.. _filter_2d:
Making your own linear filters!
********************************
Goal
=====
In this tutorial you will learn how to:
.. container:: enumeratevisibleitemswithsquare
* Use the OpenCV function :filter2d:`filter2D <>` to create your own linear filters.
Theory
=======
.. note::
The explanation below belongs to the book **Learning OpenCV** by Bradski and Kaehler.
Convolution
------------
In a very general sense, convolution 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 coefficeints along with an *anchor point* in that array, which is tipically located at the center.
.. image:: images/filter_2d_tutorial_kernel_theory.png
:alt: kernel example
:align: center
How does convolution with a kernel work?
-----------------------------------------
Assume you want to know the resulting value of a particular location in the image. The value of the convolution is calculated in the following way:
#. Place the kernel anchor on top of a determined pixel, with the rest of the kernel overlaying the corresponding local pixels in the image.
#. Multiply the kernel coefficients by the corresponding image pixel values and sum the result.
#. Place the result to the location of the *anchor* in the input image.
#. 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:
.. math::
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:`filter2D <>` so you do not have to code all these operations.
Code
======
#. **What does this program do?**
* Loads an image
* Performs a *normalized box filter*. For instance, for a kernel of size :math:`size = 3`, the kernel would be:
.. math::
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
#. The tutorial code's is shown lines below. You can also download it from `here `_
.. code-block:: cpp
#include "opencv2/imgproc/imgproc.hpp"
#include "opencv2/highgui/highgui.hpp"
#include
#include
using namespace cv;
/** @function main */
int main ( int argc, char** argv )
{
/// Declare variables
Mat src, dst;
Mat kernel;
Point anchor;
double delta;
int ddepth;
int kernel_size;
char* window_name = "filter2D Demo";
int c;
/// Load an image
src = imread( argv[1] );
if( !src.data )
{ return -1; }
/// Create window
namedWindow( window_name, CV_WINDOW_AUTOSIZE );
/// 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;
while( true )
{
c = waitKey(500);
/// Press 'ESC' to exit the program
if( (char)c == 27 )
{ break; }
/// 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 );
ind++;
}
return 0;
}
Explanation
=============
#. Load an image
.. code-block:: cpp
src = imread( argv[1] );
if( !src.data )
{ return -1; }
#. Create a window to display the result
.. code-block:: cpp
namedWindow( window_name, CV_WINDOW_AUTOSIZE );
#. Initialize the arguments for the linear filter
.. code-block:: cpp
anchor = Point( -1, -1 );
delta = 0;
ddepth = -1;
#. 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:
.. code-block:: cpp
kernel_size = 3 + 2*( ind%5 );
kernel = Mat::ones( kernel_size, kernel_size, CV_32F )/ (float)(kernel_size*kernel_size);
The first line is to update the *kernel_size* to odd values in the range: :math:`[3,11]`. The second line actually builds the kernel by setting its value to a matrix filled with :math:`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:`filter2D <>`:
.. code-block:: cpp
filter2D(src, dst, ddepth , kernel, anchor, delta, BORDER_DEFAULT );
The arguments denote:
a. *src*: Source image
#. *dst*: Destination image
#. *ddepth*: The depth of *dst*. A negative value (such as :math:`-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 convolution. By default it is :math:`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
========
#. 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:
.. image:: images/filter_2d_tutorial_result.jpg
:alt: kernel example
:align: center