Understanding the Bilateral Filter - Neighbors and Sigma

1. What is Sigma Space in bilateral filter?
2. How does a bilateral filter work?
3. How do you choose bilateral filter parameters?

What is Sigma Space in bilateral filter?

sigma space:

Enter a value to filter sigma in the coordinate space (σd). A larger value means that farther pixels will influence each other as long as their colors are close enough. When d>0 , it specifies the neighborhood size regardless of sigma space. Otherwise, d is proportional to sigma space.

How does a bilateral filter work?

A bilateral filter is a non-linear, edge-preserving, and noise-reducing smoothing filter for images. It replaces the intensity of each pixel with a weighted average of intensity values from nearby pixels. This weight can be based on a Gaussian distribution.

How do you choose bilateral filter parameters?

The bilateral filter is controlled by two parameters: σs and σr. Figure 2.3 illustrates their effect. constant over the intensity interval of the image. Increasing the spatial parameter σs smooths larger features.