Making your own linear filters!

Table of Contents

• Goal
• Theory
  • Correlation
  • What is a kernel?
  • How does correlation with a kernel work?
  • What does this program do?
• Code
• Explanation
  • Load an image
  • Initialize the arguments
  • Loop
• Results

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Original author	Ana Huamán
Compatibility	OpenCV >= 3.0

Goal

In this tutorial you will learn how to:

• Use the OpenCV function filter2D() to create your own linear filters.

Theory

Note

The explanation below belongs to the book Learning OpenCV by Bradski and Kaehler.

Correlation

In a very general sense, correlation is an operation between every part of an image and an operator (kernel).

What is a kernel?

A kernel is essentially a fixed size array of numerical coefficients along with an anchor point in that array, which is typically located at the center.

How does correlation with a kernel work?

Assume you want to know the resulting value of a particular location in the image. The value of the correlation is calculated in the following way:

1. Place the kernel anchor on top of a determined pixel, with the rest of the kernel overlaying the corresponding local pixels in the image.
2. Multiply the kernel coefficients by the corresponding image pixel values and sum the result.
3. Place the result to the location of the anchor in the input image.
4. Repeat the process for all pixels by scanning the kernel over the entire image.

Expressing the procedure above in the form of an equation we would have:

\[H(x,y) = \sum_{i=0}^{M_{i} - 1} \sum_{j=0}^{M_{j}-1} I(x+i - a_{i}, y + j - a_{j})K(i,j)\]

Fortunately, OpenCV provides you with the function filter2D() so you do not have to code all these operations.

What does this program do?

• Loads an image

• Performs a normalized box filter. For instance, for a kernel of size \(size = 3\), the kernel would be:

  \[K = \dfrac{1}{3 \cdot 3} \begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{bmatrix}\]

The program will perform the filter operation with kernels of sizes 3, 5, 7, 9 and 11.

• The filter output (with each kernel) will be shown during 500 milliseconds

Code

The tutorial code's is shown in the lines below.

C++

You can also download it from here

 
#include "opencv2/imgproc.hpp"
#include "opencv2/imgcodecs.hpp"
#include "opencv2/highgui.hpp"
 
using namespace cv;
 
int main ( int argc, char** argv )
{
    // Declare variables
    Mat src, dst;
 
    Mat kernel;
    Point anchor;
    double delta;
    int ddepth;
    int kernel_size;
    const char* window_name = "filter2D Demo";
 
    const char* imageName = argc >=2 ? argv[1] : "lena.jpg";
 
    // Loads an image
    src = imread( samples::findFile( imageName ), IMREAD_COLOR ); // Load an image
 
    if( src.empty() )
    {
        printf(" Error opening image\n");
        printf(" Program Arguments: [image_name -- default lena.jpg] \n");
        return EXIT_FAILURE;
    }
 
    // Initialize arguments for the filter
    anchor = Point( -1, -1 );
    delta = 0;
    ddepth = -1;
 
    // Loop - Will filter the image with different kernel sizes each 0.5 seconds
    int ind = 0;
    for(;;)
    {
        // Update kernel size for a normalized box filter
        kernel_size = 3 + 2*( ind%5 );
        kernel = Mat::ones( kernel_size, kernel_size, CV_32F )/ (float)(kernel_size*kernel_size);
 
        // Apply filter
        filter2D(src, dst, ddepth , kernel, anchor, delta, BORDER_DEFAULT );
        imshow( window_name, dst );
 
        char c = (char)waitKey(500);
        // Press 'ESC' to exit the program
        if( c == 27 )
        { break; }
 
        ind++;
    }
 
    return EXIT_SUCCESS;
}

Java

You can also download it from here

 
import org.opencv.core.*;
import org.opencv.core.Point;
import org.opencv.highgui.HighGui;
import org.opencv.imgcodecs.Imgcodecs;
import org.opencv.imgproc.Imgproc;
 
class Filter2D_DemoRun {
 
    public void run(String[] args) {
        // Declare variables
        Mat src, dst = new Mat();
 
        Mat kernel = new Mat();
        Point anchor;
        double delta;
        int ddepth;
        int kernel_size;
        String window_name = "filter2D Demo";
 
        String imageName = ((args.length > 0) ? args[0] : "../data/lena.jpg");
 
        // Load an image
        src = Imgcodecs.imread(imageName, Imgcodecs.IMREAD_COLOR);
 
        // Check if image is loaded fine
        if( src.empty() ) {
            System.out.println("Error opening image!");
            System.out.println("Program Arguments: [image_name -- default ../data/lena.jpg] \n");
            System.exit(-1);
        }
 
        // Initialize arguments for the filter
        anchor = new Point( -1, -1);
        delta = 0.0;
        ddepth = -1;
 
        // Loop - Will filter the image with different kernel sizes each 0.5 seconds
        int ind = 0;
        while( true )
        {
            // Update kernel size for a normalized box filter
            kernel_size = 3 + 2*( ind%5 );
            Mat ones = Mat.ones( kernel_size, kernel_size, CvType.CV_32F );
            Core.multiply(ones, new Scalar(1/(double)(kernel_size*kernel_size)), kernel);
 
            // Apply filter
            Imgproc.filter2D(src, dst, ddepth , kernel, anchor, delta, Core.BORDER_DEFAULT );
            HighGui.imshow( window_name, dst );
 
            int c = HighGui.waitKey(500);
            // Press 'ESC' to exit the program
            if( c == 27 )
            { break; }
 
            ind++;
        }
 
        System.exit(0);
    }
}
 
public class Filter2D_Demo {
    public static void main(String[] args) {
        // Load the native library.
        System.loadLibrary(Core.NATIVE_LIBRARY_NAME);
        new Filter2D_DemoRun().run(args);
    }
}

Python

You can also download it from here

"""
@file filter2D.py
@brief Sample code that shows how to implement your own linear filters by using filter2D function
"""
import sys
import cv2 as cv
import numpy as np
 
 
def main(argv):
    window_name = 'filter2D Demo'
 
    
    imageName = argv[0] if len(argv) > 0 else 'lena.jpg'
 
    # Loads an image
    src = cv.imread(cv.samples.findFile(imageName), cv.IMREAD_COLOR)
 
    # Check if image is loaded fine
    if src is None:
        print ('Error opening image!')
        print ('Usage: filter2D.py [image_name -- default lena.jpg] \n')
        return -1
    
    ddepth = -1
    
    ind = 0
    while True:
        
        kernel_size = 3 + 2 * (ind % 5)
        kernel = np.ones((kernel_size, kernel_size), dtype=np.float32)
        kernel /= (kernel_size * kernel_size)
        
        dst = cv.filter2D(src, ddepth, kernel)
        
        cv.imshow(window_name, dst)
 
        c = cv.waitKey(500)
        if c == 27:
            break
 
        ind += 1
 
    return 0
 
 
if __name__ == "__main__":
    main(sys.argv[1:])

Explanation

Load an image

C++

    const char* imageName = argc >=2 ? argv[1] : "lena.jpg";
 
    // Loads an image
    src = imread( samples::findFile( imageName ), IMREAD_COLOR ); // Load an image
 
    if( src.empty() )
    {
        printf(" Error opening image\n");
        printf(" Program Arguments: [image_name -- default lena.jpg] \n");
        return EXIT_FAILURE;
    }

Java

        String imageName = ((args.length > 0) ? args[0] : "../data/lena.jpg");
 
        // Load an image
        src = Imgcodecs.imread(imageName, Imgcodecs.IMREAD_COLOR);
 
        // Check if image is loaded fine
        if( src.empty() ) {
            System.out.println("Error opening image!");
            System.out.println("Program Arguments: [image_name -- default ../data/lena.jpg] \n");
            System.exit(-1);
        }

Python

    imageName = argv[0] if len(argv) > 0 else 'lena.jpg'
 
    # Loads an image
    src = cv.imread(cv.samples.findFile(imageName), cv.IMREAD_COLOR)
 
    # Check if image is loaded fine
    if src is None:
        print ('Error opening image!')
        print ('Usage: filter2D.py [image_name -- default lena.jpg] \n')
        return -1

Initialize the arguments

C++

    // Initialize arguments for the filter
    anchor = Point( -1, -1 );
    delta = 0;
    ddepth = -1;

Java

        // Initialize arguments for the filter
        anchor = new Point( -1, -1);
        delta = 0.0;
        ddepth = -1;

Python

    ddepth = -1

Loop

Perform an infinite loop updating the kernel size and applying our linear filter to the input image. Let's analyze that more in detail:

• First we define the kernel our filter is going to use. Here it is:

C++

        // Update kernel size for a normalized box filter
        kernel_size = 3 + 2*( ind%5 );
        kernel = Mat::ones( kernel_size, kernel_size, CV_32F )/ (float)(kernel_size*kernel_size);

Java

            // Update kernel size for a normalized box filter
            kernel_size = 3 + 2*( ind%5 );
            Mat ones = Mat.ones( kernel_size, kernel_size, CvType.CV_32F );
            Core.multiply(ones, new Scalar(1/(double)(kernel_size*kernel_size)), kernel);

Python

        kernel_size = 3 + 2 * (ind % 5)
        kernel = np.ones((kernel_size, kernel_size), dtype=np.float32)
        kernel /= (kernel_size * kernel_size)

The first line is to update the kernel_size to odd values in the range: \([3,11]\). The second line actually builds the kernel by setting its value to a matrix filled with \(1's\) and normalizing it by dividing it between the number of elements.

• After setting the kernel, we can generate the filter by using the function filter2D() :

C++

        // Apply filter
        filter2D(src, dst, ddepth , kernel, anchor, delta, BORDER_DEFAULT );

Java

            // Apply filter
            Imgproc.filter2D(src, dst, ddepth , kernel, anchor, delta, Core.BORDER_DEFAULT );

Python

        dst = cv.filter2D(src, ddepth, kernel)

• The arguments denote:
  • src: Source image
  • dst: Destination image
  • ddepth: The depth of dst. A negative value (such as \(-1\)) indicates that the depth is the same as the source.
  • kernel: The kernel to be scanned through the image
  • anchor: The position of the anchor relative to its kernel. The location Point(-1, -1) indicates the center by default.
  • delta: A value to be added to each pixel during the correlation. By default it is \(0\)
  • BORDER_DEFAULT: We let this value by default (more details in the following tutorial)
• Our program will effectuate a while loop, each 500 ms the kernel size of our filter will be updated in the range indicated.

Results

1. After compiling the code above, you can execute it giving as argument the path of an image. The result should be a window that shows an image blurred by a normalized filter. Each 0.5 seconds the kernel size should change, as can be seen in the series of snapshots below: