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Harris Corner Detector: Features, Properties, and Applications

This article explores the Harris corner detector, a popular technique for detecting and matching features in digital visual effects. Learn about the properties of features, the Harris corner detection algorithm, and its applications in various fields.

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Harris Corner Detector: Features, Properties, and Applications

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  1. Features Digital Visual Effects, Spring 2007 Yung-Yu Chuang 2007/3/20 with slides by Trevor DarrellCordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins and Jiwon Kim

  2. Outline • Features • Harris corner detector • SIFT • Applications

  3. Features

  4. Features • Properties of features • Detector: locates feature • Descriptor and matching metrics: describes and matches features

  5. Desired properties for features • Distinctive: a single feature can be correctly matched with high probability. • Invariant: invariant to scale, rotation, affine, illumination and noise for robust matching across a substantial range of affine distortion, viewpoint change and so on. That is, it is repeatable.

  6. Harris corner detector

  7. Moravec corner detector (1980) • We should easily recognize the point by looking through a small window • Shifting a window in anydirection should give a large change in intensity

  8. Moravec corner detector flat

  9. Moravec corner detector flat

  10. Moravec corner detector flat edge

  11. Moravec corner detector corner isolated point flat edge

  12. Window function Shifted intensity Intensity Moravec corner detector Change of intensity for the shift [u,v]: Four shifts: (u,v) = (1,0), (1,1), (0,1), (-1, 1) Look for local maxima in min{E}

  13. Problems of Moravec detector • Noisy response due to a binary window function • Only a set of shifts at every 45 degree is considered • Only minimum of E is taken into account • Harris corner detector (1988) solves these problems.

  14. Harris corner detector Noisy response due to a binary window function • Use a Gaussian function

  15. Harris corner detector Only a set of shifts at every 45 degree is considered • Consider all small shifts by Taylor’s expansion

  16. Harris corner detector Equivalently, for small shifts [u,v] we have a bilinear approximation: , where M is a 22 matrix computed from image derivatives:

  17. Harris corner detector Only minimum of E is taken into account • A new corner measurement

  18. Harris corner detector Intensity change in shifting window: eigenvalue analysis 1, 2 – eigenvalues of M direction of the fastest change Ellipse E(u,v) = const direction of the slowest change (max)-1/2 (min)-1/2

  19. Harris corner detector Classification of image points using eigenvalues of M: 2 edge 2 >> 1 Corner 1 and 2 are large,1 ~ 2;E increases in all directions 1 and 2 are small;E is almost constant in all directions edge 1 >> 2 flat 1

  20. Harris corner detector Measure of corner response: (k – empirical constant, k = 0.04-0.06)

  21. Harris corner detector

  22. Another view

  23. Another view

  24. Another view

  25. Summary of Harris detector

  26. Harris corner detector (input)

  27. Corner response R

  28. Threshold on R

  29. Local maximum of R

  30. Harris corner detector

  31. Harris detector: summary • Average intensity change in direction [u,v] can be expressed as a bilinear form: • Describe a point in terms of eigenvalues of M:measure of corner response • A good (corner) point should have a large intensity change in all directions, i.e. R should be large positive

  32. threshold R R x(image coordinate) x(image coordinate) Harris detector: some properties • Partial invariance to affine intensity change • Only derivatives are used => invariance to intensity shift I I+b • Intensity scale: I  aI

  33. Harris Detector: Some Properties • Rotation invariance Ellipse rotates but its shape (i.e. eigenvalues) remains the same Corner response R is invariant to image rotation

  34. Harris Detector is rotation invariant Repeatability rate: # correspondences# possible correspondences

  35. Harris Detector: Some Properties • But: non-invariant to image scale! All points will be classified as edges Corner !

  36. Harris detector: some properties • Quality of Harris detector for different scale changes Repeatability rate: # correspondences# possible correspondences

  37. Scale invariant detection • Consider regions (e.g. circles) of different sizes around a point • Regions of corresponding sizes will look the same in both images

  38. Scale invariant detection • The problem: how do we choose corresponding circles independently in each image? • Aperture problem

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