1. ECE734 Project-Scale Invariant Feature Transform Algorithm
Jing Li

2. Algorithm introdution
Outline
Background 1
Algorithm introdution 2
Program implement 3

3. Background: Scale-Invariant Feature Transform (SIFT)
Scale-Invariant Feature Transform: Apply in image recognition.
Two steps for image recognition:
1. Feature extraction
2. Feature match
SIFT algorithm can extract distinctive features.
Features: invariant to image scale and rotation
perform reliable matching between different views of object or scene.
Random Sample Consensus (RANSAC): Match features from object image to training images

4. Scale-space extrema detection
Keypoint localization
Orientation assignment
Keypoint descriptor

5. Scale-space extrema detection
Define image scale space function
  L(x, y,σ) = G(x, y, σ) ∗ I(x, y)
Detect stable keypoint locations used difference-of-Gaussian function
D(x,y,σ)= L(x, y,kσ) - L(x, y,σ)
D(x,y,σ) is the approximation of Laplacian of Gaussian (LoG) operation.
We use five steps to build the use Build difference-of-Gaussian Octaves D(x,y,σ)
use different to conversion to build each octave of scale space, based on the function: 
     

6. Keypoint localization
Maxima and minima of LoG produce the most stable image features compared to a range of other possible image functions
Detected by comparing a pixel (marked with X) to its 26 neighbors in 3x3 regions at the current and adjacent scales
Talyor expansion for D(x,y,σ) and set its derivative to 0

7. Orientation Assignment Keypoint Descriptor
Assign orientation to each keypoints by local gradient direction
Gradient magnitude, m(x, y),
Orientation θ(x,y)
Divide image into equal regions (4,16…….)
Divide each region to some small regions.
Find the orientation of small region and shift to the location of keypoint of large region. Overlay these orientation and use it to express the feature of keypoints.

8. Program Test Pgm file: Keypoint descriptor by SIFT algorithm
1021 keypoints found
An image of size 500 pixels square will typically give
over 1000 keypoints depending on image content

9. SIFT extract features from training image and store in database
SIFT extract features from training image and store in database. Set a sample image which include the same features with the training image. Compare the Euclidean distance of keypoint to test corrective of algorithm
Same features typically have the minimum Euclidean distance.
Compare Euclidean distance of each keypoints.