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:
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.
Declares functions that implement median filter algorithms.
2. Define the input image object.
VPIImage input = /*...*/;
struct VPIImageImpl * VPIImage
A handle to an image.
Definition: Types.h:256
3. Create the output image. It gets its dimensions and format from the input image.
int32_t w, h;
vpiImageGetSize(input, &w, &h);
vpiImageGetFormat(input, &format);
VPIImage output;
vpiImageCreate(w, h, format, 0, &output);
uint64_t VPIImageFormat
Pre-defined image formats.
Definition: ImageFormat.h:94
VPIStatus vpiImageGetFormat(VPIImage img, VPIImageFormat *format)
Get the image format.
VPIStatus vpiImageCreate(int32_t width, int32_t height, VPIImageFormat fmt, uint64_t flags, VPIImage *img)
Create an empty image instance with the specified flags.
VPIStatus vpiImageGetSize(VPIImage img, int32_t *width, int32_t *height)
Get the image dimensions in pixels.
4. Create the stream where the algorithm will be submitted for execution.
VPIStream stream;
vpiStreamCreate(0, &stream);
struct VPIStreamImpl * VPIStream
A handle to a stream.
Definition: Types.h:250
VPIStatus vpiStreamCreate(uint64_t flags, VPIStream *stream)
Create a stream instance.
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);
VPIStatus vpiSubmitMedianFilter(VPIStream stream, uint64_t backend, VPIImage input, VPIImage output, int32_t kernelWidth, int32_t kernelHeight, const int8_t *kernelData, VPIBorderExtension border)
Runs a 2D median filter over an image.
@ VPI_BACKEND_CPU
CPU backend.
Definition: Types.h:92
@ VPI_BORDER_LIMITED
Consider image as limited to not access outside pixels.
Definition: Types.h:282
3. Optionally, wait until the processing is done.
vpiStreamSync(stream);
VPIStatus vpiStreamSync(VPIStream stream)
Blocks the calling thread until all submitted commands in this stream queue are done (queue is empty)...
3. Cleanup phase
1. Free resources held by the stream and the input and output images.
vpiImageDestroy(output);
void vpiImageDestroy(VPIImage img)
Destroy an image instance.
void vpiStreamDestroy(VPIStream stream)
Destroy a stream instance and deallocate all HW resources.

For more information, see Median Filter in the "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.

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