lecture17 - EECS 442 Computer vision Detectors part II...

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EECS 442 – Computer vision Detectors part II Descriptors Some slides of this lectures are courtesy of prof F. Li, prof S. Lazebnik, and various other lecturers • Blob detectors • Invariance •Descr ip tors
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Goal: Identify interesting regions from the images (edges, corners, blobs…) Descriptors Matching / Indexing / Recognition e.g. SIFT
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• Repeatability – The same feature can be found in several images despite geometric and photometric transformations • Saliency – Each feature is found at an “interesting” region of the image • Locality – A feature occupies a “relatively small” area of the image;
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Repeatability Scale invariance Pose invariance •Rotation •Affine Illumination invariance
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• Saliency / •Locality /
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Harris Detector
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Detector Illumination Rotation Scale View point partial No No Harris corner Yes Invariance
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Extract useful building blocks: blobs
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Edge detection g dx d f f g dx d Source: S. Seitz Edge Derivative of Gaussian Edge = maximum of derivative
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Edge detection as zero crossing g dx d f 2 2 f g dx d 2 2 Second derivative of Gaussian (Laplacian) Edge = zero crossing of second derivative Edge Source: S. Seitz
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Edge detection as zero crossing edge edge
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From edges to blobs • Blob = superposition of nearby edges Ok, great, but what if the blob is slightly thicker or slimmer? maximum blob
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From edges to blobs Spatial selection: magnitude of the Laplacian response will achieve a maximum at the center of the blob, provided the scale of the Laplacian is “matched” to the scale of the blob maximum No longer maximum • Blob = superposition of nearby edges
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Scale selection • We want to find the characteristic scale of the blob by convolving it with Laplacians at several scales and looking for the maximum response Why does this happen? increasing σ original signal (radius=8) This should give the max response / •However, Laplacian response decays as scale increases:
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Scale normalization • The response of a derivative of Gaussian filter to a perfect step edge decreases as σ increases πσ 2 1
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Scale normalization • To keep response the same (scale- invariant), must multiply Gaussian derivative by σ • Laplacian is the second Gaussian derivative, so it must be multiplied by σ 2
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Effect of scale normalization Scale-normalized Laplacian response Unnormalized Laplacian response Original signal Maximum
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Blob detection in 2D • Laplacian of Gaussian: Circularly symmetric operator for blob detection in 2D 2 2 2 2 2 y g x g g + =
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Blob detection in 2D • Laplacian of Gaussian: Circularly symmetric operator for blob detection in 2D + = 2 2 2 2 2 2 norm y g x g g σ Scale-normalized:
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Scale selection • For a binary circle of radius r, the Laplacian achieves a maximum at 2 / r = σ r 2 / r scale ( σ ) image Laplacian response
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Characteristic scale • We define the characteristic scale as the scale that produces peak of Laplacian response characteristic scale T. Lindeberg (1998). "Feature detection with automatic scale selection." International Journal of Computer Vision 30 (2): pp 77--116.
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lecture17 - EECS 442 Computer vision Detectors part II...

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