LoG-DoG (Difference of Gaussian)
LoG can be approximated by a difference of two Gaussians (DoG) at different scales
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LoG-DoG (Difference of Gaussian)
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Scale Invariant Feature Transform • Scale space peak selection
– Potential locations for finding features • Key point localization
– Accurately locating the feature key points • Orientation assignment
– Assigning orientation to the key points • Key point descriptor
– Describing the key point as a high dimensional vector (128) (SIFT Descriptor )
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Building the Scale Space
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Peak Detection
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Assignment of the Orientation For the rotation invariance, compute the gradient magnitude
and direction at the scale of the keypoint.
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Assignment of the Orientation
• An orientation histogram is formed from the gradient orientations of sample points within a region around the keypoint.
• The orientation histogram has 36 bins covering the 360 degree range of orientations.
• The samples added to the histogram is weighted by the gradient magnitude.
• The dominate direction is the peak in the histogram.
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Full version
SIFT descriptor
• Divide the 16×16 window into a 4×4 grid of cells (2×2 case shown below)
• Compute an orientation histogram (8 bin) for each cell (relative orientation and magnitude)
• 16 cells * 8 orientations = 128 dimensional descriptor
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Properties of SIFT
Robust matching technique
– Can handle changes in viewpoint
– Can handle significant changes in illumination
– Fast and efficient—can run in real time
– Lots of code available
• Keypoint detection: repeatable and distinctive
– Corners, blobs, stable regions – Harris, LoG
• Descriptors:robust
– spatial histograms of orientation
– SIFT and variants are typically good for stitching and recognition
Which features match?
Feature matching
Given a feature in I1, how to find the best match in I2?
1. Define distance function that compares two descriptors
2. Test all the features in I2, find the one with min distance
Feature distance
How to define the difference between two features f1, f2? – Simple approach: L2 distance, ||f1 – f2 || (aka SSD)
– can give good scores to ambiguous (incorrect) matches
Feature distance
How to define the difference between two features f1, f2?
• Better approach: ratio distance = ||f1 – f2 || / || f1 – f2’ ||
• f2 is best SSD match to f1 in I2
• f2’ is 2nd best SSD match to f1 in I2
• gives large values for ambiguous matches
• How does SIFT rotate an image patch to align with its dominant orientation?
1) Compute the eigenvectors of the Harris matrix
2) Rotate to the direction same as the peak of the orientation histogram
3) SIFT do not need to do this
Feature matching example
51 matches (thresholded by ratio score)
Feature matching example
58 matches (thresholded by ratio score)
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