Digital Half-toning Error Diffusion Method (Floyd-Steinberg) - MATLAB Code

Introduction to Digital Half toning is provided in the below link

http://imageprocessing-sankarsrin.blogspot.tw/2016/12/digital-half-toning-ordered-dithering.html

The halftones are generally obtained by thresholding each image pixel with a certain value (ex. 128). In error diffusion, the error is computed between the actual and obtained output and it is distributed to the neighborhood pixels. Floyd-Stein berg, Jarvis, Stucki kernels are widely adopted  to distribute the error.

The Error Diffusion half toning is as follows

1) image(x,y) > 128  Apply thresholding (assume  the image pixel value is 157,  in that case, 255 will be assigned to output). ( as the half toning corresponds to two values 0 and 255)

2) Compute the error between actual and obtained output    E=   255-157= 98

3) In case of floyd steinberg the value 98 is distributed along the neighborhood pixels

4) This steps are performed in sequence and serpentine scan yields superior halftone output. The main problem with error diffusion technique is its sequential processing approach, and in further, dot diffusion technique is introduced to overcome this drawback. 

https://imageprocessing-sankarsrin.blogspot.com/2017/11/dot-diffusion-digital-halftoning-knuth.html

MATLAB CODE: Floyd-Steinberg (Change fc value to execute others) - Reference code from The University of Texas at Austin

function [out, qn, k] = errdiff(in, l, dir, v)

%ERRDIFF Core routine for error diffusion.

% [OUT, QN, K] = ERRDIFF(IN, L, DIR, V) performs error

% diffusion on image IN using error filter FC, modified parameter L,

% and direction DIR, where 1 is raster scan and -1 is serpentine.

% When V (verbose) is non-zero, progress is printed to the output.

% Input range is 0 to 1, as is output range.  Input image is modified

% (no error pipe) for maximum speed.  This routine is the core for all

% error diffusion routines.

%

% Ref: R. Eschbach and K. Knox, "Error diffusion algorithm with

% edge enhancement", J. Opt. Soc. Am. A, Vol. 8, No. 12, December

% 1991, pp. 1844-1850.

if nargin<5 % default to verbose

  v=1; end

if nargin<4 % default to raster

  dir=1; end

if nargin<3 % default to unmodified

  l=0; end

% default to Floyd-Steinberg

  fc=[0 -99*16 7; 3 5 1]/16; 

[ri,ci]=size(in);

[rm,cm]=size(fc);

[r0,c0]=find(fc==-99); % find origin of error filter

fc(r0,c0)=0;

rm=rm-1; cm=cm-1;

inpad=zeros(ri+rm,ci+cm); % modified input image

inpad(r0:r0+ri-1,c0:c0+ci-1)=in;

out=zeros(ri,ci); qn=out;

sp=1; ep=ci; step=1; % for direction changing

r0=r0-1; c0=c0-1;

for y=1:ri

  for x=sp:step:ep

    inpix=inpad(y+r0,x+c0);

    outpix=(inpix+l*in(y,x))>=0.5;

    out(y,x)=outpix;

    qerr=outpix-inpix;

    qn(y,x)=qerr;

    inpad(y:y+rm,x:x+cm)=inpad(y:y+rm,x:x+cm)-qerr*fc;

  end

  if dir==-1

    step=-step; temp=ep; ep=sp; sp=temp;

    fc=fc(:,cm+1:-1:1); end

  if v

   % fprintf('\rDithering... %3d%% done',round(y/ri*100)), 

   end

end

if v

  fprintf('\n')

end

if nargout==3

  xp=out(:)-0.5-qn(:);

  k=sum(abs(xp))/(2*sum(xp.^2));

end

Cheers !!

PYTHON Code: https://github.com/SankarSrin/Digital-Halftoning