Differentiation - The Canny edge detector

• \(\nabla I = [ I_x, I_y ]\) is the gradient vector.
• It has length and direction in each pixel in the image.
• Length \(||\nabla I(x,y)||^2= \nabla I^T\nabla I\)
• Select points which satisfy two criteria
  • Local optimum along the direction of the gradient
  • Larger than a chosen threshold \(\tau\).
  • Sometimes we use a soft and a hard threshold, where points between the two thresholds are selected if they are adjacent to other selected points.
• We can calculate \(\nabla I\) with either Sobel or the derivative of a Gaussian.

Connected Components

Line Fitting

Hough