# 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 grayscale 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.)

## Action!

INCLUDE "H6:LOADPPM5.ACT"

DEFINE HISTSIZE="256"

PROC PutBigPixel(INT x,y BYTE col)
IF x>=0 AND x<=79 AND y>=0 AND y<=47 THEN
y==LSH 2
col==RSH 4
IF col<0 THEN col=0
ELSEIF col>15 THEN col=15 FI
Color=col
Plot(x,y)
DrawTo(x,y+3)
FI
RETURN

PROC DrawImage(GrayImage POINTER image INT x,y)
INT i,j
BYTE c

FOR j=0 TO image.gh-1
DO
FOR i=0 TO image.gw-1
DO
c=GetGrayPixel(image,i,j)
PutBigPixel(x+i,y+j,c)
OD
OD
RETURN

INT FUNC Clamp(INT x,min,max)
IF x<min THEN
RETURN (min)
ELSEIF x>max THEN
RETURN (max)
FI
RETURN (x)

PROC Convolution3x3(GrayImage POINTER src,dst
INT ARRAY kernel INT divisor)
INT x,y,i,j,ii,jj,index,sum
BYTE c

FOR j=0 TO src.gh-1
DO
FOR i=0 TO src.gw-1
DO
sum=0 index=0
FOR jj=-1 TO 1
DO
y=Clamp(j+jj,0,src.gh-1)
FOR ii=-1 TO 1
DO
x=Clamp(i+ii,0,src.gw-1)
c=GetGrayPixel(src,x,y)
sum==+c*kernel(index)
index==+1
OD
OD
c=Clamp(sum/divisor,0,255)
SetGrayPixel(dst,i,j,c)
OD
OD
RETURN

PROC Main()
BYTE CH=$02FC ;Internal hardware value for last key pressed BYTE ARRAY dataIn(900),dataOut(900) GrayImage in,out INT ARRAY sharpenKernel=[ 65535 65535 65535 65535 9 65535 65535 65535 65535] INT size=[30],x,y,sharpenDivisor=[1] Put(125) PutE() ;clear the screen InitGrayImage(in,size,size,dataIn) InitGrayImage(out,size,size,dataOut) PrintE("Loading source image...") LoadPPM5(in,"H6:LENA30G.PPM") PrintE("Convolution...") Convolution3x3(in,out,sharpenKernel,sharpenDivisor) Graphics(9) x=(40-size)/2 y=(48-size)/2 DrawImage(in,x,y) DrawImage(out,x+40,y) DO UNTIL CH#$FF OD
CH=$FF RETURN Output: ## Ada 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)); }  ## FreeBASIC Const ancho = 208 Const alto = 228 Dim TamImag(ancho - 1, alto - 1, 2) As Integer Screenres ancho, alto, 32 Bload "i:\Lena.bmp", 0 Dim As Integer filter(2, 2) => {{-1, -1, -1}, {-1, 12, -1}, {-1, -1, -1}} Dim As Integer y, x, i, j, r, g, b, c, f For y = 1 To alto - 2 For x = 1 To ancho - 2 r = 0 : g = 0 : b = 0 For i = -1 To 1 For j = -1 To 1 c = Point(x + i, y + j) f = filter(i + 1, j + 1) r += f * (c And &HFF) g += f * ((c Shr 8) And &HFF) b += f * ((c Shr 16) And &HFF) Next j Next i If r < 0 Then r = 0 Else If r > 1020 Then r = 1020 If g < 0 Then g = 0 Else If g > 1020 Then g = 1020 If b < 0 Then b = 0 Else If b > 1020 Then b = 1020 TamImag(x, y, 0) = r \ 4 TamImag(x, y, 1) = g \ 4 TamImag(x, y, 2) = b \ 4 Next x Next y For y = 0 To alto - 1 For x = 0 To ancho - 1 Pset (x, y), Rgb(TamImag(x, y, 0), TamImag(x, y, 1), TamImag(x, y, 2)) Next x Next y Bsave "i:\LenaConvolution.bmp", 0 Sleep  ## 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 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) } }  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 pixels NB. (increasing the first two dimensions by 1 less than the kernel size) pad=: {{ rank=.#$m
'first second'=. (<.,:>.)-:$m -@(second+rank{.$) {. (first+rank{.$){.] }} kernel_filter=: {{ [: (0 >. 255 <. <.@:+&0.5) (1,:$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
id_kernel=: (=&i.-)3 3
sharpen_kernel=: ({ _1,#@,)id_kernel
blur_kernel=: ($*&%/)3 3 emboss_kernel=: id_kernel+(+/~ - >./)i.3 sobel_emboss_kernel=: (i:-:<:3)*/1+(<.|.)i.3 '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; } }  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 function function 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.addEventListener('load', function () { 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.round import java.awt.image.* import java.io.File import 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()
Output2 = "lena_gray_$1.png" const Filters = [ConvolutionFilter(kernel: @[@[-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"), ConvolutionFilter(kernel: @[@[-1.0, -1.0, -1.0], @[-1.0, 9.0, -1.0], @[-1.0, -1.0, -1.0]], divisor: 1.0, offset: 0.0, name: "Sharpen"), ConvolutionFilter(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, name: "Sobel_emboss"), ConvolutionFilter(kernel: @[@[1.0, 1.0, 1.0], @[1.0, 1.0, 1.0], @[1.0, 1.0, 1.0]], divisor: 9.0, offset: 0.0, name: "Box_blur"), ConvolutionFilter(kernel: @[@[1.0, 4.0, 7.0, 4.0, 1.0], @[4.0, 16.0, 26.0, 16.0, 4.0], @[7.0, 26.0, 41.0, 26.0, 7.0], @[4.0, 16.0, 26.0, 16.0, 4.0], @[1.0, 4.0, 7.0, 4.0, 1.0]], divisor: 273.0, offset: 0.0, name: "Gaussian_blur")] let pngImage = loadPNG24(seq[byte], Input).get() # Convert to an image managed by the "bitmap" module. let img = newImage(pngImage.width, pngImage.height) for i in 0..img.pixels.high: img.pixels[i] = color(pngImage.data[3 * i], pngImage.data[3 * i + 1], pngImage.data[3 * i + 2]) for filter in Filters: let result = img.convolve(filter) var data = newSeqOfCap[byte](result.pixels.len * 3) for color in result.pixels: data.add([color.r, color.g, color.b]) let output = Output1.format(filter.name) if savePNG24(output, data, result.w, result.h).isOk: echo "Saved: ", output let grayImg = img.toGrayImage() for filter in Filters: let result = grayImg.convolve(filter).toImage() var data = newSeqOfCap[byte](result.pixels.len * 3) for color in result.pixels: data.add([color.r, color.g, color.b]) let output = Output2.format(filter.name) if savePNG24(output, data, result.w, result.h).isOk: echo "Saved: ", output  ## 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 use strict; use warnings; use PDL; use PDL::Image2D; my$kernel = pdl [[-2, -1, 0],[-1, 1, 1], [0, 1, 2]]; # emboss

my $image = rpic 'pythagoras_tree.png'; my$smoothed = conv2d $image,$kernel, {Boundary => 'Truncate'};
wpic $smoothed, 'pythagoras_convolution.png';  Compare offsite images: frog.png vs. frog_convolution.png ## Phix Library: Phix/pGUI -- -- demo\rosetta\Image_convolution.exw -- ================================== -- without js -- imImage, im_width, im_height, im_pixel, IupImageRGB, allocate, -- imFileImageLoadBitmap, peekNS, wait_key, IupImageFromImImage include pGUI.e constant filters = {-- 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}}, -- Sobel_emboss {{-1.0, -2.0, -1.0}, { 0.0, 0.0, 0.0}, { 1.0, 2.0, 1.0}}, -- Box_blur {{ 1.0, 1.0, 1.0}, { 1.0, 1.0, 1.0}, { 1.0, 1.0, 1.0}}, -- Gaussian_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}}} function convolute(imImage img, integer fdx) integer width = im_width(img), height = im_height(img) sequence original = repeat(repeat(0,width),height), new_image, filterfdx = filters[fdx] integer fh = length(filterfdx), hh=(fh-1)/2, fw = length(filterfdx[1]), hw=(fw-1)/2, divisor = max(sum(filterfdx),1) for y=height-1 to 0 by -1 do for x=0 to width-1 do original[height-y,x+1] = im_pixel(img, x, y) end for end for new_image = original for y=hh+1 to height-hh-1 do for x=hw+1 to width-hw-1 do sequence newrgb = {0,0,0} for i=-hh to +hh do for j=-hw to +hw do newrgb = sq_add(newrgb,sq_mul(filterfdx[i+hh+1,j+hw+1],original[y+i,x+j])) end for end for new_image[y,x] = sq_max(sq_min(sq_floor_div(newrgb,divisor),255),0) end for end for new_image = flatten(new_image) -- (as needed by IupImageRGB) Ihandle new_img = IupImageRGB(width, height, new_image) return new_img end function IupOpen() constant w = machine_word(), TITLE = "Image convolution" atom pError = allocate(w) --imImage im1 = imFileImageLoadBitmap("Lenna50.jpg",0,pError) --imImage im1 = imFileImageLoadBitmap("Lenna100.jpg",0,pError) --imImage im1 = imFileImageLoadBitmap("Lena.ppm",0,pError) imImage im1 = imFileImageLoadBitmap("Quantum_frog.png",0,pError) --imImage im1 = imFileImageLoadBitmap("Quantum_frog.512.png",0,pError) if im1=NULL then ?{"error opening image",peekNS(pError,w,1)} {} = wait_key() abort(0) end if --(see also Color_quantization.exw if not an IM_RGB image) Ihandle dlg, flt = IupList("DROPDOWN=YES, VALUE=1") Ihandln image1 = IupImageFromImImage(im1), image2 = convolute(im1,1), label1 = IupLabel(), label2 = IupLabel() IupSetAttributeHandle(label1, "IMAGE", image1) IupSetAttributeHandle(label2, "IMAGE", image2) function valuechanged_cb(Ihandle /*flt*/) IupSetAttribute(dlg,"TITLE","Working...") -- IupSetAttributeHandle(label2, "IMAGE", NULL) image2 = IupDestroy(image2) image2 = convolute(im1,IupGetInt(flt,"VALUE")) IupSetAttributeHandle(label2, "IMAGE", image2) IupSetAttribute(dlg,"TITLE",TITLE) IupRefresh(dlg) return IUP_DEFAULT end function IupSetCallback(flt,"VALUECHANGED_CB",Icallback("valuechanged_cb")) IupSetAttributes(flt,1=Emboss, 2=Sharpen, 3="Sobel emboss", 4="Box_blur", 5=Gaussian_blur) IupSetAttributes(flt,"VISIBLEITEMS=6") -- (still dunno why this trick works) dlg = IupDialog(IupVbox({flt, IupFill(), IupHbox({IupFill(),label1, label2,IupFill()}), IupFill()})) IupSetAttribute(dlg, "TITLE", TITLE) IupShow(dlg) if platform()!=JS then -- (no chance...) IupMainLoop() IupClose() end if  ## 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 (ppmRead "Lenna100.ppm") '((-1.0 -1.0 -1.0) (-1.0 +9.0 -1.0) (-1.0 -1.0 -1.0)) ) "a.ppm" ) # Blur (ppmWrite (ppmConvolution (ppmRead "Lenna100.ppm") '((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/python from 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/python import numpy as np from scipy.ndimage.filters import convolve from 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"))  ## Raku (formerly Perl 6) ### Perl 5 PDL library use PDL:from<Perl5>; use PDL::Image2D:from<Perl5>; my$kernel = pdl [[-2, -1, 0],[-1, 1, 1], [0, 1, 2]]; # emboss

my $image = rpic 'frog.png'; my$smoothed = conv2d $image,$kernel, {Boundary => 'Truncate'};
wpic $smoothed, 'frog_convolution.png';  Compare offsite images: frog.png vs. frog_convolution.png ### Imagemagick library # Note: must install version from github NOT version from CPAN which needs to be updated. # Reference: # https://github.com/azawawi/perl6-magickwand # http://www.imagemagick.org/Usage/convolve/ use v6; use MagickWand; # A new magic wand my$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] );

$o.write("Lenna100-convoluted.jpg") or die; # And cleanup on exit LEAVE {$original.cleanup   if $original.defined;$o.cleanup if $o.defined; }  ## Ruby Translation of: Tcl class Pixmap # Apply a convolution kernel to a whole image def convolute(kernel) newimg = Pixmap.new(@width, @height) pb = ProgressBar.new(@width) if$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

# 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


## Tcl

Works with: Tcl version 8.6
Library: Tk
package require Tk

# 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
}
}
# 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
}
# 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 $dstImage } # Demonstration code using the teapot image from Tk's widget demo image create photo teapot -file$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]]
}


## Wren

Library: DOME

Based on the Java/Kotlin solutions, though input details are hard-coded rather than read in as command line arguments and the input and output images are displayed side by side with the latter also being saved to a file.

import "graphics" for Canvas, Color, ImageData
import "dome" for Window

class ArrayData {
construct new(width, height) {
_width  = width
_height = height
_dataArray = List.filled(width * height, 0)
}

width  { _width }
height { _height }

[x, y] { _dataArray[y * _width + x] }

[x, y]=(v) { _dataArray[y * _width + x] = v }
}

class ImageConvolution {
construct new(width, height, image1, image2, kernel, divisor) {
Window.title = "Image Convolution"
Window.resize(width, height)
Canvas.resize(width, height)
_width  = width
_height = height
_image1 = image1
_image2 = image2
_kernel = kernel
_divisor = divisor
}

init() {
var dataArrays = getArrayDatasFromImage(_image1)
for (i in 0...dataArrays.count) {
dataArrays[i] = convolve(dataArrays[i], _kernel, _divisor)
}
writeOutputImage(_image2, dataArrays)
}

bound(value, endIndex) {
if (value < 0) return 0
if (value < endIndex) return value
return endIndex - 1
}

convolve(inputData, kernel, kernelDivisor) {
var inputWidth   = inputData.width
var inputHeight  = inputData.height
var kernelWidth  = kernel.width
var kernelHeight = kernel.height
if (kernelWidth <= 0 || (kernelWidth & 1) != 1) {
Fiber.abort("Kernel must have odd width")
}
if (kernelHeight <= 0 || (kernelHeight & 1) != 1) {
Fiber.abort("Kernel must have odd height")
}
var kernelWidthRadius  = kernelWidth >> 1
var kernelHeightRadius = kernelHeight >> 1

var outputData = ArrayData.new(inputWidth, inputHeight)
for (i in inputWidth - 1..0) {
for (j in inputHeight - 1..0) {
var newValue = 0
for (kw in kernelWidth - 1..0) {
for (kh in kernelHeight - 1..0) {
newValue = newValue + kernel[kw, kh] * inputData[
bound(i + kw - kernelWidthRadius, inputWidth),
bound(j + kh - kernelHeightRadius, inputHeight)
]
outputData[i, j] = (newValue / kernelDivisor).round
}
}
}
}
return outputData
}

getArrayDatasFromImage(filename) {
var inputImage = ImageData.load(filename)
inputImage.draw(0, 0)
Canvas.print(filename, _width * 1/6,  _height * 5/6, Color.white)
var width  = inputImage.width
var height = inputImage.height
var rgbData = []
for (y in 0...height) {
for (x in 0...width) rgbData.add(inputImage.pget(x, y))
}
var reds   = ArrayData.new(width, height)
var greens = ArrayData.new(width, height)
var blues  = ArrayData.new(width, height)
for (y in 0...height) {
for (x in 0...width) {
var rgbValue = rgbData[y * width + x]
reds[x, y]   = rgbValue.r
greens[x,y]  = rgbValue.g
blues[x, y]  = rgbValue.b
}
}
return [reds, greens, blues]
}

writeOutputImage(filename, redGreenBlue) {
var reds   = redGreenBlue[0]
var greens = redGreenBlue[1]
var blues  = redGreenBlue[2]
var outputImage = ImageData.create(filename, reds.width, reds.height)
for (y in 0...reds.height) {
for (x in 0...reds.width) {
var red   = bound(reds[x, y], 256)
var green = bound(greens[x, y], 256)
var blue  = bound(blues[x, y], 256)
var c = Color.new(red, green, blue)
outputImage.pset(x, y, c)
}
}
outputImage.draw(_width/2, 0)
Canvas.print(filename, _width * 2/3,  _height * 5/6, Color.white)
outputImage.saveToFile(filename)
}

update() {}

draw(alpha) {}
}

var k = [
[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]
]

var divisor = 273

var image1 = "Pentagon.png"
var image2 = "Pentagon2.png"

System.print("Input file %(image1), output file %(image2).")
System.print("Kernel size: %(k.count) x %(k[0].count), divisor %(divisor)")
System.print(k.join("\n"))

var kernel = ArrayData.new(k.count, k[0].count)
for (y in 0...k[0].count) {
for (x in 0...k.count) kernel[x, y] = k[x][y]
}
var Game = ImageConvolution.new(700, 300, image1, image2, kernel, divisor)

Output:
Input file Pentagon.png, output file Pentagon2.png.
Kernel size: 5 x 5, 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]