# Image convolution

Image convolution
You are encouraged to solve this task according to the task description, using any language you may know.

One class of image digital filters is described by a rectangular matrix of real coefficients called kernel convoluted in a sliding window of image pixels. Usually the kernel is square ${\displaystyle K_{kl}}$, where k, l are in the range -R,-R+1,..,R-1,R. W=2R+1 is the kernel width. The filter determines the new value of a monochromatic image pixel Pij as a convolution of the image pixels in the window centered in i, j and the kernel values:

${\displaystyle P_{ij}=\displaystyle \sum _{k=-R}^{R}\sum _{l=-R}^{R}P_{i+k\ j+l}K_{kl}}$

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(n2)) with the kernel width.

Task: Write a generic convolution 3x3 kernel filter. Optionally show some end user filters that use this generic one.

(You can use, to test the functions below, these input and output solutions.)

First we define floating-point stimulus and color pixels which will be then used for filtration: <lang ada>type Float_Luminance is new Float;

type Float_Pixel is record

  R, G, B : Float_Luminance := 0.0;


end record;

function "*" (Left : Float_Pixel; Right : Float_Luminance) return Float_Pixel is

  pragma Inline ("*");


begin

  return (Left.R * Right, Left.G * Right, Left.B * Right);


end "*";

function "+" (Left, Right : Float_Pixel) return Float_Pixel is

  pragma Inline ("+");


begin

  return (Left.R + Right.R, Left.G + Right.G, Left.B + Right.B);


end "+";

function To_Luminance (X : Float_Luminance) return Luminance is

  pragma Inline (To_Luminance);


begin

  if X <= 0.0 then
return 0;
elsif X >= 255.0 then
return 255;
else
return Luminance (X);
end if;


end To_Luminance;

function To_Pixel (X : Float_Pixel) return Pixel is

  pragma Inline (To_Pixel);


begin

  return (To_Luminance (X.R), To_Luminance (X.G), To_Luminance (X.B));


end To_Pixel;</lang> Float_Luminance is an unconstrained equivalent of Luminance. Float_Pixel is one to Pixel. Conversion operations To_Luminance and To_Pixel saturate the corresponding values. The operation + is defined per channels. The operation * is defined as multiplying by a scalar. (I.e. Float_Pixel is a vector space.)

Now we are ready to implement the filter. The operation is performed in memory. The access to the image array is minimized using a slid window. The filter is in fact a triplet of filters handling each image channel independently. It can be used with other color models as well. <lang ada>type Kernel_3x3 is array (-1..1, -1..1) of Float_Luminance;

procedure Filter (Picture : in out Image; K : Kernel_3x3) is

  function Get (I, J : Integer) return Float_Pixel is
pragma Inline (Get);
begin
if I in Picture'Range (1) and then J in Picture'Range (2) then
declare
Color : Pixel := Picture (I, J);
begin
return (Float_Luminance (Color.R), Float_Luminance (Color.G), Float_Luminance (Color.B));
end;
else
return (others => 0.0);
end if;
end Get;
W11, W12, W13 : Float_Pixel; -- The image window
W21, W22, W23 : Float_Pixel;
W31, W32, W33 : Float_Pixel;
Above : array (Picture'First (2) - 1..Picture'Last (2) + 1) of Float_Pixel;
This  : Float_Pixel;


begin

  for I in Picture'Range (1) loop
W11 := Above (Picture'First (2) - 1); -- The upper row is taken from the cache
W12 := Above (Picture'First (2)    );
W13 := Above (Picture'First (2) + 1);
W21 := (others => 0.0);               -- The middle row
W22 := Get (I, Picture'First (2)    );
W23 := Get (I, Picture'First (2) + 1);
W31 := (others => 0.0);               -- The bottom row
W32 := Get (I+1, Picture'First (2)    );
W33 := Get (I+1, Picture'First (2) + 1);
for J in Picture'Range (2) loop
This :=
W11 * K (-1, -1) + W12 * K (-1, 0) + W13 * K (-1, 1) +
W21 * K ( 0, -1) + W22 * K ( 0, 0) + W23 * K ( 0, 1) +
W31 * K ( 1, -1) + W32 * K ( 1, 0) + W33 * K ( 1, 1);
Above (J-1) := W21;
W11 := W12; W12 := W13; W13 := Above (J+1);     -- Shift the window
W21 := W22; W22 := W23; W23 := Get (I,   J+1);
W31 := W32; W32 := W23; W33 := Get (I+1, J+1);
Picture (I, J) := To_Pixel (This);
end loop;
Above (Picture'Last (2)) := W21;
end loop;


end Filter;</lang> Example of use: <lang ada> F1, F2 : File_Type; begin

  Open (F1, In_File, "city.ppm");
declare
X : Image := Get_PPM (F1);
begin
Close (F1);
Create (F2, Out_File, "city_sharpen.ppm");
Filter (X, ((-1.0, -1.0, -1.0), (-1.0, 9.0, -1.0), (-1.0, -1.0, -1.0)));
Put_PPM (F2, X);
end;
Close (F2);</lang>


## BBC BASIC

<lang bbcbasic> Width% = 200

     Height% = 200

DIM out&(Width%-1, Height%-1, 2)

VDU 23,22,Width%;Height%;8,16,16,128
*DISPLAY Lena
OFF

DIM filter%(2, 2)
filter%() = -1, -1, -1, -1, 12, -1, -1, -1, -1

REM Do the convolution:
FOR Y% = 1 TO Height%-2
FOR X% = 1 TO Width%-2
R% = 0 : G% = 0 : B% = 0
FOR I% = -1 TO 1
FOR J% = -1 TO 1
C% = TINT((X%+I%)*2, (Y%+J%)*2)
F% = filter%(I%+1,J%+1)
R% += F% * (C% AND &FF)
G% += F% * (C% >> 8 AND &FF)
B% += F% * (C% >> 16)
NEXT
NEXT
IF R% < 0 R% = 0 ELSE IF R% > 1020 R% = 1020
IF G% < 0 G% = 0 ELSE IF G% > 1020 G% = 1020
IF B% < 0 B% = 0 ELSE IF B% > 1020 B% = 1020
out&(X%, Y%, 0) = R% / 4 + 0.5
out&(X%, Y%, 1) = G% / 4 + 0.5
out&(X%, Y%, 2) = B% / 4 + 0.5
NEXT
NEXT Y%

REM Display:
GCOL 1
FOR Y% = 0 TO Height%-1
FOR X% = 0 TO Width%-1
COLOUR 1, out&(X%,Y%,0), out&(X%,Y%,1), out&(X%,Y%,2)
LINE X%*2,Y%*2,X%*2,Y%*2
NEXT
NEXT Y%

REPEAT
WAIT 1
UNTIL FALSE</lang>


## C

Interface:

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

The implementation (the Ks argument is so that 1 specifies a 3×3 matrix, 2 a 5×5 matrix ... N a (2N+1)×(2N+1) matrix).

<lang c>#include "imglib.h"

inline static color_component GET_PIXEL_CHECK(image img, int x, int y, int l) {

 if ( (x<0) || (x >= img->width) || (y<0) || (y >= img->height) ) return 0;
return GET_PIXEL(img, x, y)[l];


}

image filter(image im, double *K, int Ks, double divisor, double offset) {

 image oi;
unsigned int ix, iy, l;
int kx, ky;
double cp[3];

 oi = alloc_img(im->width, im->height);
if ( oi != NULL ) {
for(ix=0; ix < im->width; ix++) {
for(iy=0; iy < im->height; iy++) {


cp[0] = cp[1] = cp[2] = 0.0; for(kx=-Ks; kx <= Ks; kx++) { for(ky=-Ks; ky <= Ks; ky++) { for(l=0; l<3; l++) cp[l] += (K[(kx+Ks) +

                       (ky+Ks)*(2*Ks+1)]/divisor) *
((double)GET_PIXEL_CHECK(im, ix+kx, iy+ky, l)) + offset;


} } for(l=0; l<3; l++) cp[l] = (cp[l]>255.0) ? 255.0 : ((cp[l]<0.0) ? 0.0 : cp[l]) ; put_pixel_unsafe(oi, ix, iy, (color_component)cp[0], (color_component)cp[1], (color_component)cp[2]);

     }
}
return oi;
}
return NULL;


}</lang>

Usage example:

The read_image function is from here.

<lang c>#include <stdio.h>

1. include "imglib.h"

const char *input = "Lenna100.jpg"; const char *output = "filtered_lenna%d.ppm";

double emboss_kernel[3*3] = {

 -2., -1.,  0.,
-1.,  1.,  1.,
0.,  1.,  2.,


};

double sharpen_kernel[3*3] = {

 -1.0, -1.0, -1.0,
-1.0,  9.0, -1.0,
-1.0, -1.0, -1.0


}; double sobel_emboss_kernel[3*3] = {

 -1., -2., -1.,
0.,  0.,  0.,
1.,  2.,  1.,


}; double box_blur_kernel[3*3] = {

 1.0, 1.0, 1.0,
1.0, 1.0, 1.0,
1.0, 1.0, 1.0,


};

double *filters[4] = {

 emboss_kernel, sharpen_kernel, sobel_emboss_kernel, box_blur_kernel


}; const double filter_params[2*4] = {

 1.0, 0.0,
1.0, 0.0,
1.0, 0.5,
9.0, 0.0


};

int main() {

 image ii, oi;
int i;
char lennanames[30];

 ii = read_image(input);
if ( ii != NULL ) {
for(i=0; i<4; i++) {
sprintf(lennanames, output, i);
oi = filter(ii, filters[i], 1, filter_params[2*i], filter_params[2*i+1]);
if ( oi != NULL ) {


FILE *outfh = fopen(lennanames, "w"); if ( outfh != NULL ) { output_ppm(outfh, oi); fclose(outfh); } else { fprintf(stderr, "out err %s\n", output); } free_img(oi);

     } else { fprintf(stderr, "err creating img filters %d\n", i); }
}
free_img(ii);
} else { fprintf(stderr, "err reading %s\n", input); }


}</lang>

## D

This requires the module from the Grayscale Image Task. <lang d>import std.string, std.math, std.algorithm, grayscale_image;

struct ConvolutionFilter {

   double[][] kernel;
double divisor, offset_;
string name;


}

Image!Color convolve(Color)(in Image!Color im,

                           in ConvolutionFilter filter)


pure nothrow in {

   assert(im !is null);
assert(!isnan(filter.divisor) && !isnan(filter.offset_));
assert(filter.divisor != 0);
assert(filter.kernel.length > 0 && filter.kernel[0].length > 0);
foreach (const row; filter.kernel) // Is rectangular.
assert(row.length == filter.kernel[0].length);
assert(filter.kernel.length % 2 == 1); // Odd sized kernel.
assert(filter.kernel[0].length % 2 == 1);
assert(im.ny >= filter.kernel.length);
assert(im.nx >= filter.kernel[0].length);


} out(result) {

   assert(result !is null);
assert(result.nx == im.nx && result.ny == im.ny);


} body {

   immutable knx2 = filter.kernel[0].length / 2;
immutable kny2 = filter.kernel.length / 2;
auto io = new Image!Color(im.nx, im.ny);

   static if (is(Color == RGB))
alias CT = typeof(Color.r); // Component type.
else static if (is(typeof(Color.c)))
alias CT = typeof(Color.c);
else
alias CT = Color;

   foreach (immutable y; kny2 .. im.ny - kny2) {
foreach (immutable x; knx2 .. im.nx - knx2) {
static if (is(Color == RGB))
double[3] total = 0.0;
else
double total = 0.0;

           foreach (immutable sy, const kRow; filter.kernel) {
foreach (immutable sx, immutable k; kRow) {
immutable p = im[x + sx - knx2, y + sy - kny2];
static if (is(Color == RGB)) {
total[0] += p.r * k;
total[1] += p.g * k;
total[2] += p.b * k;
} else {
total += p * k;
}
}
}

           immutable D = filter.divisor;
immutable O = filter.offset_ * CT.max;
static if (is(Color == RGB)) {
io[x, y] = Color(
cast(CT)min(max(total[0]/ D + O, CT.min), CT.max),
cast(CT)min(max(total[1]/ D + O, CT.min), CT.max),
cast(CT)min(max(total[2]/ D + O, CT.min), CT.max));
} else static if (is(typeof(Color.c))) {
io[x, y] = Color(
cast(CT)min(max(total / D + O, CT.min), CT.max));
} else {
// If Color doesn't have a 'c' field, then Color is
// assumed to be a built-in type.
io[x, y] =
cast(CT)min(max(total / D + O, CT.min), CT.max);
}
}
}

   return io;


}

void main() {

   immutable ConvolutionFilter[] filters = [
{[[-2.0, -1.0, 0.0],
[-1.0,  1.0, 1.0],
[ 0.0,  1.0, 2.0]], divisor:1.0, offset_:0.0, name:"Emboss"},

       {[[-1.0, -1.0, -1.0],
[-1.0,  9.0, -1.0],
[-1.0, -1.0, -1.0]], divisor:1.0, 0.0, "Sharpen"},

       {[[-1.0, -2.0, -1.0],
[ 0.0,  0.0,  0.0],
[ 1.0,  2.0,  1.0]], divisor:1.0, 0.5, "Sobel_emboss"},

       {[[1.0, 1.0, 1.0],
[1.0, 1.0, 1.0],
[1.0, 1.0, 1.0]], divisor:9.0, 0.0, "Box_blur"},

       {[[1,  4,  7,  4, 1],
[4, 16, 26, 16, 4],
[7, 26, 41, 26, 7],
[4, 16, 26, 16, 4],
[1,  4,  7,  4, 1]], divisor:273, 0.0, "Gaussian_blur"}];

   Image!RGB im;

   foreach (immutable filter; filters)
im.convolve(filter)
.savePPM6(format("lenna_%s.ppm", filter.name));

   const img = im.rgb2grayImage();
foreach (immutable filter; filters)
img.convolve(filter)
.savePGM(format("lenna_gray_%s.ppm", filter.name));


}</lang>

## Go

Using standard image library: <lang go>package main

import (

   "fmt"
"image"
"image/color"
"image/jpeg"
"math"
"os"


)

// kf3 is a generic convolution 3x3 kernel filter that operatates on // images of type image.Gray from the Go standard image library. func kf3(k *[9]float64, src, dst *image.Gray) {

   for y := src.Rect.Min.Y; y < src.Rect.Max.Y; y++ {
for x := src.Rect.Min.X; x < src.Rect.Max.X; x++ {
var sum float64
var i int
for yo := y - 1; yo <= y+1; yo++ {
for xo := x - 1; xo <= x+1; xo++ {
if (image.Point{xo, yo}).In(src.Rect) {
sum += k[i] * float64(src.At(xo, yo).(color.Gray).Y)
} else {
sum += k[i] * float64(src.At(x, y).(color.Gray).Y)
}
i++
}
}
dst.SetGray(x, y,
color.Gray{uint8(math.Min(255, math.Max(0, sum)))})
}
}


}

var blur = [9]float64{

   1. / 9, 1. / 9, 1. / 9,
1. / 9, 1. / 9, 1. / 9,
1. / 9, 1. / 9, 1. / 9}


// blurY example function applies blur kernel to Y channel // of YCbCr image using generic kernel filter function kf3 func blurY(src *image.YCbCr) *image.YCbCr {

   dst := *src

   // catch zero-size image here
if src.Rect.Max.X == src.Rect.Min.X || src.Rect.Max.Y == src.Rect.Min.Y {
return &dst
}

   // pass Y channels as gray images
srcGray := image.Gray{src.Y, src.YStride, src.Rect}
dstGray := srcGray
dstGray.Pix = make([]uint8, len(src.Y))
kf3(&blur, &srcGray, &dstGray) // call generic convolution function

   // complete result
dst.Y = dstGray.Pix                   // convolution result
dst.Cb = append([]uint8{}, src.Cb...) // Cb, Cr are just copied
dst.Cr = append([]uint8{}, src.Cr...)
return &dst


}

func main() {

   // Example file used here is Lenna100.jpg from the task "Percentage
// difference between images"
f, err := os.Open("Lenna100.jpg")
if err != nil {
fmt.Println(err)
return
}
img, err := jpeg.Decode(f)
if err != nil {
fmt.Println(err)
return
}
f.Close()
y, ok := img.(*image.YCbCr)
if !ok {
fmt.Println("expected color jpeg")
return
}
f, err = os.Create("blur.jpg")
if err != nil {
fmt.Println(err)
return
}
err = jpeg.Encode(f, blurY(y), &jpeg.Options{90})
if err != nil {
fmt.Println(err)
}


}</lang> Alternative version, building on code from bitmap task.

New function for raster package: <lang go>package raster

import "math"

func (g *Grmap) KernelFilter3(k []float64) *Grmap {

   if len(k) != 9 {
return nil
}
r := NewGrmap(g.cols, g.rows)
// Filter edge pixels with minimal code.
// Execution time per pixel is high but there are few edge pixels
// relative to the interior.
o3 := [][]int{
{-1, -1}, {0, -1}, {1, -1},
{-1, 0}, {0, 0}, {1, 0},
{-1, 1}, {0, 1}, {1, 1}}
edge := func(x, y int) uint16 {
var sum float64
for i, o := range o3 {
c, ok := g.GetPx(x+o[0], y+o[1])
if !ok {
c = g.pxRow[y][x]
}
sum += float64(c) * k[i]
}
return uint16(math.Min(math.MaxUint16, math.Max(0,sum)))
}
for x := 0; x < r.cols; x++ {
r.pxRow[0][x] = edge(x, 0)
r.pxRow[r.rows-1][x] = edge(x, r.rows-1)
}
for y := 1; y < r.rows-1; y++ {
r.pxRow[y][0] = edge(0, y)
r.pxRow[y][r.cols-1] = edge(r.cols-1, y)
}
if r.rows < 3 || r.cols < 3 {
return r
}

   // Interior pixels can be filtered much more efficiently.
otr := -g.cols + 1
obr := g.cols + 1
z := g.cols + 1
c2 := g.cols - 2
for y := 1; y < r.rows-1; y++ {
tl := float64(g.pxRow[y-1][0])
tc := float64(g.pxRow[y-1][1])
tr := float64(g.pxRow[y-1][2])
ml := float64(g.pxRow[y][0])
mc := float64(g.pxRow[y][1])
mr := float64(g.pxRow[y][2])
bl := float64(g.pxRow[y+1][0])
bc := float64(g.pxRow[y+1][1])
br := float64(g.pxRow[y+1][2])
for x := 1; ; x++ {
r.px[z] = uint16(math.Min(math.MaxUint16, math.Max(0,
tl*k[0] + tc*k[1] + tr*k[2] +
ml*k[3] + mc*k[4] + mr*k[5] +
bl*k[6] + bc*k[7] + br*k[8])))
if x == c2 {
break
}
z++
tl, tc, tr = tc, tr, float64(g.px[z+otr])
ml, mc, mr = mc, mr, float64(g.px[z+1])
bl, bc, br = bc, br, float64(g.px[z+obr])
}
z += 3
}
return r


}</lang> Demonstration program: <lang go>package main

// Files required to build supporting package raster are found in: // * This task (immediately above) // * Bitmap // * Grayscale image // * Read a PPM file // * Write a PPM file

import (

   "fmt"
"raster"


)

var blur = []float64{

   1./9, 1./9, 1./9,
1./9, 1./9, 1./9,
1./9, 1./9, 1./9}


var sharpen = []float64{

   -1, -1, -1,
-1,  9, -1,
-1, -1, -1}


func main() {

   // Example file used here is Lenna100.jpg from the task "Percentage
// difference between images" converted with with the command
// convert Lenna100.jpg -colorspace gray Lenna100.ppm
if err != nil {
fmt.Println(err)
return
}
g0 := b.Grmap()
g1 := g0.KernelFilter3(blur)
err = g1.Bitmap().WritePpmFile("blur.ppm")
if err != nil {
fmt.Println(err)
}


}</lang>

## J

<lang J>NB. pad the first n dimensions of an array with zeros NB. (increasing all dimensions by 1 less than the kernel size) pad=: adverb define

 adj1=: <.m%2
(-@(adj2 + ]) {. (adj1 + ]) {. [) (#m) {. $ ) kernel_filter=: adverb define  [: ,/"(-#$m) ($m) +/@(,/^:(_1+#$m))@:*&m;._3  ($m)pad  )</lang> 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). Example use:  NB. kernels borrowed from C and TCL implementations sharpen_kernel=: _1+10*4=i.3 3 blur_kernel=: 3 3$%9
emboss_kernel=: _2 _1 0,_1 1 1,:0 1 2
sobel_emboss_kernel=: _1 _2 _1,0,:1 2 1

   'blurred.ppm' writeppm~ blur_kernel kernel_filter readppm 'original.ppm'


## Java

Code: <lang Java>import java.awt.image.*; import java.io.File; import java.io.IOException; import javax.imageio.*;

public class ImageConvolution {

 public static class ArrayData
{
public final int[] dataArray;
public final int width;
public final int height;

public ArrayData(int width, int height)
{
this(new int[width * height], width, height);
}

public ArrayData(int[] dataArray, int width, int height)
{
this.dataArray = dataArray;
this.width = width;
this.height = height;
}

public int get(int x, int y)
{  return dataArray[y * width + x];  }

public void set(int x, int y, int value)
{  dataArray[y * width + x] = value;  }
}

private static int bound(int value, int endIndex)
{
if (value < 0)
return 0;
if (value < endIndex)
return value;
return endIndex - 1;
}

public static ArrayData convolute(ArrayData inputData, ArrayData kernel, int kernelDivisor)
{
int inputWidth = inputData.width;
int inputHeight = inputData.height;
int kernelWidth = kernel.width;
int kernelHeight = kernel.height;
if ((kernelWidth <= 0) || ((kernelWidth & 1) != 1))
throw new IllegalArgumentException("Kernel must have odd width");
if ((kernelHeight <= 0) || ((kernelHeight & 1) != 1))
throw new IllegalArgumentException("Kernel must have odd height");
int kernelWidthRadius = kernelWidth >>> 1;
int kernelHeightRadius = kernelHeight >>> 1;

ArrayData outputData = new ArrayData(inputWidth, inputHeight);
for (int i = inputWidth - 1; i >= 0; i--)
{
for (int j = inputHeight - 1; j >= 0; j--)
{
double newValue = 0.0;
for (int kw = kernelWidth - 1; kw >= 0; kw--)
for (int kh = kernelHeight - 1; kh >= 0; kh--)
newValue += kernel.get(kw, kh) * inputData.get(
bound(i + kw - kernelWidthRadius, inputWidth),
bound(j + kh - kernelHeightRadius, inputHeight));
outputData.set(i, j, (int)Math.round(newValue / kernelDivisor));
}
}
return outputData;
}

public static ArrayData[] getArrayDatasFromImage(String filename) throws IOException
{
int width = inputImage.getWidth();
int height = inputImage.getHeight();
int[] rgbData = inputImage.getRGB(0, 0, width, height, null, 0, width);
ArrayData reds = new ArrayData(width, height);
ArrayData greens = new ArrayData(width, height);
ArrayData blues = new ArrayData(width, height);
for (int y = 0; y < height; y++)
{
for (int x = 0; x < width; x++)
{
int rgbValue = rgbData[y * width + x];
reds.set(x, y, (rgbValue >>> 16) & 0xFF);
greens.set(x, y, (rgbValue >>> 8) & 0xFF);
blues.set(x, y, rgbValue & 0xFF);
}
}
return new ArrayData[] { reds, greens, blues };
}

public static void writeOutputImage(String filename, ArrayData[] redGreenBlue) throws IOException
{
ArrayData reds = redGreenBlue[0];
ArrayData greens = redGreenBlue[1];
ArrayData blues = redGreenBlue[2];
BufferedImage outputImage = new BufferedImage(reds.width, reds.height,
BufferedImage.TYPE_INT_ARGB);
for (int y = 0; y < reds.height; y++)
{
for (int x = 0; x < reds.width; x++)
{
int red = bound(reds.get(x, y), 256);
int green = bound(greens.get(x, y), 256);
int blue = bound(blues.get(x, y), 256);
outputImage.setRGB(x, y, (red << 16) | (green << 8) | blue | -0x01000000);
}
}
ImageIO.write(outputImage, "PNG", new File(filename));
return;
}

public static void main(String[] args) throws IOException
{
int kernelWidth = Integer.parseInt(args[2]);
int kernelHeight = Integer.parseInt(args[3]);
int kernelDivisor = Integer.parseInt(args[4]);
System.out.println("Kernel size: " + kernelWidth + "x" + kernelHeight +
", divisor=" + kernelDivisor);
int y = 5;
ArrayData kernel = new ArrayData(kernelWidth, kernelHeight);
for (int i = 0; i < kernelHeight; i++)
{
System.out.print("[");
for (int j = 0; j < kernelWidth; j++)
{
kernel.set(j, i, Integer.parseInt(args[y++]));
System.out.print(" " + kernel.get(j, i) + " ");
}
System.out.println("]");
}

ArrayData[] dataArrays = getArrayDatasFromImage(args[0]);
for (int i = 0; i < dataArrays.length; i++)
dataArrays[i] = convolute(dataArrays[i], kernel, kernelDivisor);
writeOutputImage(args[1], dataArrays);
return;
}


}</lang>

Example 5x5 Gaussian blur, using Pentagon.png from the Hough transform task:
java ImageConvolution pentagon.png JavaImageConvolution.png 5 5 273 1 4 7 4 1  4 16 26 16 4  7 26 41 26 7  4 16 26 16 4  1 4 7 4 1
Kernel size: 5x5, divisor=273
[ 1  4  7  4  1 ]
[ 4  16  26  16  4 ]
[ 7  26  41  26  7 ]
[ 4  16  26  16  4 ]
[ 1  4  7  4  1 ]

## Liberty BASIC

In the following a 128x128 bmp file is loaded and its brightness values are read into an array.
We then convolve it with a 'sharpen' 3x3 matrix. Results are shown directly on screen.
NB Things like convolution would be best done by combining LB with ImageMagick, which is easily called from LB. <lang lb>

   dim result( 300, 300), image( 300, 300), mask( 100, 100)
w =128
h =128

   nomainwin

   WindowWidth  = 460
WindowHeight = 210

   open "Convolution" for graphics_nsb_nf as #w

   #w "trapclose [quit]"

   #w "down ; fill darkblue"

   hw = hwnd( #w)
calldll #user32,"GetDC", hw as ulong, hdc as ulong

   loadbmp "img", "alpha25.bmp"'   128x128 pixels
#w "drawbmp img   20, 20"

   #w "up ; color white ; goto 292 20 ; down ; box 420 148"
#w "up ; goto 180 60 ; down ; backcolor darkblue ; color cyan"
#w "\"; "Convolved with"

   for y =0 to 127 '   fill in the input matrix
for x =0 to 127
xx =x + 20
yy =y + 20
CallDLL #gdi32, "GetPixel", hdc as uLong, xx as long, yy as long, pixcol as ulong
call getRGB pixcol, b, g, r
image( x, y) =b
'#w "color "; image( x, y); " 0 "; 255 -image( x, y)
'#w "set "; x + 20; " "; y +20 +140
next x
next y

   #w "flush"
print " Input matrix filled."

   #w "size 8"
for y =0 to 2  '   fill in the mask matrix
for x =0 to 2
if mask = ( 0 -1) then #w "color yellow" else #w "color red"
#w "set "; 8 *x +200; " "; 8 *y +80
next x
next y
data -1,-1,-1,-1,9,-1,-1,-1,-1

   #w "flush"

   #w "size 1"
mxx =0: mnn =0

   for x =0 to 127 -2 '   since any further overlaps image edge
for y =0 to 127 -2
result( x, y) =0
for kx =0 to 2
for ky =0 to 2
result( x, y) =result( x, y) +image( x +kx, y +ky) *mask( kx, ky)
next ky
if mxx <result( x, y) then mxx =result( x, y)
if mnn >result( x, y) then mnn =result( x, y)
next kx
scan
next y
next x

   range =mxx -mnn
for x =0 to 127 -2
for y =0 to 127 -2
c =int( 255 *( result( x, y) -mnn) /range)
'#w "color "; c; " "; c; " "; c
if c >128 then #w "color white" else #w "color black"
#w "set "; x +292 +1; " "; y +20 +1
scan
next y
next x
#w "flush"

   wait

   sub getRGB pixcol, byref r, byref g, byref b
b = int( pixcol / (256 *256))
g = int( ( pixcol - b *256 *256) / 256)
r = int( pixcol - b *256 *256 - g *256)
end sub

   [quit]
close #w
CallDLL #user32, "ReleaseDC", hw as ulong, hdc as ulong
end


</lang>

Screenview is available at [[1]]


## Mathematica

Most image processing functions introduced in Mathematica 7 <lang mathematica>img = Import[NotebookDirectory[] <> "Lenna50.jpg"]; kernel = {{0, -1, 0}, {-1, 4, -1}, {0, -1, 0}}; ImageConvolve[img, kernel] ImageConvolve[img, GaussianMatrix[35] ] ImageConvolve[img, BoxMatrix[1] ]</lang>

## OCaml

<lang ocaml>let get_rgb img x y =

 let _, r_channel,_,_ = img in
let width = Bigarray.Array2.dim1 r_channel
and height = Bigarray.Array2.dim2 r_channel in
if (x < 0) || (x >= width) then (0,0,0) else
if (y < 0) || (y >= height) then (0,0,0) else  (* feed borders with black *)
get_pixel img x y


let convolve_get_value img kernel divisor offset = fun x y ->

 let sum_r = ref 0.0
and sum_g = ref 0.0
and sum_b = ref 0.0 in

 for i = -1 to 1 do
for j = -1 to 1 do
let r, g, b = get_rgb img (x+i) (y+j) in
sum_r := !sum_r +. kernel.(j+1).(i+1) *. (float r);
sum_g := !sum_g +. kernel.(j+1).(i+1) *. (float g);
sum_b := !sum_b +. kernel.(j+1).(i+1) *. (float b);
done;
done;
( !sum_r /. divisor +. offset,
!sum_g /. divisor +. offset,
!sum_b /. divisor +. offset )


let color_to_int (r,g,b) =

 (truncate r,
truncate g,
truncate b)


let bounded (r,g,b) =

 ((max 0 (min r 255)),
(max 0 (min g 255)),
(max 0 (min b 255)))


let convolve_value ~img ~kernel ~divisor ~offset =

 let _, r_channel,_,_ = img in
let width = Bigarray.Array2.dim1 r_channel
and height = Bigarray.Array2.dim2 r_channel in

 let res = new_img ~width ~height in

 let conv = convolve_get_value img kernel divisor offset in

 for y = 0 to pred height do
for x = 0 to pred width do
let color = conv x y in
let color = color_to_int color in
put_pixel res (bounded color) x y;
done;
done;
(res)</lang>


<lang ocaml>let emboss img =

 let kernel = [|
[| -2.; -1.;  0. |];
[| -1.;  1.;  1. |];
[|  0.;  1.;  2. |];
|] in
convolve_value ~img ~kernel ~divisor:1.0 ~offset:0.0;


let sharpen img =

 let kernel = [|
[| -1.; -1.; -1. |];
[| -1.;  9.; -1. |];
[| -1.; -1.; -1. |];
|] in
convolve_value ~img ~kernel ~divisor:1.0 ~offset:0.0;


let sobel_emboss img =

 let kernel = [|
[| -1.; -2.; -1. |];
[|  0.;  0.;  0. |];
[|  1.;  2.;  1. |];
|] in
convolve_value ~img ~kernel ~divisor:1.0 ~offset:0.5;


let box_blur img =

 let kernel = [|
[|  1.;  1.;  1. |];
[|  1.;  1.;  1. |];
[|  1.;  1.;  1. |];
|] in
convolve_value ~img ~kernel ~divisor:9.0 ~offset:0.0;

</lang>

## Octave

Use package Image

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

   r = im2uint8(mat2gray(conv2(a(:,:,1), c)));
g = im2uint8(mat2gray(conv2(a(:,:,2), c)));
b = im2uint8(mat2gray(conv2(a(:,:,3), c)));


endfunction

im = jpgread("Lenna100.jpg"); emboss = [-2, -1, 0; -1, 1, 1; 0, 1, 2 ]; sobel = [-1., -2., -1.; 0., 0., 0.; 1., 2., 1. ]; sharpen = [ -1.0, -1.0, -1.0; -1.0, 9.0, -1.0; -1.0, -1.0, -1.0 ];

[r, g, b] = rgbconv2(im, emboss); jpgwrite("LennaEmboss.jpg", r, g, b, 100); [r, g, b] = rgbconv2(im, sobel); jpgwrite("LennaSobel.jpg", r, g, b, 100); [r, g, b] = rgbconv2(im, sharpen); jpgwrite("LennaSharpen.jpg", r, g, b, 100);</lang>

## PicoLisp

<lang PicoLisp>(scl 3)

(de ppmConvolution (Ppm Kernel)

  (let (Len (length (car Kernel))  Radius (/ Len 2))
(make
(for (Y Ppm  T  (cdr Y))
(NIL (nth Y Len)
(make
(for (X (head Len Y) T)
(NIL (nth X 1 Len)
(make
(for C 3
(let Val 0
(for K Len
(for L Len
(inc 'Val
(* (get X K L C) (get Kernel K L)) ) ) )
(link (min 255 (max 0 (*/ Val 1.0)))) ) ) ) )
(map pop X) ) ) ) ) ) ) )</lang>


Test using 'ppmRead' from Bitmap/Read a PPM file#PicoLisp and 'ppmWrite' from Bitmap/Write a PPM file#PicoLisp:

# Sharpen
(ppmWrite
(ppmConvolution
'((-1.0 -1.0 -1.0) (-1.0 +9.0 -1.0) (-1.0 -1.0 -1.0)) )
"a.ppm" )

# Blur
(ppmWrite
(ppmConvolution
'((0.1 0.1 0.1) (0.1 0.1 0.1) (0.1 0.1 0.1)) )
"b.ppm" )

## Racket

This example uses typed/racket, since that gives access to inline-build-flomap, which delivers quite a performance boost over build-flomap.

<lang racket>#lang typed/racket (require images/flomap racket/flonum)

(provide flomap-convolve)

(: perfect-square? (Nonnegative-Fixnum -> (U Nonnegative-Fixnum #f))) (define (perfect-square? n)

 (define rt-n (integer-sqrt n))
(and (= n (sqr rt-n)) rt-n))


(: flomap-convolve (flomap FlVector -> flomap)) (define (flomap-convolve F K)

 (unless (flomap? F) (error "arg1 not a flowmap"))
(unless (flvector? K) (error "arg2 not a flvector"))
(define R (perfect-square? (flvector-length K)))
(cond
[(not (and R (odd? R))) (error "K is not odd-sided square")]
[else
(define R/2 (quotient R 2))
(define R/-2 (quotient R -2))
(define-values (sz-w sz-h) (flomap-size F))
(define-syntax-rule (convolution c x y i)
(if (= 0 c)
(flomap-ref F c x y) ; c=3 is alpha channel
(for*/fold: : Flonum
((acc : Flonum 0.))
(kl (in-value (+ (* k R) l)))
(kx (in-value (+ x k R/-2)))
(ly (in-value (+ y l R/-2)))
#:when (< 0 kx (sub1 sz-w))
#:when (< 0 ly (sub1 sz-h)))
(+ acc (* (flvector-ref K kl) (flomap-ref F c kx ly))))))

(inline-build-flomap 4 sz-w sz-h convolution)]))


(module* test racket

 (require racket/draw images/flomap racket/flonum (only-in 2htdp/image save-image))
(require (submod ".."))
(save-image
(flomap->bitmap (flomap-convolve flmp (flvector 1.)))
"out/convolve-unit-1x1.png")
(save-image
(flomap->bitmap (flomap-convolve flmp (flvector 0. 0. 0. 0. 1. 0. 0. 0. 0.)))
"out/convolve-unit-3x3.png")
(save-image
(flomap->bitmap (flomap-convolve flmp (flvector -1. -1. -1. -1. 4. -1. -1. -1. -1.)))
"out/convolve-etch-3x3.png"))</lang>


## Ruby

Translation of: Tcl

<lang ruby>class Pixmap

 # Apply a convolution kernel to a whole image
def convolute(kernel)
newimg = Pixmap.new(@width, @height)
pb = ProgressBar.new(@width) if $DEBUG @width.times do |x| @height.times do |y| apply_kernel(x, y, kernel, newimg) end pb.update(x) if$DEBUG
end
pb.close if $DEBUG newimg end   # Applies a convolution kernel to produce a single pixel in the destination def apply_kernel(x, y, kernel, newimg) x0 = x==0 ? 0 : x-1 y0 = y==0 ? 0 : y-1 x1 = x y1 = y x2 = x+1==@width ? x : x+1 y2 = y+1==@height ? y : y+1 r = g = b = 0.0 [x0, x1, x2].zip(kernel).each do |xx, kcol| [y0, y1, y2].zip(kcol).each do |yy, k| r += k * self[xx,yy].r g += k * self[xx,yy].g b += k * self[xx,yy].b end end newimg[x,y] = RGBColour.new(luma(r), luma(g), luma(b)) end   # Function for clamping values to those that we can use with colors def luma(value) if value < 0 0 elsif value > 255 255 else value end end  end 1. Demonstration code using the teapot image from Tk's widget demo teapot = Pixmap.open('teapot.ppm') [ ['Emboss', [[-2.0, -1.0, 0.0], [-1.0, 1.0, 1.0], [0.0, 1.0, 2.0]]],  ['Sharpen', [[-1.0, -1.0, -1.0], [-1.0, 9.0, -1.0], [-1.0, -1.0, -1.0]]], ['Blur', [[0.1111,0.1111,0.1111],[0.1111,0.1111,0.1111],[0.1111,0.1111,0.1111]]],  ].each do |label, kernel|  savefile = 'teapot_' + label.downcase + '.ppm' teapot.convolute(kernel).save(savefile)  end</lang> ## Tcl Works with: Tcl version 8.6 Library: Tk <lang tcl>package require Tk 1. Function for clamping values to those that we can use with colors proc tcl::mathfunc::luma channel {  set channel [expr {round($channel)}]
if {$channel < 0} {  return 0  } elseif {$channel > 255} {


return 255

   } else {


return $channel  }  } 1. Applies a convolution kernel to produce a single pixel in the destination proc applyKernel {srcImage x y -- kernel -> dstImage} {  set x0 [expr {$x==0 ? 0 : $x-1}] set y0 [expr {$y==0 ? 0 : $y-1}] set x1$x
set y1 $y set x2 [expr {$x+1==[image width $srcImage] ?$x : $x+1}] set y2 [expr {$y+1==[image height $srcImage] ?$y : $y+1}]   set r [set g [set b 0.0]] foreach X [list$x0 $x1$x2] kcol $kernel {  foreach Y [list$y0 $y1$y2] k $kcol { lassign [$srcImage get $X$Y] rPix gPix bPix set r [expr {$r +$k * $rPix}] set g [expr {$g + $k *$gPix}] set b [expr {$b +$k * $bPix}] }  }  $dstImage put [format "#%02x%02x%02x" \


[expr {luma($r)}] [expr {luma($g)}] [expr {luma($b)}]]\ -to$x $y } 1. Apply a convolution kernel to a whole image proc convolve {srcImage kernel {dstImage ""}} {  if {$dstImage eq ""} {


set dstImage [image create photo]

   }
set w [image width $srcImage] set h [image height$srcImage]
for {set x 0} {$x <$w} {incr x} {


for {set y 0} {$y <$h} {incr y} { applyKernel $srcImage$x $y --$kernel -> $dstImage }  } return$dstImage


}

1. Demonstration code using the teapot image from Tk's widget demo

image create photo teapot -file $tk_library/demos/images/teapot.ppm pack [labelframe .src -text Source] -side left pack [label .src.l -image teapot] foreach {label kernel} {  Emboss {  {-2. -1. 0.} {-1. 1. 1.} { 0. 1. 2.}  } Sharpen {  {-1. -1. -1} {-1. 9. -1} {-1. -1. -1}  } Blur {  {.1111 .1111 .1111} {.1111 .1111 .1111} {.1111 .1111 .1111}  }  } {  set name [string tolower$label]
update
pack [labelframe .$name -text$label] -side left
pack [label .$name.l -image [convolve teapot$kernel]]


}</lang>