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Canny Edge and Line Detection CS/BIOEN 6640, Fall 2010 Guido Gerig - - PowerPoint PPT Presentation
Canny Edge and Line Detection CS/BIOEN 6640, Fall 2010 Guido Gerig - - PowerPoint PPT Presentation
Canny Edge and Line Detection CS/BIOEN 6640, Fall 2010 Guido Gerig with some slides from Tsai Sing Lee with some slides from Tsai Sing Lee, CMU and from J. Cannys Papers Optimal Operator for Noisy Step p p y p Edge: SNR*LOC
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“Optimal Operator” for Noisy Step p p y p Edge: SNR*LOC
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Optimization Optimization
∑ Λ ∑ Λ r ∑: SNR Λ: Localization (how close to true position) X max: distance between adjacent maxima (fraction of operator width) X_max: distance between adjacent maxima (fraction of operator width) r: multiple response performance
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Optimal Operators Optimal Operators
∑ Λ r X_max _
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Optimal Operator versus First D i i f G i Derivative of Gaussian
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“Optimal Operator” for Noisy Step p p y p Edge: SNR*LOC*MULT
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2D Edge Filter: Output at different scales
1st order Gaussian Derivatives
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Response at different scales Response at different scales
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Non-Maximum Suppression Non Maximum Suppression
Detect local maxima and suppress all other signals.
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What about 2D? What about 2D?
At every position in the edge-
- riginal
edge orientation edge At every position in the edge magnitude output, there is a coordinate system with normal and tangent. edge positions coded by edge it d magnitude
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Non-Maximum Suppression
- Canny: Interpolate Gradient along
Non Maximum Suppression
Canny: Interpolate Gradient along gradients (plus and minus a certain distance) and check if center is larger than neighbors.
- Simplified: Test for each Gradient
B
Magnitude pixel if neighbors along gradient direction (closest neighbors) are smaller than center: Mark C as
B
are smaller than center: Mark C as maximum if A<C and B<C
C A
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Results Results
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Canny: Hysteresis Thresholding Canny: Hysteresis Thresholding
- Thresholding/binarization of edge map:
Thresholding/binarization of edge map:
– Noise and image structures have different structure structure – Simple thresholding: If too low, too many structures appear, if too high, contours are structures appear, if too high, contours are broken into pieces – Idea: Hysteresis: Upper and lower threshold, y pp , keep all connected edges (dm metric) that are connected to upper but above lower threshold
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Hysteresis Thresholding Hysteresis Thresholding
too little too many combi ti many nation
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Optimal Operators for Other Structures
Resembles 2nd derivative of Gaussian
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Gaussian Derivatives Gaussian Derivatives
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2nd Derivative Operator to detect lines and curves
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Multidimensional Derivatives Multidimensional Derivatives
- Nabla operator:
Nabla operator:
- Gradient:
- Laplacian:
- Hessian:
(matrix of 2nd derivatives, gradient of gradient of L)
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Laplacian Laplacian
Local kernels Laplacian of 2D Gaussian kernel
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Laplacian of Gaussian (LoG) Laplacian of Gaussian (LoG)
Enhances line-like structures (glasses), creates zero-crossing at edges (positive and negative response at both sides of edges) Source: http://homepages.inf.ed.ac.uk/rbf/HIPR2/log.htm and negative response at both sides of edges)
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Often used: Zero-Crossings of LoG for Edge Detection
Hint: Remember that edge positions are extrema of first derivative → zero- crossings of 2nd derivatives. Be careful: Extrema or maxima & minima!
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