Bilateral Filter, cross/joint bilateral filter_filter

Asked today to cross bilateral filter, although I know this is definitely a filtering algorithm, but what it is related to bilateral filter. Feel, as an image processing researcher, must be a solid foundation, so hurry to see.

Nerdland in tech stuff describes "joint bilateral filter is also referred to as Cross filter". That means both mean the same. The original marvellous cross bilateral filter (CBF) is a common joint bilateral filter (JBF), JBF is very common.

Under

Low pass filtering
, look at the Low-pass filter below (the filtering). The author says that the layman is called smoothing (in layman's language smoothing), alas, I dare not call smoothing again.
An image is fundamentally composed of two types of frequency component, low and high. The low frequency components signify smooth and constant regions the where as high frequency components signify edges and corners. So a low pass filter passes low frequency components untouched but smooths of the high frequency. It is used to reduce noise. The typical kernel is a uniform or a Gaussian kernel. These kernels work very the-in-general but have issues near. They include artifacts because the resulting value after smoothing in the boundary pixel comes from two different. The edges are not preserved.
The description is really good, read English, more clearly than the translation.

Bilateral Filter is a technique so can be used to perform edge preserving smoothing. There are variants to this namely anisotropic diffusion. In ' short, bilateral modifies the kernel based on the ' local content so ' edges are.
Example:
A Typical example is if you have color image and depth image and, want to smooth the color image such T Hat color does not bleed across depth boundaries. This is the Joint/cross bilateral filter. Here's the kernel is a combination of weights based on the color similarity and depth similarity. Thus the filter would use only smooth values with similar color and depth depth and keep the rest untouched. This is a simple but elegant solution that has tremendous (extremely good) application
Nernland is used to smooth color images in the preprocessing phase to prevent fragmentation. (Smooth the color image as a preprocessing step to perform over-segmentation)

Without an additional source of information could only apply to bilateral filter, not cross bilateral filter.
Then we have to make a good distinction between bilateral filter and cross bilateral filter.

Bilateral filter
The wiki explains: A bilateral filter is a non-linear,edge-preserving and noise-reducing smoothing the filter for images. That is, the two-sided filtering has three characteristics: nonlinearity, preserving edges, and removing noise. The intensity value at each pixel in a and replaced by a weighted average of intensity values from nearby pixels. The value of each pixel is replaced by the weighted value of the surrounding pixels.
This weight can is based a Gaussian distribution. Crucially, the weights depend not only on Euclidean distance of Pixels,but also on the radiometric difference (e.g. Range differences, such as color intensity, depth distance, etc. This preserves sharp edges by systematically looping through all pixel and adjusting weights to the adjacent pixels dingly.

Bilateral filter is defined as:

Normalized items:

Parameter definition:

for pixels (I,J), its neighborhood (k,l) calculates the value of its weight w (i,j,k,l):

Rachel Zhang has also done a more detailed explanation and implementation here.

Cross/joint Bilateral filter
Bilateral uses the similarity between the Euclidean distance and the strength value in an image to define weights. Joint bilateral requires a reference image.
There was no explanation on the wiki. Let's explain it by reference to the paper.

The biggest difference between the joint-bilateral filter and the bilateral filter is that the joint-bilateral filter uses a guide graph to compute the weights.

The paper "Image Fusion based on pixel significance using cross bilateral filter" has some explanations for this:
The definition of a BF is this:

Accordingly, the definition of CBF is this:

What is the benefit of doing so? Why would you do that?
My understanding is that when there is a missing in B, it is more accurate to refer to the similarity of the intensity values in the corresponding A. For example, using a color map as a guide, and using JBF for processing, the final depth graph is obtained by weighting the similarity of the Euclidean distance between pixels in the depth graph and the intensity values in the color graph. The similarity of depth values is not very credible due to the lack of depth values in depth graphs at this time.

Anisotropic Diffusion
Wiki explains in image processing and computer vision, Anisotropic diffusion, also called Perona-ma Lik diffusion, are a technique aiming at reducing image noise without removing significant parts of the image content, Typi Cally edges, lines or other details this are important for the interpretation of the image.
The specific content of follow-up to add it.