Canny Edge detector

Steps:

  • Apply Gaussian filtering to smooth out noise in the image
  • Compute gradients: Compute horizontal($G_x$) and vertical gradients ($G_y$). Magnitude and direction of gradients can then be compluted as $$\begin{aligned} m &= \sqrt{G_x^2+G_y^2} & \theta &= \tan ^{-1}\left(\frac{G_y}{G_x}\right) \end{aligned}$$ The angle is then rounded off so that $\theta \in {0,45,90,135}$
  • Non-maximal suppression: For each pixel $(m,\theta)$, if its gradient intensity is maximum among the pixels in negative and positive gradient direction, the value is preserved. Otherwise it is suppressed.
  • Double thresholding $$\begin{aligned} m \geq t_h &\implies \text{strong edge pixel} \\ t_l < m < t_h &\implies \text{weak edge pixel} \\ m \leq t_l &\implies \text{suppress} \end{aligned}$$
  • Edge tracking by hysteresis: All strong pixels are selected as true edge pixels. All the weak pixels which has a strong pixel in its $8 \times 8$ neighbourhood are also selected as a true edge. All the others are removed.



tags: computer-vision