Gaussian Filter

Overview

Gaussian Filter is a low-pass discrete Gaussian filter that smooths out the image by doing a Gaussian-weighted averaging of neighbor pixels of a given input pixel. It produces images with less artifacts than Box Filter, but could potentially be more costly to compute.

It supports two modes of operation:

• Kernel support size is automatically calculated based on the filter standard deviation (sigma).
• Use both user-provided kernel support size and filter standard deviation.

Input	Gaussian kernel	Output
	7x7 support, \[ \sigma=1.7 \]

Implementation

Gaussian filter is implemented as a convolution operation on the input image where the kernel has the following weights:

\[ w_g[x,y] = \frac{1}{2\pi\sigma^2} \cdot e^{-\frac{x^2+y^2}{2\sigma^2}} \]

When the input kernel support size is 0 for a given dimension (or both), it is calculated from the given standard deviation by assuming that the weights outside \(\pm3\sigma\) window are zero.

In this case, the following formula is used:

\[ w = \max\{3,2 \times \lceil 3\sigma\rceil-1\} \]

Note

We clamp the minimum kernel size to 3 because a kernel with size 1 doesn't have enough samples to properly characterize a Gaussian function.

C API functions

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

Function	Description
vpiSubmitGaussianFilter	Runs a 2D Gaussian filter over an image.

Usage

Language: C/C++ Python

1. Import VPI module

   import vpi

2. Use the CPU backend to filter the input image with a 7x7 Gaussian kernel with \(\sigma=1.7\), using ZERO boundary condition. Input and output are VPI images.

   with vpi.Backend.CPU:
       output = input.gaussian_filter(7, 1.7, border=vpi.Border.ZERO)

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

      #include <vpi/algo/GaussianFilter.h>

   2. Define the input image object.

          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 along with other parameters. It'll be executed by the CPU backend. It defines a Gaussian filter with 7x7 support and \(\sigma=1.7\) in both horizontal and vertical directions, along with a zero border extension.

          vpiSubmitGaussianFilter(stream, VPI_BACKEND_CPU, input, output, 7, 7, 1.7, 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 Gaussian 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