The document describes using the Scale Invariant Feature Transform (SIFT) algorithm for sub-image matching. It discusses rejecting the chain code algorithm and instead using SIFT. It then explains the various steps of SIFT including creating scale-space and Difference of Gaussian pyramids, extrema detection, noise elimination, orientation assignment, descriptor computation, and keypoints matching.

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2. Team Members : Chinmay Samant
Rajdeep Mandrekar
Shanker Naik
Scale Invariant Feature Transform Laxman Pednekar
Guide : Prof. Rachael Dhanraj

3. Sub-Image Matching
• Sub-Image Matching – the main part of
our project.
• Rejection of the Chain code Algorithm.
• Using Scale invariant Feature Transform
(or SIFT) Algorithm.
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4. Sub-Image Matching
Scale-invariant feature transform Algorithm
• Creating Scale-space and Difference of
Gaussian pyramid
• Extrema detection
• Noise Elimination
• Orientation assignment
• Descriptor Computation
• Keypoints matching
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5. Creating Scale-space and Difference of Gaussian
pyramid
• In scale Space we take the image and
generate progressively blurred out images,
then resize the original image to half and
generate blurred images.
• Images that are of same size but different
scale are called octaves.
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6. How Blurring is performed?
• Mathematically blurring is defined as convolution of Gaussian
operator and image.
• where G= Gaussian Blur operator
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7. Difference of Gaussian(DoG)
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8. Extrema detection
In the image X is current pixel, while green circles are its
neighbors, X is marked as Keypoint if it is greatest or least of all 26
neighboring pixels.
First and last scale are not checked for keypoints as there are not
enough neighbors to compare.
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9. Noise Elimination
1. Removing Low Contrast features
- If magnitude of intensity at current pixel is less
than certain value then it is rejected.
2. Removing edges
– For poorly defined peaks in the DoG function,
the principal curvature across the edge would
be much larger than the principal curvature
along it
– To determine edges Hessian matrix is used.
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10. Tr (H) = Dxx + Dyy
Det(H) = DxxDyy - (Dxy )2
R=Tr(H)^2/Det(H)
If the value of R is greater for a candidate keypoint, then that keypoint
is poorly localized and hence rejected.
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11. Orientation assignment
• The gradient magnitude, m(x, y), and
orientation, θ(x, y), is precomputed using
pixel differences:
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12. Orientation assignment
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13. Descriptor Computation
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14. Keypoints matching
• Each keypoint in the original image
is compared to every keypoints in
the transformed image using the
descriptors.
• The descriptors of the two respective,
keypoints must be closest. Then match is
found.
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15. Thank You
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