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Scale Invariant Feature Transform (SIFT)PowerPoint Presentation

Scale Invariant Feature Transform (SIFT)

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Scale Invariant Feature Transform (SIFT)

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Scale Invariant Feature Transform (SIFT)

- What is SIFT
- Algorithm overview
- Object Detection
- Summary

- 1999
- Generates image features, “keypoints”
- invariant to image scaling and rotation
- partially invariant to change in illumination and 3D camera viewpoint
- many can be extracted from typical images
- highly distinctive

- Scale-space extrema detection
- Uses difference-of-Gaussian function

- Keypoint localization
- Sub-pixel location and scale fit to a model

- Orientation assignment
- 1 or more for each keypoint

- Keypoint descriptor
- Created from local image gradients

- Definition:
where

- Keypoints are detected using scale-space extrema in difference-of-Gaussian function D
- D definition:
- Efficient to compute

- Close approximation to scale-normalized Laplacian of Gaussian,
- Diffusion equation:
- Approximate ∂G/∂σ:
- giving,

- When D has scales differing by a constant factor it already incorporates the σ2 scale normalization required for scale-invariance

2k2σ

2kσ

2σ

kσ

σ

2kσ

2σ

kσ

σ

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- There is no minimum
- Best frequency determined experimentally

- Increasing σ increases robustness, but costs
- σ = 1.6 a good tradeoff
- Doubling the image initially increases number of keypoints

- Sample point is selected only if it is a minimum or a maximum of these points

Extrema in this image

DoG scale space

- 3D quadratic function is fit to the local sample points
- Start with Taylor expansion with sample point as the origin
- where

- Take the derivative with respect to X, and set it to 0, giving
- is the location of the keypoint
- This is a 3x3 linear system

- Derivatives approximated by finite differences,
- example:

- If X is > 0.5 in any dimension, process repeated

- Contrast (use prev. equation):
- If | D(X) | < 0.03, throw it out

- Edge-iness:
- Use ratio of principal curvatures to throw out poorly defined peaks
- Curvatures come from Hessian:
- Ratio of Trace(H)2 and Determinant(H)
- If ratio > (r+1)2/(r), throw it out (SIFT uses r=10)

- Descriptor computed relative to keypoint’s orientation achieves rotation invariance
- Precomputed along with mag. for all levels (useful in descriptor computation)
- Multiple orientations assigned to keypoints from an orientation histogram
- Significantly improve stability of matching

- Descriptor has 3 dimensions (x,y,θ)
- Orientation histogram of gradient magnitudes
- Position and orientation of each gradient sample rotated relative to keypoint orientation

- Weight magnitude of each sample point by Gaussian weighting function
- Distribute each sample to adjacent bins by trilinear interpolation (avoids boundary effects)

- Best results achieved with 4x4x8 = 128 descriptor size
- Normalize to unit length
- Reduces effect of illumination change

- Cap each element to 0.2, normalize again
- Reduces non-linear illumination changes
- 0.2 determined experimentally

- Create a database of keypoints from training images
- Match keypoints to a database
- Nearest neighbor search

- Different descriptor (same keypoints)
- Apply PCA to the gradient patch
- Descriptor size is 20 (instead of 128)
- More robust, faster

- Scale space
- Difference-of-Gaussian
- Localization
- Filtering
- Orientation assignment
- Descriptor, 128 elements