CT扫描的二值化图像的多重分形计算，

%% % Author: Tegy J. Vadakkan % Date: 09/08/2009 % input a binary image % the multifractal spectra is calculated based on the ideas in the paper by % Posadas et al., Soil Sci. Soc. Am. J. 67:1361-1369, 2003 clc; clear all; close all; %% indata=inputdlg({'input filename'}); a = imread(indata{1}); [rows, cols] = size(a); figure;imshow(a); npix = sum(sum(a)); %% calculates niL which is the number of pixels in the ith box of size L % ideas from boxcount.m by F. Moisy have been borrowed here width = rows; p = log(width)/log(2); max_boxes = power(rows,2)/power(2,2); nL = double(zeros(max_boxes,p)); for g=(p-1):-1:0 siz = 2^(p-g); sizm1 = siz - 1; index = log2(siz); count = 0; for i=1:siz:(width-siz+1) for j=1:siz:(width-siz+1) count = count + 1; sums = sum(sum(a(i:i+sizm1,j:j+sizm1))); nL(count,index) = sums; end end end %% qran = 1; logl = zeros(p,1); for l=1:p logl(l) = log(power(2,l)); end %% normalized masses pL = double(zeros(max_boxes,p)); for l=1:p nboxes = power(rows,2)/power(power(2,l),2); norm = sum(nL(1:nboxes,l)); if(norm ~= npix) display('error'); end for i=1:nboxes pL(i,l) = nL(i,l)/norm; end end %% %falpha, alpha for l=1:p count = 0; nboxes = power(rows,2)/power(power(2,l),2); for q = -qran:+0.1:qran %denominator of muiql qsum = 0.0; for i=1:nboxes if(pL(i,l) ~= 0) qsum = qsum + power(pL(i,l),q); end end fqnum = 0.0; aqnum = 0.0; smuiqL = 0.0; for i=1:nboxes if(pL(i,l) ~= 0) muiqL = power(pL(i,l),q)/qsum; fqnum = fqnum + (muiqL * log(muiqL)); aqnum = aqnum + (muiqL * log(pL(i,l))); smuiqL = smuiqL + muiqL; end end if(uint8(smuiqL)~=1) display('error'); end count = count + 1; fql(l,count) = fqnum; aql(l,count) = aqnum; qval(count) = q; end end %% % alpha_q for i=1:count line = polyfit(logl,aql(:,i),1); aq(i) = line(1); yfit = polyval(line,logl); sse = sum(power(aql(:,i)-yfit,2)); sst = sum(power(aql(:,i)-mean(aql(:,i)),2)); ar2(i) = 1-(sse/sst); end % f_q for i=1:count line = polyfit(logl,fql(:,i),1); fq(i) = line(1); yfit = polyval(line,logl); sse = sum(power(fql(:,i)-yfit,2)); sst = sum(power(fql(:,i)-mean(fql(:,i)),2)); fr2(i) = 1-(sse/sst); end figure;plot(qval,aq,'r:o',qval,fq,'g:o'); h = legend('alpha(q)','f(q)',1); xlabel('q','FontSize',14); figure;plot(aq,fq,'r:o'); xlabel('alpha(q)','FontSize',14); ylabel('f(q)','FontSize',14); line=polyfit(aq,fq,2); pfit = polyval(line,aq); figure;plot(aq,fq,'r:o',aq,pfit,'g:o'); h = legend('f(q)','Parabolic fit to f(q)',3); xlabel('alpha(q)','FontSize',14);