Edge Detection

Summary: