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Edge Lecture

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title: Lecture: Edge Detection
categories: lecture
---

# 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