道格拉斯-普克抽稀算法曲线平滑

最新推荐文章于 2025-07-12 16:29:43 发布

转载最新推荐文章于 2025-07-12 16:29:43 发布 · 5.9k 阅读

本文介绍了一种用于图形数据压缩的算法，通过道拉斯-普克抽稀算法和垂直距离法来删除冗余顶点，提高数据处理效率。详细解释了算法原理、实现代码及与垂距法的比较，特别强调了道拉斯-普克法在保持线要素形态特征方面的优势。

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switch(m_SmoothMode)
        {
        case 0: //三点线性
            for(i=2+offsetpos;i<datanum-2;i++)
            {
                m_pfDataArray[i] = (m_pfDataArray[i-1]+m_pfDataArray[i]+m_pfDataArray[i+1])/3;
            }
            break;
        case 1://五点二次滤波
            for(i=2+offsetpos;i<datanum-2;i++)
            {
                m_pfDataArray[i] = (12*(m_pfDataArray[i-1]+m_pfDataArray[i+1])
                    -3*(m_pfDataArray[i-2]+m_pfDataArray[i+2])
                    +17*m_pfDataArray[i])/35;
            }
            break;
        case 2://三点钟形滤波
            for(i=2+offsetpos;i<datanum-2;i++)
            {
                m_pfDataArray[i] = (short)(0.212f*m_pfDataArray[i-1]+0.576f*m_pfDataArray[i]
                +0.212f*m_pfDataArray[i+1]);
            }
            break;
        case 3://五点钟形滤波
            for(i=2+offsetpos;i<datanum-2;i++)
            {
                m_pfDataArray[i] = (short)(0.11f*(m_pfDataArray[i-2]+m_pfDataArray[i+2])
                    +0.24f*(m_pfDataArray[i-1]+m_pfDataArray[i+1])
                    +0.3f*m_pfDataArray[i]);
            }
            break;
        case 4://三点汉明滤波
            for(i=2+offsetpos;i<datanum-2;i++)
            {
                m_pfDataArray[i] = (short)(0.07f*m_pfDataArray[i-1]+0.86f*m_pfDataArray[i]
                +0.07f*m_pfDataArray[i+1]);
            }
            break;
        default://五点汉明滤波
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            {
                m_pfDataArray[i] = (short)(0.04f*(m_pfDataArray[i-2]+m_pfDataArray[i+2])
                    +0.24f*(m_pfDataArray[i-1]+m_pfDataArray[i+1])
                    +0.44f*m_pfDataArray[i]);
            }
            break;
        }

道格拉斯-普克抽稀算法

道格拉斯-普克抽稀算法，是用来对大量冗余的图形数据点进行压缩以提取必要的数据点。该算法实现抽稀的过程是：先将一条曲线首尾点虚连一条直线，求其余各点到该直线的距离，取其最大者与规定的临界值相比较，若小于临界值，则将直线两端间各点全部舍去，否则将离该直线距离最大的点保留，并将原线条分成两部分，对每部分线条再实施该抽稀过程，直到结束。抽稀结果点数随选取限差临界值的增大而减少，应用时应根据精度来选取限差临界值，以获得最好的效果。

--------------------------------------------------------------------------

以下转载自：垂距法与道格拉斯-普克法删除冗余顶点效率的比较
彭认灿 ,董　箭 ,郑义东 ,李改肖
(大连舰艇学院海洋测绘工程系 ,辽宁大连 116018)

道格拉斯- 普克法可描述为:将一条曲线首末顶点虚连一条直线 ,求出其余各顶点到该直线的距离 ,选其最大者与规定的限差相比较 ,若小于等于限差 ,则将直线两端间各点全部删去;若大于限差 ,则离该直线距离最大的顶点保留 ,并以此为界 ,把曲线分为两部分 ,对这两部分重复使用上述方法 ,直至最终无法作进一步的压缩为止 (见图 3)。

道格拉斯 2 普克法有一个十分突出的优点 ,即它是一个整体算法 ,在一般情况下可保留较大弯曲形态上的特征点。经道格拉斯-普克法压缩后得到的图形如图 4所示。由于该算法可准确删除小弯曲上的定点 ,故能从体上有效地保持线要素的形态特征。正是因为道格拉斯-普克法具有这样突出的优点 ,所以已经在线要素地自动制图中得到了较广泛的应用。但道格拉斯- 普克法较垂距法复杂 ,且通常编程实现时需要采用递归方 ,有一定的难度。

----------------------------------------------------------转载end

此算法可以在获取手写笔顺的特征点时应用。

C++代码

//=================================================================================================================

double PerpendicularDistance(CPoint Point1, CPoint Point2, CPoint Point)
{
    //Area = |(1/2)(x1y2 + x2y3 + x3y1 - x2y1 - x3y2 - x1y3)|   *Area of triangle
    //Base = v((x1-x2)2+(x1-x2)2)                               *Base of Triangle*
    //Area = .5*Base*H                                          *Solve for height
    //Height = Area/.5/Base

    double area = abs(0.5 * (Point1.x * Point2.y + Point2.x * Point.y + Point.x * Point1.y - Point2.x * Point1.y - Point.x * Point2.y - Point1.x * Point.y));
    double bottom = sqrt(pow(Point1.x - Point2.x, 2) + pow(Point1.y - Point2.y, 2));
    double height = area / bottom * 2;

return height;

}

void DouglasPeuckerReduction(vector<CPoint>points, int firstPoint, int lastPoint, double tolerance, list<int> &pointIndexsToKeep)
{
    double maxDistance = 0;
    int indexFarthest = 0;

    for (int index = firstPoint; index < lastPoint; index++)
    {
        double distance = PerpendicularDistance
            (points[firstPoint], points[lastPoint], points[index]);
        if (distance > maxDistance)
        {
            maxDistance = distance;
            indexFarthest = index;
        }
    }

    if (maxDistance > tolerance && indexFarthest != 0)
    {
        //Add the largest point that exceeds the tolerance
        pointIndexsToKeep.push_back(indexFarthest);

        DouglasPeuckerReduction(points, firstPoint,
        indexFarthest, tolerance, pointIndexsToKeep);

        DouglasPeuckerReduction(points, indexFarthest,
        lastPoint, tolerance, pointIndexsToKeep);
    }
}

vector<CPoint> DouglasPeucker(vector<CPoint> &Points, double Tolerance)
{
if (Points.empty() || (Points.size() < 3))
return Points;

    int firstPoint = 0;
    int lastPoint = Points.size() - 1;
    list<int> pointIndexsToKeep ;

    //Add the first and last index to the keepers
    pointIndexsToKeep.push_back(firstPoint);
    pointIndexsToKeep.push_back(lastPoint);

    //The first and the last point cannot be the same
    while (Points[firstPoint]==(Points[lastPoint]))
    {
        lastPoint--;
    }

DouglasPeuckerReduction(Points, firstPoint, lastPoint,
Tolerance, pointIndexsToKeep);

    vector<CPoint> returnPoints ;
    pointIndexsToKeep.sort();
list<int>::iterator theIterator;
    for( theIterator = pointIndexsToKeep.begin(); theIterator != pointIndexsToKeep.end(); theIterator++ )
    {
        returnPoints.push_back(Points[*theIterator]);
    }

return returnPoints;
}

//==============================

matlab算法：

function curve = dp(pnts)
%dp点抽稀算法
clc;
close all;
clear all;

x =  1:0.01:  2;
num = size(x,2);

pnts = 2*sin(8*pi*x) ; % + rand(1,num)*0.8;
pnts = x .* sin(8*pi*x) + rand(1,num)*0.5;
figure; plot( x, pnts,'-.'); title('pnts');

head = [x(1), pnts(1)] ;
tail = [x(end), pnts(end)] ;
  
%距离阈值
dist_th = 0.1; 
 
hold on;
max_dist = 0;
max_dist_i = 0;
%把起始点和终止点加进去
curve = [head; tail];
pnt_index = [1, num];
 
while(1)         
    %目前抽稀后的曲线上的点数
    curve_num = size(curve,1);
   
    %标记是否添加了新点，若有，表明还要继续处理
    add_new_pnt = 0; 
    %  对区间头尾连线，然后计算各点到这条直线的距离 
    for nx = 1:curve_num-1
        cur_pnt = curve(nx,:);
        %下一个抽稀了的曲线上的点
        next_pnt = curve(nx+1,:);
        pnt_d = next_pnt - cur_pnt ;
         
        th = atan2(pnt_d(2), pnt_d(1));
        angle = th*180/pi;
        %直线方程
        % y = kx + b
        k = tan(th);
        b = cur_pnt(2) - k*cur_pnt(1);
        k2 = k*k;
        deno = sqrt(1 + k *k) ;
 
         max_dist = 0;
         pnt_index(nx);
         pnt_index(nx+1);
         
        %对这一区间的点计算到直线的距离
        for i= pnt_index(nx) : pnt_index(nx+1)
            dist = abs(pnts(i) - k*x(i) - b)/deno ;

            if(dist> max_dist)      
                max_dist = dist;
                max_dist_i = i;        
            end 
        end 
        max_dist;
        max_dist_i; 

        far_pnt = [x(max_dist_i), pnts(max_dist_i)];

        %最远的点加进去
        if(max_dist > dist_th)
             curve = [curve(1:nx,:); far_pnt; curve(nx+1:end,:)]; 
             pnt_index = [pnt_index(1:nx), max_dist_i, pnt_index(nx+1:end)];
             %标记添加了新点，可能还要继续处理
             add_new_pnt = 1;        
        end 
    end 
    close all ;
    figure; plot( x, pnts,'-.'); title('pnts');
    hold on;
    plot(curve(:,1), curve(:,2), '-g*');
    drawnow;
     
     %如果各点到直线距离都没有超过阈值则退出
     %处理完毕了，ok了，退出
     if(0 == add_new_pnt)
        break;
     end      
end