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="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="go">package raster

return uint16(math.FminMin(math.MaxUint16, math.FmaxMax(0,sum)))

r.px[z] = uint16(math.FminMin(math.MaxUint16, math.FmaxMax(0,

}</langsyntaxhighlight>

<langsyntaxhighlight lang="go">package main

}</langsyntaxhighlight>

<langsyntaxhighlight Jlang="j">NB. pad the first n dimensionsedges of an array with zerosborder pixels

NB. (increasing allthe first two dimensions by 1 less than the kernel size)

pad=: adverb define{{

adj1=: <rank=.#$m%2

( -@(adj2 second+ ]rank{.$) {. (adj1 first+ ]) rank{. [$) (#m) {. $]

kernel_filter=: adverb define{{

[: ,/"(-#$m0 >. 255 <. <.@:+&0.5) (1,:$m) +/@ .*~&(,/^:(_1+#$m))@:*&m;._3 m ($m)pad

This code assumes that the leading dimensions of the array represent pixels and any trailing dimensions represent structure to be preserved (this is a fairly common approach and matches the J implementation at [[Basic bitmap storage]]). Note also that we assume that the image is larger than a single pixel in both directions. Any sized kernel is supported (as long as it's at least one pixel in each direction).

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

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

=={{header|Mathematica}} / {{header|Wolfram Language}}==

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

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

<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="ruby">class Pixmap

end</langsyntaxhighlight>

<langsyntaxhighlight lang="tcl">package require Tk

}</langsyntaxhighlight>