Median Filter

Overview

The median filter algorithm performs a two dimensional (2D) filter operation on the input image with the provided 2D kernel. The kernel defines the pixel neighborhood for the filtering operation. The filter performs a non linear operation where the pixel it is working on is replaced by the median of the set of pixels in the input image masked by the kernel. The median filter operation is used for impulse noise reduction, image smoothing, analysis, etc.

Input	Kernel	Output
	\[ \begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{bmatrix} \]

Implementation

VPI implements median filter in the following way

Median Filter algorithm high-level implementation

Discrete 2D median filter is implemented using the following discrete function:

\[ I'[x,y] = \underset{m \in [0 .. k_h-1] \\ n \in [0 .. k_w-1]}{median} \Big\{ K[m,n] \times I[x-(n-\lfloor k_w/2 \rfloor), y-(m-\lfloor k_h/2 \rfloor)] \Big\} \]

Where:

• \(I\) is the input image.
• \(I'\) is the result image.
• \(K\) is the neighborhood kernel, where \(K \in \{0 \vee 1\}\).
• \(k_w, k_h\) are the kernel's width and height, respectively.
• \(median\) is the median filter operation.

C API functions

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

Function	Description
vpiSubmitMedianFilter	Runs a 2D median filter over an image.

Usage

Language: C/C++ Python

1. Import VPI module

   import vpi

2. Define a 3x3 morphological kernel to perform full neighborhood search.

   kernel = [[1, 1, 1],
             [1, 1, 1],
             [1, 1, 1]]

3. Run median filter on input image using the CPU backend and the given kernel. Input and output are VPI images.

   with vpi.Backend.CUDA:
       output = input.median_filter(kernel, border=vpi.Border.ZERO)

1. Initialization phase
   1. Include the header that defines the needed functions and structures.

      #include <vpi/algo/MedianFilter.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 format;
          vpiImageGetFormat(input, &format);
       
          VPIImage output;
          vpiImageCreate(w, h, format, 0, &output);

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

          VPIStream stream;
          vpiStreamCreate(0, &stream);

2. Processing phase
   1. Define the kernel to be used. In this case, a simple 3x3 full neighborhood.

          int8_t kernel[3 * 3] = { 1, 1, 1,
                                   1, 1, 1,
                                   1, 1, 1 };

   2. Submit the algorithm for the median filter. The border extension chosen it VPI_BORDER_LIMITED because it ignores all pixels outside the image. It'll be executed by the CPU backend.

          vpiSubmitMedianFilter(stream, VPI_BACKEND_CPU, input, output, 3, 3, kernel, VPI_BORDER_LIMITED);

   3. 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 Median Filter in the "API Reference" section of VPI - Vision Programming Interface.

Performance

Performance benchmarks will be added at a later time.