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Lab 4

Canny Edge Detectors

Slides Courtesy: Stanford Vision

Ayush Jain

aj3152@nyu.edu

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Edge Detection Recap

  • Goal is to identify sudden changes (discontinuities) in an image.

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  • Intuitively, most semantic and shape information from the image can be encoded in the edges – More compact than pixels

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  • Ideal: artist’s line drawing (but artist is also using object-level knowledge)

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Why edges matter?

  • Extract information, recognize objects

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  • Recover geometry and viewpoint

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How to find edges?

  • surface normal discontinuity

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  • depth discontinuity

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  • surface color discontinuity

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  • illumination discontinuity

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Spotting edges by example

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Spotting edges by example

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Spotting edges by example

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Characterizing edges

  • An edge is a place of rapid change in the image intensity function

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Characterizing edges

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Finite Difference Example

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Noise

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Smoothing

  • Finite difference filters respond strongly to noise.

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  • Image noise results in pixels that look very different from their neighbors.

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  • Generally, the larger the noise the stronger the response.

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  • What is to be done? – Smoothing the image should help, by forcing pixels different to their neighbors (=noise pixels?) to look more like neighbors

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Smoothing with different filters

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Solution: Smoothing

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Solution: Smoothing

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Derivative of Gaussian filter

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Designing an optimal edge detector?

  • Good detection: the optimal detector must minimize the probability of false positives (detecting spurious edges caused by noise), as well as that of false negatives (missing real edges)
  • Good localization: the edges detected must be as close as possible to the true edges
  • Single response: the detector must return one point only for each true edge point; that is, minimize the number of local maxima around the true edge

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Canny edge detectors

  • Suppress Noise

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  • Compute gradient magnitude and direction

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  • Apply Non-Maximum Suppression – Assures minimal response

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  • Use hysteresis and connectivity analysis to detect edges

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Example

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Derivative of Gaussian filter

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Compute Gradients

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Get orientation at each pixel

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Get orientation at each pixel

  • Edge occurs where gradient reaches a maxima

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  • Suppress non-maxima gradient even if it passes threshold

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  • Only eight angle directions possible – Suppress all pixels in each direction which are not maxima – Do this in each marked pixel neighborhood

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Remove spurious gradients

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Non-maximal suppression

  • Edge occurs where gradient reaches a maxima

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  • Suppress non-maxima gradient even if it passes threshold

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  • Only eight angle directions possible – Suppress all pixels in each direction which are not maxima – Do this in each marked pixel neighborhood

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Non-maximal suppression

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Example

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Hysteresis Thresholding

  • Define two thresholds: Low and High
    • If less than Low, not an edge
    • If greater than High, strong edge
    • If between Low and High, weak edge

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  • For weak edges,
    • Consider its neighbors iteratively
    • Then declare it an “edge pixel” if it is connected to an ‘strong edge pixel’ directly or via pixels between Low and High

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Hysteresis Thresholding

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Canny Edge Detector

  • Filter image with x, y derivatives of Gaussian

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  • Find magnitude and orientation of gradient

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  • Non-maximum suppression: – Thin multi-pixel wide “ridges” down to single pixel width

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  • Thresholding and linking (hysteresis): – Define two thresholds: low and high – Use the high threshold to start edge curves and the low threshold to continue them

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Effect of σ (Gaussian kernel spread/size)

Large-scale edges

Fine edges

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Homework 2 &

Canny Edge Detectors

Slides courtesy: Irmak Guzey

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Homework 2

  • Follow the Canny edge detector algorithm discussed in previous slides

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  • Download the homework2.zip file under Assignments tab in Brightspace

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  • Complete only the Canny_Skeleton_Code_Lab.ipynb notebook, zip all files and submit by 10th March 11:59 PM EST.

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  • Following tutorial: https://docs.opencv.org/3.4/da/d22/tutorial_py_canny.html might be really useful for the homework 2.

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Further Reading

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