Till now, we have discussed various smoothing filters like Averaging, Median, Gaussian, etc. All these filters are effective in removing different types of noises but at the same time produce an undesirable side effect of blurring the edges also. So isn’t it be nice, if we somehow prevent averaging across edges, while still smoothing other regions. This is what exactly Bilateral filtering does.

Let’s first refresh some basic concepts which will be needed to understand Bilateral filtering.

I hope you are all familiar with the domain and range of any function. If not then let’s refresh these concepts. Domain and range are the set of all plausible values that the independent and dependent variables can take respectively. We all know that the image is also a function (a 2-D light intensity function F(x,y)). Thus for an image, the domain is the set of all possible pixel locations and range corresponds to all possible intensity values.

Now, let’s use these concepts to understand Bilateral filtering.

All the filters we read till now like Median, Gaussian, etc. were domain filters. This means that the filter weights are assigned using the spatial closeness (i.e. domain). This has an issue as it will blur the edges also. Let’s take an example to see how.

Below is a small 3×3 patch extracted from a large image having a diagonal edge. Because in domain filters, we are assigning filter weights according to the spatial closeness, more weights are given to the nearer pixels as compared to the distant pixels. This leads to the edge blurring. See how the central pixel value changed from 10 to 4.

Thus, domain filters doesn’t consider whether a pixel is an edge pixel or not. It just assigns weights according to spatial closeness and thus leads to edge blurring.

Now, let’s see what will happen if we consider range filters. In range filters, we assign weights according to the intensity difference. This ensures that only those pixels with similar intensity to the central pixel is considered for blurring. Because in range filtering, we are not considering the spatial relationship. So, now the similar intensity pixels that are far away from the central pixel affect the final value of the central pixel more as compared to the nearby approx. similar pixels. This makes no sense.

Thus, range filtering alone also doesn’t solve the problem of edge blurring.

Now, what if we combine both domain and range filtering. That will solve our problem. Because now, first, the domain filter will make sure that only nearby pixels (say a 3×3 window) are considered for blurring and then the range filter will make sure that the weights in this 3×3 window are given according to the intensity difference wrt. center pixel. This way it will preserve the edges. This is known as Bilateral filtering (bi for both domain and range filtering).

I hope you understood Bilateral filtering. Now, let’s see how to do this using OpenCV-Python

OpenCV-Python

OpenCV provides an inbuilt function for bilateral filtering as shown below. You can read more about it here but a short description is given below

• If the sigma values are small (< 10), the filter will not have much effect, whereas if they are large (> 150), they will have a very strong effect, making the image look “cartoonish”.
• Large filters (d > 5) are very slow, so it is recommended to use d=5 for real-time applications, and perhaps d=9 for offline applications that need heavy noise filtering.

Let’s take an example to understand this

There exist several extensions to this filter like the guided filter that deals with the artifacts generated by this. Hope you enjoy reading.

If you have any doubt/suggestion please feel free to ask and I will do my best to help or improve myself. Good-bye until next time.