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 grayscale 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.)
Action!
<lang 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</lang>
- Output:
Screenshot from Atari 8-bit computer
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
<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>
- 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>
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. <lang lisp>(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)))
</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>
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
<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]]
![[1]](http://www.diga.me.uk/convolved.gif){kind=link}
Maple
Builtin command ImageTools:-Convolution() <lang Maple>pic:=Import("smiling_dog.jpg"): mask := Matrix([[1,2,3],[4,5,6],[7,8,9]]); pic := ImageTools:-Convolution(pic, mask);</lang>
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 kernel:\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 kernel 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 kernel 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 kernel 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 kernel) % % 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 kernel:
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 kernel 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
Nim
As in the D version, we use the modules built for the "bitmap" and "grayscale image" tasks. But we have chosen to read and write PNG files rather than PPM files, using for this purpose the "nimPNG" third party module.
<lang Nim>import math, lenientops, strutils import nimPNG, bitmap, grayscale_image
type ConvolutionFilter = object
kernel: seq[seq[float]] divisor: float offset: float name: string
func convolve[T: Image|GrayImage](img: T; filter: ConvolutionFilter): T =
assert not img.isNil assert filter.divisor.classify != fcNan and filter.offset.classify != fcNan assert filter.divisor != 0 assert filter.kernel.len > 0 and filter.kernel[0].len > 0 for row in filter.kernel: assert row.len == filter.kernel[0].len assert filter.kernel.len mod 2 == 1 assert filter.kernel[0].len mod 2 == 1 assert img.h >= filter.kernel.len assert img.w >= filter.kernel[0].len
let knx2 = filter.kernel[0].len div 2 let kny2 = filter.kernel.len div 2
when T is Image: result = newImage(img.w, img.h) else: result = newGrayImage(img.w, img.h)
for y in kny2..<(img.h - kny2):
for x in knx2..<(img.w - knx2):
when T is Image:
var total: array[3, float]
else:
var total: float
for sy, kRow in filter.kernel:
for sx, k in kRow:
let p = img[x + sx - knx2, y + sy - kny2]
when T is Image:
total[0] += p.r * k
total[1] += p.g * k
total[2] += p.b * k
else:
total += p * k
let d = filter.divisor
let off = filter.offset * Luminance.high
when T is Image:
result[x, y] = color(min(max(total[0] / d + off, Luminance.low.float),
Luminance.high.float).toInt,
min(max(total[1] / d + off, Luminance.low.float),
Luminance.high.float).toInt,
min(max(total[2] / d + off, Luminance.low.float),
Luminance.high.float).toInt)
else:
result[x, y] = Luminance(min(max(total / d + off, Luminance.low.float),
Luminance.high.float).toInt)
const
Input = "lena.png" Output1 = "lena_$1.png" 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</lang>
OCaml
<lang ocaml>let get_rgb img x y =
let _, r_channel,_,_ = img in let width = Bigarray.Array2.dim1 r_channel and height = Bigarray.Array2.dim2 r_channel in if (x < 0) || (x >= width) then (0,0,0) else if (y < 0) || (y >= height) then (0,0,0) else (* feed borders with black *) get_pixel img x y
let convolve_get_value img kernel divisor offset = fun x y ->
let sum_r = ref 0.0 and sum_g = ref 0.0 and sum_b = ref 0.0 in
for i = -1 to 1 do
for j = -1 to 1 do
let r, g, b = get_rgb img (x+i) (y+j) in
sum_r := !sum_r +. kernel.(j+1).(i+1) *. (float r);
sum_g := !sum_g +. kernel.(j+1).(i+1) *. (float g);
sum_b := !sum_b +. kernel.(j+1).(i+1) *. (float b);
done;
done;
( !sum_r /. divisor +. offset,
!sum_g /. divisor +. offset,
!sum_b /. divisor +. offset )
let color_to_int (r,g,b) =
(truncate r, truncate g, truncate b)
let bounded (r,g,b) =
((max 0 (min r 255)), (max 0 (min g 255)), (max 0 (min b 255)))
let convolve_value ~img ~kernel ~divisor ~offset =
let _, r_channel,_,_ = img in let width = Bigarray.Array2.dim1 r_channel and height = Bigarray.Array2.dim2 r_channel in
let res = new_img ~width ~height in
let conv = convolve_get_value img kernel divisor offset in
for y = 0 to pred height do
for x = 0 to pred width do
let color = conv x y in
let color = color_to_int color in
put_pixel res (bounded color) x y;
done;
done;
(res)</lang>
<lang ocaml>let emboss img =
let kernel = [| [| -2.; -1.; 0. |]; [| -1.; 1.; 1. |]; [| 0.; 1.; 2. |]; |] in convolve_value ~img ~kernel ~divisor:1.0 ~offset:0.0;
let sharpen img =
let kernel = [| [| -1.; -1.; -1. |]; [| -1.; 9.; -1. |]; [| -1.; -1.; -1. |]; |] in convolve_value ~img ~kernel ~divisor:1.0 ~offset:0.0;
let sobel_emboss img =
let kernel = [| [| -1.; -2.; -1. |]; [| 0.; 0.; 0. |]; [| 1.; 2.; 1. |]; |] in convolve_value ~img ~kernel ~divisor:1.0 ~offset:0.5;
let box_blur img =
let kernel = [| [| 1.; 1.; 1. |]; [| 1.; 1.; 1. |]; [| 1.; 1.; 1. |]; |] in convolve_value ~img ~kernel ~divisor:9.0 ~offset:0.0;
- </lang>
Octave
Use package Image
<lang octave>function [r, g, b] = rgbconv2(a, c)
r = im2uint8(mat2gray(conv2(a(:,:,1), c))); g = im2uint8(mat2gray(conv2(a(:,:,2), c))); b = im2uint8(mat2gray(conv2(a(:,:,3), c)));
endfunction
im = jpgread("Lenna100.jpg"); emboss = [-2, -1, 0; -1, 1, 1; 0, 1, 2 ]; sobel = [-1., -2., -1.; 0., 0., 0.; 1., 2., 1. ]; sharpen = [ -1.0, -1.0, -1.0; -1.0, 9.0, -1.0; -1.0, -1.0, -1.0 ];
[r, g, b] = rgbconv2(im, emboss); jpgwrite("LennaEmboss.jpg", r, g, b, 100); [r, g, b] = rgbconv2(im, sobel); jpgwrite("LennaSobel.jpg", r, g, b, 100); [r, g, b] = rgbconv2(im, sharpen); jpgwrite("LennaSharpen.jpg", r, g, b, 100);</lang>
Perl
<lang 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';</lang> Compare offsite images: frog.png vs. frog_convolution.png
Phix
-- -- 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
<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>
Raku
(formerly Perl 6)
Perl 5 PDL library
<lang perl6>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';</lang> Compare offsite images: frog.png vs. frog_convolution.png
Imagemagick library
<lang perl6>
- 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;
}</lang>
Ruby
<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 $DEBUG
newimg
end
# Applies a convolution kernel to produce a single pixel in the destination
def apply_kernel(x, y, kernel, newimg)
x0 = x==0 ? 0 : x-1
y0 = y==0 ? 0 : y-1
x1 = x
y1 = y
x2 = x+1==@width ? x : x+1
y2 = y+1==@height ? y : y+1
r = g = b = 0.0
[x0, x1, x2].zip(kernel).each do |xx, kcol|
[y0, y1, y2].zip(kcol).each do |yy, k|
r += k * self[xx,yy].r
g += k * self[xx,yy].g
b += k * self[xx,yy].b
end
end
newimg[x,y] = RGBColour.new(luma(r), luma(g), luma(b))
end
# Function for clamping values to those that we can use with colors
def luma(value)
if value < 0
0
elsif value > 255
255
else
value
end
end
end
- Demonstration code using the teapot image from Tk's widget demo
teapot = Pixmap.open('teapot.ppm') [ ['Emboss', [[-2.0, -1.0, 0.0], [-1.0, 1.0, 1.0], [0.0, 1.0, 2.0]]],
['Sharpen', [[-1.0, -1.0, -1.0], [-1.0, 9.0, -1.0], [-1.0, -1.0, -1.0]]], ['Blur', [[0.1111,0.1111,0.1111],[0.1111,0.1111,0.1111],[0.1111,0.1111,0.1111]]],
].each do |label, kernel|
savefile = 'teapot_' + label.downcase + '.ppm' teapot.convolute(kernel).save(savefile)
end</lang>
Tcl
<lang tcl>package require Tk
- Function for clamping values to those that we can use with colors
proc tcl::mathfunc::luma channel {
set channel [expr {round($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]]
}</lang>
Wren
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. <lang ecmascript>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.loadFromFile(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)</lang>
- 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]