Matlab中FrechetDistance方法实现---比较两条曲线的相似性，并绘制曲线

1. function [cm, cSq] = DiscreteFrechetDist(P,Q,dfcn)
   
   plot(P)%绘制曲线P
   plot(Q)%绘制曲线Q
   
   sP = size(P);
   sQ = size(Q);
   
   % check validity of inputs
   if sP(2)~=sQ(2)
       error('Curves P and Q must be of the same dimension')
   elseif sP(1)==0
       cm = 0;
       return;
   end
   
   % initialize CA to a matrix of -1s
   CA = ones(sP(1),sQ(1)).*-1;
   
   % distance function
   if nargin==2
       dfcn = @(u,v) sqrt(sum( (u-v).^2 )); %  @表示定义匿名函数
   end
   
   % final coupling measure value
   cm = c(sP(1),sQ(1));
   
   % obtain coupling measure via backtracking procedure
   if nargout==2
       cSq = zeros(sQ(1)+sP(1)+1,2);    % coupling sequence
       CApad = [ones(1,sQ(1)+1)*inf; [ones(sP(1),1)*inf CA]];  % pad CA
       Pi=sP(1)+1; Qi=sQ(1)+1; count=1;  % counting variables
       while Pi~=2 || Qi~=2
           % step down CA gradient
           [v,ix] = min([CApad(Pi-1,Qi) CApad(Pi-1,Qi-1) CApad(Pi,Qi-1)]);
           if ix==1
               cSq(count,:) = [Pi-1 Qi];
               Pi=Pi-1;
           elseif ix==2
               cSq(count,:) = [Pi-1 Qi-1];
               Pi=Pi-1; Qi=Qi-1;
           elseif ix==3
               cSq(count,:) = [Pi Qi-1];
               Qi=Qi-1;
           end
           count=count+1;
       end
       % format output: remove extra zeroes, reverse order, subtract off
       % padding value, and add in the last point
       cSq = [flipud(cSq(1:find(cSq(:,1)==0,1,'first')-1,:))-1; sP(1) sQ(1)];
   end
   
   
   % debug
   % assignin('base','CAw',CA)
   
   function CAij = c(i,j)
       % coupling search function
       if CA(i,j)>-1
           % don't update CA in this case
           CAij = CA(i,j);
       elseif i==1 && j==1
           CA(i,j) = dfcn(P(1,:),Q(1,:));     % update the CA permanent
           CAij = CA(i,j);                    % set the current relevant value
       elseif i>1 && j==1
           CA(i,j) = max( c(i-1,1), dfcn(P(i,:),Q(1,:)) );
           CAij = CA(i,j);
       elseif i==1 && j>1
           CA(i,j) = max( c(1,j-1), dfcn(P(1,:),Q(j,:)) );
           CAij = CA(i,j);
       elseif i>1 && j>1
           CA(i,j) = max( min([c(i-1,j), c(i-1,j-1), c(i,j-1)]),...
               dfcn(P(i,:),Q(j,:)) );
           CAij = CA(i,j);
       else
           CA(i,j) = inf;
       end
   end     % end function, c
   
   end     % end main function
   
   

   2.在命令行中输入以下语句

   >> [data1,data2]=textread('dataP.txt','%n%n',2);
   >> [data3,data4]=textread('dataQ.txt','%n%n',2);
   >> P=[data1,data2];
   >> Q=[data3,data4];
   >> DiscreteFrechetDist(P,Q)    

   3.返回值ans就是曲线的相似度，当然数值越小说明越相似。