Bilateral Filter

Overview

The Bilateral Filter is a non-linear, edge-preserving smoothing filter that is commonly used in Computer Vision as a simple noise-reduction stage in a pipeline. It calculates the intensity of each output pixel as a weighted average of intensity values from nearby pixels in the input image. Crucially, the weights depend not only on the Euclidean distance between current and neighbor pixels, but also on the radiometric differences (e.g., color intensity differences) between them. The outcome is that edges are preserved while regions with similar intensities are smoothed out.

Input	Parameters	Output
	\begin{align*} \mathit{kernelSize} &= 7x7 \\ \sigma_s &= 1.7 \\ \sigma_r &= 50 \end{align*}

Implementation

The bilateral filter is defined as:

\[ I'(p) = \frac{1}{W_p} \sum_{q\in\Omega}I(p)k_r(\|I(q) - I(p)\|)k_s(\|p-q\|) \]

and the normalization term, W, is defined as:

\[ W_p = \sum_{q\in\Omega}k_r(\|I(p)-I(q)\|)k_s(\|p-q\|) \]

where

• \(I\) and \(I'\) are the input and output images, respectively.
• \(k_r\) and \(k_s\) are the range and space kernels, respectively, defined as the following non-normalized Gaussian functions:

  \begin{align*} k_r(p) &= e^{-\frac{\|p\|^2}{2\sigma_r^2}} \\ k_s(p) &= e^{-\frac{\|p\|^2}{2\sigma_s^2}} \end{align*}

• \(\sigma_r\) controls the intensity range that is smoothed out. Higher values will lead to larger regions being smoothed out. The \(\sigma_r\) value should be selected with the dynamic range of the image pixel values in mind.
• \(\sigma_s\) controls smoothing factor. Higher values will lead to more smoothing.

C API functions

For list of limitations, constraints and backends that implements the algorithm, consult reference documentation of the following functions:

Function	Description
vpiSubmitBilateralFilter	Runs a 2D bilateral filter over an image.

Usage

Language: C/C++ Python

1. Import VPI module

   import vpi

2. Run bilateral filter on input image using the CUDA backend. It's using a 7x7 kernel with \(\sigma_r=50\) and \(\sigma_s=1.7\), and ZERO boundary condition. Input and output are VPI images.

   with vpi.Backend.CUDA:
       output = input.bilateral_filter(5, 7, 50, border=vpi.Border.ZERO)

1. Initialization phase
   1. Include the header that defines the Bilateral filter function.

      #include <vpi/algo/BilateralFilter.h>

   2. Define the input image.

          VPIImage input = /*...*/;

   3. Create the output image. It gets its dimensions and format from the input image.

          int32_t w, h;
          vpiImageGetSize(input, &w, &h);
       
          VPIImageFormat type;
          vpiImageGetFormat(input, &type);
       
          VPIImage output;
          vpiImageCreate(w, h, type, 0, &output);

   4. Create the stream where the algorithm will be submitted for execution.

          VPIStream stream;
          vpiStreamCreate(0, &stream);

2. Processing phase
   1. Submit the algorithm to the stream using the CUDA backend, along with all parameters. Here we're using a 7x7 kernel with \(\sigma_r=50\) and \(\sigma_s=1.7\).

          vpiSubmitBilateralFilter(stream, VPI_BACKEND_CUDA, input, output, 7, 50, 1.7, VPI_BORDER_ZERO);

   2. Optionally, wait until the processing is done.

          vpiStreamSync(stream);

3. Cleanup phase
   1. Free resources held by the stream and the input and output images.

          vpiStreamDestroy(stream);
          vpiImageDestroy(input);
          vpiImageDestroy(output);

For more information, see Bilateral Filter in the "C API Reference" section of VPI - Vision Programming Interface.

Performance

For information on how to use the performance table below, see Algorithm Performance Tables.
Before comparing measurements, consult Comparing Algorithm Elapsed Times.
For further information on how performance was benchmarked, see Performance Benchmark.

clear filters Device: Jetson AGX Xavier Jetson AGX Orin  -  Streams: 1 2 4 8