# 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:

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;

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.

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;

Example of use:

   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);

## BBC BASIC

      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

## C

Interface:

image filter(image img, double *K, int Ks, double, double);

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).

#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;}

Usage example:

The read_image function is from here.

#include <stdio.h>#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); }}

## Common Lisp

Uses the RGB pixel buffer package defined here Basic bitmap storage#Common Lisp. Also the PPM file IO functions defined in Bitmap/Read a PPM file#Common_Lisp and Bitmap/Write a PPM file#Common_Lisp merged into one package.

(load "rgb-pixel-buffer")(load "ppm-file-io") (defpackage #:convolve  (:use #:common-lisp #:rgb-pixel-buffer #:ppm-file-io)) (in-package #:convolve)(defconstant +row-offsets+ '(-1 -1 -1 0 0 0 1 1 1))(defconstant +col-offsets+ '(-1 0 1 -1 0 1 -1 0 1))(defstruct cnv-record descr width kernel divisor offset)(defparameter *cnv-lib* (make-hash-table))(setf (gethash 'emboss *cnv-lib*)      (make-cnv-record :descr "emboss-filter" :width 3                        :kernel '(-2.0 -1.0 0.0 -1.0 1.0 1.0 0.0 1.0 2.0) :divisor 1.0))(setf (gethash 'sharpen *cnv-lib*)      (make-cnv-record :descr "sharpen-filter" :width 3                        :kernel '(-1.0 -1.0 -1.0 -1.0 9.0 -1.0 -1.0 -1.0 -1.0) :divisor 1.0))(setf (gethash 'sobel-emboss *cnv-lib*)      (make-cnv-record :descr "sobel-emboss-filter" :width 3                        :kernel '(-1.0 -2.0 -1.0 0.0 0.0 0.0 1.0 2.0 1.0 :divisor 1.0 :offset 0.5)))(setf (gethash 'box-blur *cnv-lib*)      (make-cnv-record :descr "box-blur-filter" :width 3                        :kernel '(1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0) :divisor 9.0)) (defun convolve (filename params)  (let* ((buf (read-ppm-file-to-rgb-pixel-buffer filename))         (width (first (array-dimensions buf)))         (height (second (array-dimensions buf)))         (obuf (make-rgb-pixel-buffer width height)))     ;;; constrain a value to some range    ;;; (int,int,int)->int    (defun constrain (val minv maxv)      (declare (type integer val minv maxv))      (min maxv (max minv val)))     ;;; convolve a single channel    ;;; list ubyte8->ubyte8    (defun convolve-channel (band)      (constrain (round (apply #'+ (mapcar #'* band (cnv-record-kernel params)))) 0 255))       ;;; return the rgb convolution of a list of pixels     ;;; list uint24->uint24    (defun convolve-pixels (pixels)      (let ((reds (list)) (greens (list)) (blues (list)))        (dolist (pel (reverse pixels))           (push (rgb-pixel-red pel) reds)          (push (rgb-pixel-green pel) greens)          (push (rgb-pixel-blue pel) blues))        (make-rgb-pixel (convolve-channel reds) (convolve-channel greens) (convolve-channel blues))))     ;;; return the list of pixels to which the kernel will be applied    ;;; (int,int)->list uint24    (defun kernel-pixels (c r)      (mapcar (lambda (coff roff) (rgb-pixel buf (constrain (+ c coff) 0 (1- width)) (constrain (+ r roff) 0 (1- height))))              +col-offsets+ +row-offsets+))     ;;; body of function    (dotimes (r height)      (dotimes (c width)        (setf (rgb-pixel obuf c r) (convolve-pixels (kernel-pixels c r)))))     (write-rgb-pixel-buffer-to-ppm-file (concatenate 'string (format nil "convolve-~A-" (cnv-record-descr params)) filename) obuf))) (in-package #:cl-user)(defun main ()  (loop for pars being the hash-values of convolve::*cnv-lib*     do (princ (convolve::convolve "lena_color.ppm" pars)) (terpri)))

## D

This requires the module from the Grayscale Image Task.

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(!filter.divisor.isNaN && !filter.offset_.isNaN);    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;    im.loadPPM6("Lenna100.ppm");     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));}

## Go

Using standard image library:

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 kf3func 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)    }}

Alternative version, building on code from bitmap task.

New function for raster package:

package raster import "math" func (g *Grmap) KernelFilter3(k []float64) *Grmap {    if len(k) != 9 {        return nil    }    r := NewGrmap(g.cols, g.rows)    r.Comments = append([]string{}, g.Comments...)    // 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}

Demonstration program:

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    b, err := raster.ReadPpmFile("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)    }}

## J

NB. pad the edges of an array with border pixelsNB. (increasing the first two dimensions by 1 less than the kernel size)pad=: adverb define  'a b'=. (<. ,. >.) 0.5 0.5 p. $m a"_(0 , ] - 1:)(# 1:)}~&# # b"_(0 , ] - 1:)(# 1:)}~&(1 {$) #"1 ]) kernel_filter=: adverb define   ($m)+/ .*&(,m)&(,/);._3 m pad) This code assumes that the leading dimensions of the array represent pixels and any trailing dimensions represent structure to be preserved (this is a fairly common approach and matches the J implementation at Basic bitmap storage). Note also that we assume that the image is larger than a single pixel in both directions. Any sized kernel is supported (as long as it's at least one pixel in each direction). Example use:  NB. kernels borrowed from C and TCL implementations sharpen_kernel=: _1+10*4=i.3 3 blur_kernel=: 3 3$%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:

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  {    BufferedImage inputImage = ImageIO.read(new File(filename));    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;  }}

Output from example pentagon image
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 ]

## JavaScript

Code:

// Image imageIn, Array kernel, function (Error error, Image imageOut)// precondition: Image is loaded// returns loaded Image to asynchronous callback functionfunction convolve(imageIn, kernel, callback) {    var dim = Math.sqrt(kernel.length),        pad = Math.floor(dim / 2);     if (dim % 2 !== 1) {        return callback(new RangeError("Invalid kernel dimension"), null);    }     var w = imageIn.width,        h = imageIn.height,        can = document.createElement('canvas'),        cw,        ch,        ctx,        imgIn, imgOut,        datIn, datOut;     can.width = cw = w + pad * 2; // add padding    can.height = ch = h + pad * 2; // add padding     ctx = can.getContext('2d');    ctx.fillStyle = '#000'; // fill with opaque black    ctx.fillRect(0, 0, cw, ch);    ctx.drawImage(imageIn, pad, pad);     imgIn = ctx.getImageData(0, 0, cw, ch);    datIn = imgIn.data;     imgOut = ctx.createImageData(w, h);    datOut = imgOut.data;     var row, col, pix, i, dx, dy, r, g, b;     for (row = pad; row <= h; row++) {        for (col = pad; col <= w; col++) {            r = g = b = 0;             for (dx = -pad; dx <= pad; dx++) {                for (dy = -pad; dy <= pad; dy++) {                    i = (dy + pad) * dim + (dx + pad); // kernel index                    pix = 4 * ((row + dy) * cw + (col + dx)); // image index                    r += datIn[pix++] * kernel[i];                    g += datIn[pix++] * kernel[i];                    b += datIn[pix  ] * kernel[i];                }            }             pix = 4 * ((row - pad) * w + (col - pad)); // destination index            datOut[pix++] = (r + .5) ^ 0;            datOut[pix++] = (g + .5) ^ 0;            datOut[pix++] = (b + .5) ^ 0;            datOut[pix  ] = 255; // we want opaque image        }    }     // reuse canvas    can.width = w;    can.height = h;     ctx.putImageData(imgOut, 0, 0);     var imageOut = new Image();     imageOut.addEventListener('load', function () {        callback(null, imageOut);    });     imageOut.addEventListener('error', function (error) {        callback(error, null);    });     imageOut.src = can.toDataURL('image/png');}

Example Usage:

var image = new Image();

image.alt = 'Player';
document.body.appendChild(image);

// laplace filter
convolve(image,
[0, 1, 0,
1,-4, 1,
0, 1, 0],
function (error, result) {
if (error !== null) {
console.error(error);
} else {
result.alt = 'Boundary';
document.body.appendChild(result);
}
}
);
});

image.src = '/img/player.png';

## Julia

 using FileIO, Images img = load("image.jpg") sharpenkernel = reshape([-1.0, -1.0, -1.0, -1.0,  9.0, -1.0, -1.0, -1.0, -1.0], (3,3)) imfilt = imfilter(img, sharpenkernel) save("imagesharper.png", imfilt)

## Kotlin

Translation of: Java
// version 1.2.10 import kotlin.math.roundimport java.awt.image.*import java.io.Fileimport javax.imageio.* class ArrayData(val width: Int, val height: Int) {    var dataArray = IntArray(width * height)     operator fun get(x: Int, y: Int) = dataArray[y * width + x]     operator fun set(x: Int, y: Int, value: Int) {        dataArray[y * width + x] = value    }} fun bound(value: Int, endIndex: Int) = when {    value < 0        -> 0    value < endIndex -> value    else             -> endIndex - 1} fun convolute(    inputData: ArrayData,    kernel: ArrayData,    kernelDivisor: Int): ArrayData {    val inputWidth = inputData.width    val inputHeight = inputData.height    val kernelWidth = kernel.width    val kernelHeight = kernel.height    if (kernelWidth <= 0 || (kernelWidth and 1) != 1)        throw IllegalArgumentException("Kernel must have odd width")      if (kernelHeight <= 0 || (kernelHeight and 1) != 1)        throw IllegalArgumentException("Kernel must have odd height")    val kernelWidthRadius = kernelWidth ushr 1    val kernelHeightRadius = kernelHeight ushr 1     val outputData = ArrayData(inputWidth, inputHeight)    for (i in inputWidth - 1 downTo 0) {        for (j in inputHeight - 1 downTo 0) {            var newValue = 0.0            for (kw in kernelWidth - 1 downTo 0) {                for (kh in kernelHeight - 1 downTo 0) {                    newValue += kernel[kw, kh] * inputData[                        bound(i + kw - kernelWidthRadius, inputWidth),                        bound(j + kh - kernelHeightRadius, inputHeight)                    ].toDouble()                    outputData[i, j] = round(newValue / kernelDivisor).toInt()                }            }        }    }    return outputData} fun getArrayDatasFromImage(filename: String): Array<ArrayData> {    val inputImage = ImageIO.read(File(filename))    val width = inputImage.width    val height = inputImage.height    val rgbData = inputImage.getRGB(0, 0, width, height, null, 0, width)    val reds = ArrayData(width, height)    val greens = ArrayData(width, height)    val blues = ArrayData(width, height)    for (y in 0 until height) {        for (x in 0 until width) {            val rgbValue = rgbData[y * width + x]            reds[x, y] = (rgbValue ushr 16) and 0xFF            greens[x,y] = (rgbValue ushr 8) and 0xFF            blues[x, y] = rgbValue and 0xFF        }    }    return arrayOf(reds, greens, blues)} fun writeOutputImage(filename: String, redGreenBlue: Array<ArrayData>) {    val (reds, greens, blues) = redGreenBlue    val outputImage = BufferedImage(        reds.width, reds.height, BufferedImage.TYPE_INT_ARGB    )    for (y in 0 until reds.height) {        for (x in 0 until reds.width) {            val red = bound(reds[x , y], 256)            val green = bound(greens[x , y], 256)            val blue = bound(blues[x, y], 256)            outputImage.setRGB(                x, y, (red shl 16) or (green shl 8) or blue or -0x01000000            )        }    }    ImageIO.write(outputImage, "PNG", File(filename))} fun main(args: Array<String>) {    val kernelWidth = args[2].toInt()    val kernelHeight = args[3].toInt()    val kernelDivisor = args[4].toInt()    println("Kernel size: $kernelWidth x$kernelHeight, divisor = $kernelDivisor") var y = 5 val kernel = ArrayData(kernelWidth, kernelHeight) for (i in 0 until kernelHeight) { print("[") for (j in 0 until kernelWidth) { kernel[j, i] = args[y++].toInt() print("${kernel[j, i]} ")        }        println("]")    }     val dataArrays = getArrayDatasFromImage(args[0])    for (i in 0 until dataArrays.size) {        dataArrays[i] = convolute(dataArrays[i], kernel, kernelDivisor)    }    writeOutputImage(args[1], dataArrays)}
Output:
Same as Java entry when using identical command line arguments


## 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.

     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            read mask            mask( x, y) =mask            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"    print " Mask matrix filled."     #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
Screenview is available at [[1]]


## Maple

Builtin command ImageTools:-Convolution()

pic:=Import("smiling_dog.jpg"):mask := Matrix([[1,2,3],[4,5,6],[7,8,9]]);pic := ImageTools:-Convolution(pic, mask);

## Mathematica / Wolfram Language

Most image processing functions introduced in Mathematica 7

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] ]

## MATLAB

The built-in function conv2 handles the basic convolution. Below is a program that has several more options that may be useful in different image processing applications (see comments under convImage for specifics).

function testConvImage    Im = [1 2 1 5 5 ; ...          1 2 7 9 9 ; ...          5 5 5 5 5 ; ...          5 2 2 2 2 ; ...          1 1 1 1 1 ];      % Sample image for example illustration only    Ker = [1 2 1 ; ...           2 4 2 ; ...           1 2 1 ];         % Gaussian smoothing (without normalizing)    fprintf('Original image:\n')    disp(Im)    fprintf('Original kernal:\n')    disp(Ker)    fprintf('Padding with zeroes:\n')    disp(convImage(Im, Ker, 'zeros'))    fprintf('Padding with fives:\n')    disp(convImage(Im, Ker, 'value', 5))    fprintf('Duplicating border pixels to pad image:\n')    disp(convImage(Im, Ker, 'extend'))    fprintf('Renormalizing kernal and using only values within image:\n')    disp(convImage(Im, Ker, 'partial'))    fprintf('Only processing inner (non-border) pixels:\n')    disp(convImage(Im, Ker, 'none'))%     Ker = [1 2 1 ; ...%            2 4 2 ; ...%            1 2 1 ]./16;%     Im = imread('testConvImageTestImage.png', 'png');%     figure%     imshow(imresize(Im, 10))%     title('Original image')%     figure%     imshow(imresize(convImage(Im, Ker, 'zeros'), 10))%     title('Padding with zeroes')%     figure%     imshow(imresize(convImage(Im, Ker, 'value', 50), 10))%     title('Padding with fifty: 50')%     figure%     imshow(imresize(convImage(Im, Ker, 'extend'), 10))%     title('Duplicating border pixels to pad image')%     figure%     imshow(imresize(convImage(Im, Ker, 'partial'), 10))%     title('Renormalizing kernal and using only values within image')%     figure%     imshow(imresize(convImage(Im, Ker, 'none'), 10))%     title('Only processing inner (non-border) pixels')end function ImOut = convImage(Im, Ker, varargin)% ImOut = convImage(Im, Ker)%   Filters an image using sliding-window kernal convolution.%   Convolution is done layer-by-layer. Use rgb2gray if single-layer needed.%   Zero-padding convolution will be used if no border handling is specified.%   Im - Array containing image data (output from imread)%   Ker - 2-D array to convolve image, needs odd number of rows and columns%   ImOut - Filtered image, same dimensions and datatype as Im%% ImOut = convImage(Im, Ker, 'zeros')%   Image will be padded with zeros when calculating convolution%   (useful for magnitude calculations).%% ImOut = convImage(Im, Ker, 'value', padVal)%   Image will be padded with padVal when calculating convolution%   (possibly useful for emphasizing certain data with unusual kernal)%% ImOut = convImage(Im, Ker, 'extend')%   Image will be padded with the value of the closest image pixel%   (useful for smoothing or blurring filters).%% ImOut = convImage(Im, Ker, 'partial')%   Image will not be padded. Borders will be convoluted with only valid pixels,%   and convolution matrix will be renormalized counting only the pixels within%   the image (also useful for smoothing or blurring filters).%% ImOut = convImage(Im, Ker, 'none')%   Image will not be padded. Convolution will only be applied to inner pixels%   (useful for edge and corner detection filters)     % Handle input    if mod(size(Ker, 1), 2) ~= 1 || mod(size(Ker, 2), 2) ~= 1        eid = sprintf('%s:evenRowsCols', mfilename);        error(eid,'''Ker'' parameter must have odd number of rows and columns.')    elseif nargin > 4        eid = sprintf('%s:maxrhs', mfilename);        error(eid, 'Too many input arguments.');    elseif nargin == 4 && ~strcmp(varargin{1}, 'value')        eid = sprintf('%s:invalidParameterCombination', mfilename);        error(eid, ['The ''padVal'' parameter is only valid with the ' ...            '''value'' option.'])    elseif nargin < 4 && strcmp(varargin{1}, 'value')        eid = sprintf('%s:minrhs', mfilename);        error(eid, 'Not enough input arguments.')    elseif nargin < 3        method = 'zeros';    else        method = lower(varargin{1});        if ~any(strcmp(method, {'zeros' 'value' 'extend' 'partial' 'none'}))            eid = sprintf('%s:invalidParameter', mfilename);            error(eid, 'Invalid option parameter. Must be one of:%s', ...                sprintf('\n\t\t%s', ...                'zeros', 'value', 'extend', 'partial', 'none'))        end    end     % Gather information and prepare for convolution    [nImRows, nImCols, nImLayers] = size(Im);    classIm = class(Im);    Im = double(Im);    ImOut = zeros(nImRows, nImCols, nImLayers);    [nKerRows, nKerCols] = size(Ker);    nPadRows = nImRows+nKerRows-1;    nPadCols = nImCols+nKerCols-1;    padH = (nKerRows-1)/2;    padW = (nKerCols-1)/2;     % Convolute on a layer-by-layer basis    for k = 1:nImLayers        if strcmp(method, 'zeros')            ImOut(:, :, k) = conv2(Im(:, :, k), Ker, 'same');        elseif strcmp(method, 'value')            padding = varargin{2}.*ones(nPadRows, nPadCols);            padding(padH+1:end-padH, padW+1:end-padW) = Im(:, :, k);            ImOut(:, :, k) = conv2(padding, Ker, 'valid');        elseif strcmp(method, 'extend')            padding = zeros(nPadRows, nPadCols);            padding(padH+1:end-padH, padW+1:end-padW) = Im(:, :, k);  % Middle            padding(1:padH, 1:padW) = Im(1, 1, k);                    % TopLeft            padding(end-padH+1:end, 1:padW) = Im(end, 1, k);          % BotLeft            padding(1:padH, end-padW+1:end) = Im(1, end, k);          % TopRight            padding(end-padH+1:end, end-padW+1:end) = Im(end, end, k);% BotRight            padding(padH+1:end-padH, 1:padW) = ...                repmat(Im(:, 1, k), 1, padW);                         % Left            padding(padH+1:end-padH, end-padW+1:end) = ...                repmat(Im(:, end, k), 1, padW);                       % Right            padding(1:padH, padW+1:end-padW) = ...                repmat(Im(1, :, k), padH, 1);                         % Top            padding(end-padH+1:end, padW+1:end-padW) = ...                repmat(Im(end, :, k), padH, 1);                       % Bottom            ImOut(:, :, k) = conv2(padding, Ker, 'valid');        elseif strcmp(method, 'partial')            ImOut(padH+1:end-padH, padW+1:end-padW, k) = ...                conv2(Im(:, :, k), Ker, 'valid');                     % Middle            unprocessed = true(nImRows, nImCols);            unprocessed(padH+1:end-padH, padW+1:end-padW) = false;    % Border            for r = 1:nImRows                for c = 1:nImCols                    if unprocessed(r, c)                        limitedIm = Im(max(1, r-padH):min(nImRows, r+padH), ...                            max(1, c-padW):min(nImCols, c+padW), k);                        limitedKer = Ker(max(1, 2-r+padH): ...                            min(nKerRows, nKerRows+nImRows-r-padH), ...                            max(1, 2-c+padW):...                            min(nKerCols, nKerCols+nImCols-c-padW));                        limitedKer = limitedKer.*sum(Ker(:))./ ...                            sum(limitedKer(:));                        ImOut(r, c, k) = sum(sum(limitedIm.*limitedKer));                    end                end            end        else    % method is 'none'            ImOut(:, :, k) = Im(:, :, k);            ImOut(padH+1:end-padH, padW+1:end-padW, k) = ...                conv2(Im(:, :, k), Ker, 'valid');        end    end     % Convert back to former image data type    ImOut = cast(ImOut, classIm);end
Output:
Original image:
1     2     1     5     5
1     2     7     9     9
5     5     5     5     5
5     2     2     2     2
1     1     1     1     1

Original kernal:
1     2     1
2     4     2
1     2     1

12    24    43    66    57
27    50    79   104    84
46    63    73    82    63
42    46    40    40    30
18    19    16    16    12

47    44    63    86    92
47    50    79   104   104
66    63    73    82    83
62    46    40    40    50
53    39    36    36    47

Duplicating border pixels to pad image:
20    30    52    82    96
35    50    79   104   112
62    63    73    82    84
58    46    40    40    40
29    23    20    20    20

Renormalizing kernal and using only values within image:
21.3333   32.0000   57.3333   88.0000  101.3333
36.0000   50.0000   79.0000  104.0000  112.0000
61.3333   63.0000   73.0000   82.0000   84.0000
56.0000   46.0000   40.0000   40.0000   40.0000
32.0000   25.3333   21.3333   21.3333   21.3333

Only processing inner (non-border) pixels:
1     2     1     5     5
1    50    79   104     9
5    63    73    82     5
5    46    40    40     2
1     1     1     1     1

## 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)
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;;;

## Octave

Use package Image

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);

## Perl 6

#!/usr/bin/env perl6 # Reference:# https://github.com/azawawi/perl6-magickwand# http://www.imagemagick.org/Usage/convolve/ use v6; use MagickWand; # A new magic wandmy $original = MagickWand.new; # Read an image$original.read("./Lenna100.jpg") or die; my $o =$original.clone; # using coefficients from kernel "Sobel"# http://www.imagemagick.org/Usage/convolve/#sobel$o.convolve( [ 1, 0, -1, 2, 0, -2, 1, 0, -1] );$o.write("Lenna100-convoluted.jpg") or die; # And cleanup on exitLEAVE {  $original.cleanup if$original.defined;  $o.cleanup if$o.defined;}

## PicoLisp

(scl 3) (de ppmConvolution (Ppm Kernel)   (let (Len (length (car Kernel))  Radius (/ Len 2))      (make         (chain (head Radius Ppm))         (for (Y Ppm  T  (cdr Y))            (NIL (nth Y Len)               (chain (tail Radius Y)) )            (link               (make                  (chain (head Radius (get Y (inc Radius))))                  (for (X (head Len Y) T)                     (NIL (nth X 1 Len)                        (chain (tail Radius (get X (inc Radius)))) )                     (link                        (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) ) ) ) ) ) ) )

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" )

## Python

Image manipulation is normally done using an image processing library. For PIL/Pillow do:

#!/bin/pythonfrom PIL import Image, ImageFilter if __name__=="__main__":	im = Image.open("test.jpg") 	kernelValues = [-2,-1,0,-1,1,1,0,1,2] #emboss	kernel = ImageFilter.Kernel((3,3), kernelValues) 	im2 = im.filter(kernel) 	im2.show()

Alternatively, SciPy can be used but programmers need to be careful about the colors being clipped since they are normally limited to the 0-255 range:

#!/bin/pythonimport numpy as npfrom scipy.ndimage.filters import convolvefrom scipy.misc import imread, imshow if __name__=="__main__":	im = imread("test.jpg", mode="RGB")	im = np.array(im, dtype=float) #Convert to float to prevent clipping colors 	kernel = np.array([[[0,-2,0],[0,-1,0],[0,0,0]],						[[0,-1,0],[0,1,0],[0,1,0]],						[[0,0,0],[0,1,0],[0,2,0]]])#emboss 	im2 = convolve(im, kernel)	im3 = np.array(np.clip(im2, 0, 255), dtype=np.uint8) #Apply color clipping 	imshow(im3)

## Racket

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

#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.))             ((k (in-range 0 (add1 R/2)))              (l (in-range 0 (add1 R/2)))              (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 ".."))  (define flmp (bitmap->flomap (read-bitmap "jpg/271px-John_Constable_002.jpg")))  (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"))

## Ruby

Translation of: Tcl