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。

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