Image convolution: Difference between revisions

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save("imagesharper.png", imfilt)
save("imagesharper.png", imfilt)
</lang>
</lang>

=={{header|Kotlin}}==
{{trans|Java}}
<lang scala>// 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()
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)
}</lang>

{{out}}
<pre>
Same as Java entry when using identical command line arguments
</pre>


=={{header|Liberty BASIC}}==
=={{header|Liberty BASIC}}==

Revision as of 16:44, 22 January 2018

Task
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 , 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:

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.)

Ada

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

type Float_Pixel is record 

  R, G, B : Float_Luminance := 0.0;

end record;

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

  pragma Inline ("*");

begin 

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

end "*";

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

  pragma Inline ("+");

begin 

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

end "+";

function To_Luminance (X : Float_Luminance) return Luminance is 

  pragma Inline (To_Luminance);

begin 

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

end To_Luminance;

function To_Pixel (X : Float_Pixel) return Pixel is 

  pragma Inline (To_Pixel);

begin 

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

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

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

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

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

begin 

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

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

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

BBC BASIC

Works with: BBC BASIC for Windows

<lang bbcbasic> Width% = 200 

     Height% = 200
     
     DIM out&(Width%-1, Height%-1, 2)
     
     VDU 23,22,Width%;Height%;8,16,16,128
     *DISPLAY Lena
     OFF
     
     DIM filter%(2, 2)
     filter%() = -1, -1, -1, -1, 12, -1, -1, -1, -1
     
     REM Do the convolution:
     FOR Y% = 1 TO Height%-2
       FOR X% = 1 TO Width%-2
         R% = 0 : G% = 0 : B% = 0
         FOR I% = -1 TO 1
           FOR J% = -1 TO 1
             C% = TINT((X%+I%)*2, (Y%+J%)*2)
             F% = filter%(I%+1,J%+1)
             R% += F% * (C% AND &FF)
             G% += F% * (C% >> 8 AND &FF)
             B% += F% * (C% >> 16)
           NEXT
         NEXT
         IF R% < 0 R% = 0 ELSE IF R% > 1020 R% = 1020
         IF G% < 0 G% = 0 ELSE IF G% > 1020 G% = 1020
         IF B% < 0 B% = 0 ELSE IF B% > 1020 B% = 1020
         out&(X%, Y%, 0) = R% / 4 + 0.5
         out&(X%, Y%, 1) = G% / 4 + 0.5
         out&(X%, Y%, 2) = B% / 4 + 0.5
       NEXT
     NEXT Y%
     
     REM Display:
     GCOL 1
     FOR Y% = 0 TO Height%-1
       FOR X% = 0 TO Width%-1
         COLOUR 1, out&(X%,Y%,0), out&(X%,Y%,1), out&(X%,Y%,2)
         LINE X%*2,Y%*2,X%*2,Y%*2
       NEXT
     NEXT Y%
     
     REPEAT
       WAIT 1
     UNTIL FALSE</lang>

C

Interface:

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

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

<lang c>#include "imglib.h"

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

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

}

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

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

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

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

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

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

     }
   }
   return oi;
 }
 return NULL;

}</lang>

Usage example:

The read_image function is from here.

<lang c>#include <stdio.h>

  1. include "imglib.h"

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

double emboss_kernel[3*3] = { 

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

};

double sharpen_kernel[3*3] = { 

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

}; double sobel_emboss_kernel[3*3] = { 

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

}; double box_blur_kernel[3*3] = { 

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

};

double *filters[4] = { 

 emboss_kernel, sharpen_kernel, sobel_emboss_kernel, box_blur_kernel

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

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

};

int main() { 

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

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

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

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

}</lang>

D

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

struct ConvolutionFilter { 

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

}


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

                           in ConvolutionFilter filter)

pure nothrow in { 

   assert(im !is null);
   assert(!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));

}</lang>

Go

Using standard image library: <lang go>package main

import ( 

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

)

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

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

}

var blur = [9]float64{ 

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

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

   dst := *src

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

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

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

}

func main() { 

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

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

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

import "math"

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

   if len(k) != 9 {
       return nil
   }
   r := NewGrmap(g.cols, g.rows)
   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

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

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

import ( 

   "fmt"
   "raster"

)

var blur = []float64{ 

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

var sharpen = []float64{ 

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

func main() { 

   // Example file used here is Lenna100.jpg from the task "Percentage
   // difference between images" converted with with the command
   // convert Lenna100.jpg -colorspace gray Lenna100.ppm
   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)
   }

}</lang>

J

<lang 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=: 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

)</lang>


This code assumes that the leading dimensions of the array represent pixels and any trailing dimensions represent structure to be preserved (this is a fairly common approach and matches the J implementation at Basic bitmap storage). 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:

<lang J> 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'</lang>

Java

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

public class ImageConvolution { 

 public static class ArrayData
 {
   public final int[] dataArray;
   public final int width;
   public final int height;
   
   public ArrayData(int width, int height)
   {
     this(new int[width * height], width, height);
   }
   
   public ArrayData(int[] dataArray, int width, int height)
   {
     this.dataArray = dataArray;
     this.width = width;
     this.height = height;
   }
   
   public int get(int x, int y)
   {  return dataArray[y * width + x];  }
   
   public void set(int x, int y, int value)
   {  dataArray[y * width + x] = value;  }
 }
 
 private static int bound(int value, int endIndex)
 {
   if (value < 0)
     return 0;
   if (value < endIndex)
     return value;
   return endIndex - 1;
 }
 
 public static ArrayData convolute(ArrayData inputData, ArrayData kernel, int kernelDivisor)
 {
   int inputWidth = inputData.width;
   int inputHeight = inputData.height;
   int kernelWidth = kernel.width;
   int kernelHeight = kernel.height;
   if ((kernelWidth <= 0) || ((kernelWidth & 1) != 1))
     throw new IllegalArgumentException("Kernel must have odd width");
   if ((kernelHeight <= 0) || ((kernelHeight & 1) != 1))
     throw new IllegalArgumentException("Kernel must have odd height");
   int kernelWidthRadius = kernelWidth >>> 1;
   int kernelHeightRadius = kernelHeight >>> 1;
   
   ArrayData outputData = new ArrayData(inputWidth, inputHeight);
   for (int i = inputWidth - 1; i >= 0; i--)
   {
     for (int j = inputHeight - 1; j >= 0; j--)
     {
       double newValue = 0.0;
       for (int kw = kernelWidth - 1; kw >= 0; kw--)
         for (int kh = kernelHeight - 1; kh >= 0; kh--)
           newValue += kernel.get(kw, kh) * inputData.get(
                         bound(i + kw - kernelWidthRadius, inputWidth),
                         bound(j + kh - kernelHeightRadius, inputHeight));
       outputData.set(i, j, (int)Math.round(newValue / kernelDivisor));
     }
   }
   return outputData;
 }
 
 public static ArrayData[] getArrayDatasFromImage(String filename) throws IOException
 {
   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;
 }

}</lang>


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: <lang javascript>// 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');

}</lang>

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

<lang 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) </lang>

Kotlin

Translation of: Java

<lang scala>// 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()
           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)

}</lang>

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. <lang lb> 

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

   nomainwin

   WindowWidth  = 460
   WindowHeight = 210

   open "Convolution" for graphics_nsb_nf as #w

   #w "trapclose [quit]"

   #w "down ; fill darkblue"

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

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

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

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

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

   #w "size 8"
   for y =0 to 2  '   fill in the mask matrix
       for x =0 to 2
           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

</lang> 

Screenview is available at [[1]]


Mathematica / Wolfram Language

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

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). <lang MATLAB>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</lang>

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

Padding with zeroes:
    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

Padding with fives:
    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

<lang ocaml>let get_rgb img x y = 

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


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

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

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


let color_to_int (r,g,b) = 

 (truncate r,
  truncate g,
  truncate b)

let bounded (r,g,b) = 

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


let convolve_value ~img ~kernel ~divisor ~offset = 

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

 let res = new_img ~width ~height in

 let conv = convolve_get_value img kernel divisor offset in

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

<lang ocaml>let emboss img = 

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

let sharpen img = 

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

let sobel_emboss img = 

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

let box_blur img = 

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

Octave

Use package Image

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

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

endfunction

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

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

PicoLisp

<lang PicoLisp>(scl 3)

(de ppmConvolution (Ppm Kernel) 

  (let (Len (length (car Kernel))  Radius (/ Len 2))
     (make
        (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) ) ) ) ) ) ) )</lang>

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:

<lang python>#!/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()</lang>

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:

<lang python>#!/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)</lang>

Racket

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

271px-John_Constable_002.jpg convolve-etch-3x3.png


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

(provide flomap-convolve)

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

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

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

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

Ruby

Translation of: Tcl

<lang ruby>class Pixmap 

 # Apply a convolution kernel to a whole image
 def convolute(kernel)
   newimg = Pixmap.new(@width, @height)
   pb = ProgressBar.new(@width) if $DEBUG
   @width.times do |x|
     @height.times do |y|
       apply_kernel(x, y, kernel, newimg)
     end
     pb.update(x) if $DEBUG
   end
   pb.close if $DEBUG
   newimg
 end

 # Applies a convolution kernel to produce a single pixel in the destination
 def apply_kernel(x, y, kernel, newimg)
   x0 = x==0 ? 0 : x-1
   y0 = y==0 ? 0 : y-1
   x1 = x
   y1 = y
   x2 = x+1==@width  ? x : x+1
   y2 = y+1==@height ? y : y+1

   r = g = b = 0.0
   [x0, x1, x2].zip(kernel).each do |xx, kcol|
     [y0, y1, y2].zip(kcol).each do |yy, k|
       r += k * self[xx,yy].r
       g += k * self[xx,yy].g
       b += k * self[xx,yy].b
     end
   end
   newimg[x,y] = RGBColour.new(luma(r), luma(g), luma(b))
 end

 # Function for clamping values to those that we can use with colors
 def luma(value)
   if value < 0
     0
   elsif value > 255
     255
   else
     value
   end
 end

end


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

teapot = Pixmap.open('teapot.ppm') [ ['Emboss', [[-2.0, -1.0, 0.0], [-1.0, 1.0, 1.0], [0.0, 1.0, 2.0]]], 

 ['Sharpen', [[-1.0, -1.0, -1.0], [-1.0, 9.0, -1.0], [-1.0, -1.0, -1.0]]], 
 ['Blur',    [[0.1111,0.1111,0.1111],[0.1111,0.1111,0.1111],[0.1111,0.1111,0.1111]]],

].each do |label, kernel| 

 savefile = 'teapot_' + label.downcase + '.ppm'
 teapot.convolute(kernel).save(savefile)

end</lang>

Tcl

Works with: Tcl version 8.6
Library: Tk

<lang tcl>package require Tk

  1. Function for clamping values to those that we can use with colors

proc tcl::mathfunc::luma channel { 

   set channel [expr {round($channel)}]
   if {$channel < 0} {

return 0 

   } elseif {$channel > 255} {

return 255 

   } else {

return $channel 

   }

}

  1. Applies a convolution kernel to produce a single pixel in the destination

proc applyKernel {srcImage x y -- kernel -> dstImage} { 

   set x0 [expr {$x==0 ? 0 : $x-1}]
   set y0 [expr {$y==0 ? 0 : $y-1}]
   set x1 $x
   set y1 $y
   set x2 [expr {$x+1==[image width $srcImage]  ? $x : $x+1}]
   set y2 [expr {$y+1==[image height $srcImage] ? $y : $y+1}]

   set r [set g [set b 0.0]]
   foreach X [list $x0 $x1 $x2] kcol $kernel {

foreach Y [list $y0 $y1 $y2] k $kcol { lassign [$srcImage get $X $Y] rPix gPix bPix set r [expr {$r + $k * $rPix}] set g [expr {$g + $k * $gPix}] set b [expr {$b + $k * $bPix}] } 

   }

   $dstImage put [format "#%02x%02x%02x" \

[expr {luma($r)}] [expr {luma($g)}] [expr {luma($b)}]]\ -to $x $y }

  1. Apply a convolution kernel to a whole image

proc convolve {srcImage kernel {dstImage ""}} { 

   if {$dstImage eq ""} {

set dstImage [image create photo] 

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

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

   }
   return $dstImage

}

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

image create photo teapot -file $tk_library/demos/images/teapot.ppm pack [labelframe .src -text Source] -side left pack [label .src.l -image teapot] foreach {label kernel} { 

   Emboss {

{-2. -1. 0.} {-1. 1. 1.} { 0. 1. 2.} 

   }
   Sharpen {

{-1. -1. -1} {-1. 9. -1} {-1. -1. -1} 

   }
   Blur {

{.1111 .1111 .1111} {.1111 .1111 .1111} {.1111 .1111 .1111} 

   }

} { 

   set name [string tolower $label]
   update
   pack [labelframe .$name -text $label] -side left
   pack [label .$name.l -image [convolve teapot $kernel]]

}</lang>

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