Matlab利用垂距法实现提取离散坐标数据特征点

function [newPntSet,vertPnt]=getFeaturePnt(pntSet)
% @author:slandarer
% newPntSet : 特征点
% vertPnt   : 原始曲线垂足
[rows,cols]=size(pntSet);
if rows<4||cols<2,error('数据点过少或维度异常');end

innerPntSet=pntSet(2:end-1,:);             % 内部点
adjPnt1V=innerPntSet-pntSet(1:end-2,:);    % 当前点与前一点向量
adjPnt2V=pntSet(3:end,:)-pntSet(1:end-2,:);% 当前点的两个相邻点向量
adjPnt2V=adjPnt2V./vecnorm(adjPnt2V')';    % 归一化

lVert=sum(adjPnt1V.*adjPnt2V,2);   
vertPnt=adjPnt2V.*lVert+pntSet(1:end-2,:); % 获取垂足
vertL=vecnorm((innerPntSet-vertPnt)');     % 计算垂线距离
vertL(isinf(vertL)|isnan(vertL))=0;        % 修正/0的情况
innerPntSet(vertL<median(vertL),:)=[];     % 删掉特征性不强的点
newPntSet=[pntSet(1,:);innerPntSet;pntSet(end,:)];
end

% 随机构造数据
X=linspace(0,25,10)';
Y=randi([0,10],[10,1]);
pntSet=[X,Y];
% 获取特征点
[nPntSet,vertPnt]=getFeaturePnt(pntSet);
% 坐标区域修饰
hold on
ax=gca;
ax.DataAspectRatio=[1,1,1];
% 绘制原始数据曲线
plot(pntSet(:,1),pntSet(:,2),'Color',[0 0.4470 0.7410],'LineWidth',2,'Marker','*');
% 绘制新数据曲线
plot(nPntSet(:,1),nPntSet(:,2),'Color',[0.6350 0.0780 0.1840 .7],'LineWidth',2,'Marker','s');
legend('original-curve','feature-curve')

% 随机构造数据
X=linspace(0,25,10)';
Y=randi([0,10],[10,1]);
pntSet=[X,Y];
% 获取特征点
[nPntSet,vertPnt]=getFeaturePnt(pntSet);
% 坐标区域修饰
hold on
ax=gca;
ax.YLim=[0,10];
ax.DataAspectRatio=[1,1,1];
ax.Color=[1,1,1];
ax.XColor=[1,1,1].*.3;
ax.YColor=[1,1,1].*.3;
ax.LineWidth=1.5;
ax.FontName='cambria';
% 绘制原始数据曲线
l1=plot(pntSet(:,1),pntSet(:,2),'Color',[0 0.4470 0.7410],'LineWidth',2,'Marker','*');
% 绘制辅助线及垂线
innerPntSet=pntSet(2:end-1,:);
l2=plot([innerPntSet(:,1),vertPnt(:,1)]',[innerPntSet(:,2),vertPnt(:,2)]','Color',[.3,.3,.3],'LineWidth',1.2,'LineStyle','-.');
plot([pntSet(3:end,1),pntSet(1:end-2,1)]',[pntSet(3:end,2),pntSet(1:end-2,2)]','Color',[.3,.3,.3],'LineWidth',1.2,'LineStyle','-.')
% 绘制新数据曲线
l3=plot(nPntSet(:,1),nPntSet(:,2),'Color',[0.6350 0.0780 0.1840 .7],'LineWidth',2,'Marker','s');
% 增添图例
legend([l1,l2(1),l3],{'original-curve','auxiliary-line','feature-curve'});

% 随机构造数据
X=linspace(0,25,10)';
Y=randi([0,10],[10,1]);
Z=randi([0,10],[10,1]);
pntSet=[X,Y,Z];
% 获取特征点
[nPntSet,vertPnt]=getFeaturePnt(pntSet);
% 坐标区域修饰
hold on
grid on
ax=gca;
ax.YLim=[0,10];
ax.ZLim=[0,10];
ax.DataAspectRatio=[1,1,1];
ax.Color=[1,1,1];
ax.XColor=[1,1,1].*.3;
ax.YColor=[1,1,1].*.3;
ax.ZColor=[1,1,1].*.3;
ax.LineWidth=1.5;
ax.FontName='cambria';
% 绘制原始数据曲线
l1=plot3(pntSet(:,1),pntSet(:,2),pntSet(:,3),'Color',[0 0.4470 0.7410],'LineWidth',2,'Marker','*');
% 绘制辅助线
innerPntSet=pntSet(2:end-1,:);
l2=plot3([innerPntSet(:,1),vertPnt(:,1)]',[innerPntSet(:,2),vertPnt(:,2)]',...
    [innerPntSet(:,3),vertPnt(:,3)]','Color',[.3,.3,.3],'LineWidth',1.2,'LineStyle','-.');
plot3([pntSet(3:end,1),pntSet(1:end-2,1)]',[pntSet(3:end,2),pntSet(1:end-2,2)]',...
    [pntSet(3:end,3),pntSet(1:end-2,3)]','Color',[.3,.3,.3],'LineWidth',1.2,'LineStyle','-.')
% 绘制新数据曲线
l3=plot3(nPntSet(:,1),nPntSet(:,2),nPntSet(:,3),'Color',[0.6350 0.0780 0.1840 .7],'LineWidth',2,'Marker','s');
% 增添图例
legend([l1,l2(1),l3],{'original-curve','auxiliary-line','feature-curve'});
view(3)