Scale Invariant Feature Transform(SIFT)

SIFT is the image feature extraction algorithm. It detects the features from the image that is invariant from the scale and rotation.

Scale-Space extrema detection

When a person looks images, he looks the big chunk of the image or looks the detailed part of the image. In other words, entire picture and detailed part are both neccessary for a person sees the image. Depending on the distance from the object and object itself, the object we see could be vivid or vague. Likewise, from the SIFT, it adopts the concept of how we see the object in real world by implementing four octave images with five degree of blurring for each scale. The Scale space is the group of the image with variant scales.

It is mathematically proven that detail from the image is removed by introducing the Gaussian blur.

• Gaussian Blur

  

• Symbols:
  • L is blurred image.
  • G is Gaussian Blur operator
  • I is an image
  • x, y : location of the coordinate
  • σ is the scale parameter

• Difference of Gaussian(DoG)

  It is used to increase the visibility of edge and detail part of the images.

  • Subtracting two adjacent images so that four images are created from 5 images at each octave.

    

Finding Keypoints

Finding the local extrema. meaning that key point is the best represented in that scale.

• From the three adjacent images from each octave, there are 26pixels like it is specified in the picture below.

• From the each octave, only second and third picture can provide local extrema since first and fourth image can’t have two adjacent images.

  

Keypoints Localization

The DoG we got previous could be not accurate key points, so it could be not much useful as a feature. So Taylor series is used to get more precise DoG value. If the extrema is less than threshold then it is removed. Also, extrema has high response for edge so edges are also removed from the candidates of extrema points.

Taylor Series

• It is used to predict the value of every point of the function at any point, if the value of the function and value of all its derivatives are knows as a single point.

Orientation assignment