Generally, is f(x) a function that is negatively related to x?
Kent
Learning about the bilateral filter sparked my curiosity regarding more advanced filters, and after a bit of searching I managed to find a trilateral filter that does an even better job of filtering! You can find a link to the trilateral filtering paper here: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.95.3170&rep=rep1&type=pdf
Their trilateral filter is a single-pass nonlinear filter that preserves edges and smoothens visual details. It is built from two modified forms of previous bilateral filter and provides stronger noise reduction and better outlier rejection in high-gradient regions than bilateral filters. The paper has a lot of complex math but it might be worth a read if you're curious about more complex filtering mechanisms!
dawwctor
I know that G tends to be a Gaussian blur kernel, but what different types of functions can f(x) take on? Are there certain properties that need to be maintained?
hteo
There's probably an error in the normalization factor $W_p$'s equation: it should be $\sum_{i,j} f(\cdot) G(\cdot)$ without the image values, otherwise the bilateral filter is going to output an image of all ones.
Generally, is f(x) a function that is negatively related to x?
Learning about the bilateral filter sparked my curiosity regarding more advanced filters, and after a bit of searching I managed to find a trilateral filter that does an even better job of filtering! You can find a link to the trilateral filtering paper here: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.95.3170&rep=rep1&type=pdf
Their trilateral filter is a single-pass nonlinear filter that preserves edges and smoothens visual details. It is built from two modified forms of previous bilateral filter and provides stronger noise reduction and better outlier rejection in high-gradient regions than bilateral filters. The paper has a lot of complex math but it might be worth a read if you're curious about more complex filtering mechanisms!
I know that G tends to be a Gaussian blur kernel, but what different types of functions can f(x) take on? Are there certain properties that need to be maintained?
There's probably an error in the normalization factor $W_p$'s equation: it should be $\sum_{i,j} f(\cdot) G(\cdot)$ without the image values, otherwise the bilateral filter is going to output an image of all ones.