Image convolution: Difference between revisions

One class of image digital filters is described by a rectangular matrix of real coefficients called [https://en.wikipedia.org/wiki/Kernel_(image_processing) '''kernel'''] convoluted in a sliding window of image pixels. Usually the kernel is square <math>K_{kl}</math>, where <i>k</i>, <i>l</i> are in the range -<i>R</i>,-<i>R</i>+1,..,<i>R</i>-1,<i>R</i>. <i>W</i>=2<i>R</i>+1 is the kernel width. The filter determines the new value of a monochromatic image pixel P_<i>ij</i> as a convolution of the image pixels in the window centered in <i>i</i>, <i>j</i> and the kernel values:

'''Color images''' are usually split into the channels which are filtered independently. A color model can be changed as well, i.e. filtration is performed not necessarily in RGB. Common kernels sizes are 3x3 and 5x5. The complexity of filtrating grows quadratically ([[O]](<i>n</i>²)) with the kernel width.

<langsyntaxhighlight lang="ada">type Float_Luminance is new Float;

end To_Pixel;</langsyntaxhighlight>

<langsyntaxhighlight lang="ada">type Kernel_3x3 is array (-1..1, -1..1) of Float_Luminance;

end Filter;</langsyntaxhighlight>

<langsyntaxhighlight lang="ada"> F1, F2 : File_Type;

Close (F2);</langsyntaxhighlight>

<langsyntaxhighlight lang="bbcbasic"> Width% = 200

UNTIL FALSE</langsyntaxhighlight>

<langsyntaxhighlight lang="c">image filter(image img, double *K, int Ks, double, double);</langsyntaxhighlight>

<langsyntaxhighlight lang="c">#include "imglib.h"

}</langsyntaxhighlight>

<langsyntaxhighlight lang="c">#include <stdio.h>

}</langsyntaxhighlight>

<langsyntaxhighlight lang="d">import std.string, std.math, std.algorithm, grayscale_image;

}</langsyntaxhighlight>

<langsyntaxhighlight lang="go">package main

}</langsyntaxhighlight>

<langsyntaxhighlight lang="go">package raster

}</langsyntaxhighlight>

<langsyntaxhighlight lang="go">package main

}</langsyntaxhighlight>

<langsyntaxhighlight Jlang="j">NB. pad the edges of an array with border pixels

pad=: adverb define{{

kernel_filter=: adverb define{{

[: (0 >. 255 <. <.@:+&0.5) (1,:$m)+/ .*&(,m)~&(,/)&m;._3 m pad

<syntaxhighlight lang J="j"> NB. kernels borrowed from C and TCL implementations

sharpen_kernelid_kernel=: _1+10*4(=&i.-)3 3

'blurred.ppm' writeppm~ blur_kernel kernel_filter readppm 'original.ppm'</langsyntaxhighlight>

<langsyntaxhighlight Javalang="java">import java.awt.image.*;

}</langsyntaxhighlight>

<langsyntaxhighlight lang="javascript">// Image imageIn, Array kernel, function (Error error, Image imageOut)

}</langsyntaxhighlight>

<langsyntaxhighlight lang="mathematica">img = Import[NotebookDirectory[] <> "Lenna50.jpg"];

ImageConvolve[img, BoxMatrix[1] ]</langsyntaxhighlight>

<langsyntaxhighlight MATLABlang="matlab">function testConvImage

fprintf('Original kernalkernel:\n')

fprintf('Renormalizing kernalkernel and using only values within image:\n')

% title('Renormalizing kernalkernel and using only values within image')

% Filters an image using sliding-window kernalkernel convolution.

% (possibly useful for emphasizing certain data with unusual kernalkernel)

end</langsyntaxhighlight>

Original kernalkernel:

Renormalizing kernalkernel and using only values within image:

<langsyntaxhighlight lang="ocaml">let get_rgb img x y =

(res)</langsyntaxhighlight>

<langsyntaxhighlight lang="ocaml">let emboss img =

;;</langsyntaxhighlight>

<langsyntaxhighlight lang="octave">function [r, g, b] = rgbconv2(a, c)

jpgwrite("LennaSharpen.jpg", r, g, b, 100);</langsyntaxhighlight>

<langsyntaxhighlight PicoLisplang="picolisp">(scl 3)

(map pop X) ) ) ) ) ) ) )</langsyntaxhighlight>

<langsyntaxhighlight lang="python">#!/bin/python

im2.show()</langsyntaxhighlight>

<langsyntaxhighlight lang="python">#!/bin/python

im = imread("test.jpg", mode="RGB")

imshow(im3)</langsyntaxhighlight>

<langsyntaxhighlight lang="racket">#lang typed/racket

"out/convolve-etch-3x3.png"))</langsyntaxhighlight>

<langsyntaxhighlight lang="ruby">class Pixmap

end</langsyntaxhighlight>

<langsyntaxhighlight lang="tcl">package require Tk

}</langsyntaxhighlight>