c++ - 使用 C++ 和 opencv 进行图像缩放的 Spline Catmull-Rom

Question

我正在尝试使用 C++ 和 OpenCV 实现用于图像缩放的样条 Catmull-Rom。我进行了两个测试，第一个是图像缩放 (X2)，第二个是图像重建(缩放图像抽取)。我的问题是，当我显示像素值时，在插值图像中出现一些白色和黑色像素( image1 )我发现白色像素具有负值，黑色像素具有大于 255 的值，重建的图像也是如此出现模糊( image2 和 image3 )。

 float CalCurveInt(float t, float p0, float p1, float p2, float p3)
    {
    
        float t2 = t * t;
        float t3 = t2 * t;
    
        float x = 0.5f * ((2.0f * p1) +
            (-p0 + p2) * t +
            (2.0f * p0 - 5.0f * p1 + 4 * p2 - p3) * t2 +
            (-p0 + 3.0f * p1 - 3.0f * p2 + p3) * t3);
    return x;
    }

    Mat CalcCatmull(Mat &src, int zoom)
    {
        int v1, v2, v3, v4, Ptr, Xmax, Ymax;
        float Result, t, c1, c2, c3, c4;
        //------------------------------------------------------------
        Xmax = src.cols;
        Ymax = src.rows;
        Size srcSize(zoom*Xmax, Ymax);
        Mat dst(srcSize, CV_8UC1);
    
        for (int j = 0; j < Ymax; j++)
        {
            Ptr = 0;
            for (int i = 0; i < Xmax; i++)
            {
                v1 = i - 1; v2 = i; v3 = i + 1; v4 = i + 2;
    
                if (i - 1 < 0)      v1 = 0;
                if (Xmax <= i + 1)  v3 = Xmax - 1;
                if (Xmax <= i + 2)  v4 = Xmax - 1;
    
                for (double J = 1; J <= zoom; J++)
                {
                    t = J / zoom;
                    Result = 0.0;
    
                    c1 = src.at<uchar>(j, v1);
                    c2 = src.at<uchar>(j, v2);
                    c3 = src.at<uchar>(j, v3);
                    c4 = src.at<uchar>(j, v4);
    
                    Result = CalCurveInt(t, c1, c2, c3, c4);
                    dst.at<uchar>(j, Ptr) = abs(Result);
                    Ptr++;
                }
            }
        }

        //------------------------------------------------
        Xmax = dst.cols;
        Ymax = dst.rows;
    
        Size srcSize1(Xmax, zoom*Ymax);
        Mat dest(srcSize1, CV_8UC1);
    
        for (int i = 0; i < Xmax; i++)
        {
            Ptr = 0;
            for (int j = 0; j < Ymax; j++)
            {
    
                v1 = j - 1; v2 = j; v3 = j + 1; v4 = j + 2;
    
                if (j - 1 < 0)      v1 = 0;
                if (Ymax <= j + 1)  v3 = Ymax - 1;
                if (Ymax <= j + 2)  v4 = Ymax - 1;
    
                for (double J = 1; J <= zoom; J++)
                {
                    t = J / zoom;
                    Result = 0.0;
    
                    c1 = dst.at<uchar>(v1, i);
                    c2 = dst.at<uchar>(v2, i);
                    c3 = dst.at<uchar>(v3, i);
                    c4 = dst.at<uchar>(v4, i);
                    Result = CalCurveInt(t, c1, c2, c3, c4);           
                    dest.at<uchar>(Ptr, i) = Result;
                    Ptr++;
                }
            }
        }
    
        return dest;
    }
    
    float zoom = 2.0;

    
    int main()
    {
        Mat src = imread("fruits.png", CV_LOAD_IMAGE_GRAYSCALE);
        int width = src.cols;
        int hight = src.rows;
    
        /*Image Decimation*/
        Size srcdSize(int(width / zoom), int(hight / zoom));
        Mat srcd;
        pyrDown(src, srcd, srcdSize);
        imshow("decimation", srcd);
    
        Mat dst = CalcCatmull(srcd, zoom);
    
        imshow("Image Source", src);
        imshow("Image dest", dst);
        imwrite("Image dest.png", dst);
    
        waitKey(0);
        return 0;
    }

提前致谢。

Answer 1

我的旧实现似乎运行良好。

#include <iostream>
#include <vector>
#include <stdio.h>
#include <stdarg.h>
#include "opencv2/opencv.hpp"
#include "fstream"
#include "iostream"
using namespace std;
using namespace cv;

//-----------------------------------------------------------------------------------------------------
// Take 2 points, compute values between p1 and p2, p0 and p3 need for tangents computation
// on the bouunds. Parameter t - changes in range 0 to 1 (0 - we are in p1, 1 - we are in p2)
//-----------------------------------------------------------------------------------------------------
void PointOnCurve(Point2f &out, float t, Point2f p0, Point2f p1, Point2f p2, Point2f p3)
{
    float t2 = t * t;
    float t3 = t2 * t;
    out.x = 0.5f * ( ( 2.0f * p1.x ) + ( -p0.x + p2.x ) * t +
        ( 2.0f * p0.x - 5.0f * p1.x + 4 * p2.x - p3.x ) * t2 +
        ( -p0.x + 3.0f * p1.x - 3.0f * p2.x + p3.x ) * t3 );
    out.y = 0.5f * ( ( 2.0f * p1.y ) +  ( -p0.y + p2.y ) * t +
        ( 2.0f * p0.y - 5.0f * p1.y + 4 * p2.y - p3.y ) * t2 +
        ( -p0.y + 3.0f * p1.y - 3.0f * p2.y + p3.y ) * t3 );
}
//-----------------------------------------------------------------------------------------------------
// interpolation of 4х4 patch
// 
//          S * S * S * S 
//          * * * * * * * 
//          S * S * S * S 
//          * * * * * * * 
//          S * S * S * S 
//          * * * * * * * 
//          S * S * S * S 
//  
//          S- pixels of source imgage
//
//          sequentially take 2 middle columns and computte D.
//
//          S * 1 * 2 * S
//          * * * * * * *
//          S * 1 * 2 * S
//          * * D * D * *
//          S * 1 * 2 * S
//          * * * * * * *
//          S * 1 * 2 * S
//
//          same for rows and we will have F
//
//          S * S * S * S
//          * * * * * * *
//          3 * 3 F 3 * 3
//          * * D * D * *
//          4 * 4 F 4 * 4
//          * * * * * * *
//          S * S * S * S
//
//          then compute diagonals and after averafing with neihbours will find С
//
//          1 * S * S * 2
//          * * * * * * *
//          S * 1 F 2 * S
//          * * D C D * *
//          S * 2 F 1 * S
//          * * * * * * *
//          2 * S * S * 1
//-----------------------------------------------------------------------------------------------------
void PointOnSurface(Mat& src,Mat& dst)
{
float t=0.5;
Point2f out;
dst=Mat(3,3,CV_32FC1);
// Угловые точки результата совпадают с точками центральной ячейки исходного патча
dst.at<float>(0,0)=src.at<float>(1,1);
dst.at<float>(2,0)=src.at<float>(2,1);

dst.at<float>(0,2)=src.at<float>(1,2);
dst.at<float>(2,2)=src.at<float>(2,2);

Point2f p0;
Point2f p1;
Point2f p2;
Point2f p3;

p0.x=0;p0.y=src.at<float>(0,1);
p1.x=1;p1.y=src.at<float>(1,1);
p2.x=2;p2.y=src.at<float>(2,1);
p3.x=3;p3.y=src.at<float>(3,1);

PointOnCurve(out,t,p0,p1,p2,p3);
dst.at<float>(1,0)=out.y;

p0.x=0;p0.y=src.at<float>(0,2);
p1.x=1;p1.y=src.at<float>(1,2);
p2.x=2;p2.y=src.at<float>(2,2);
p3.x=3;p3.y=src.at<float>(3,2);

PointOnCurve(out,t,p0,p1,p2,p3);
dst.at<float>(1,2)=out.y;

p0.x=0;p0.y=src.at<float>(1,0);
p1.x=1;p1.y=src.at<float>(1,1);
p2.x=2;p2.y=src.at<float>(1,2);
p3.x=3;p3.y=src.at<float>(1,3);


PointOnCurve(out,t,p0,p1,p2,p3);
dst.at<float>(0,1)=out.y;

p0.x=0;p0.y=src.at<float>(2,0);
p1.x=1;p1.y=src.at<float>(2,1);
p2.x=2;p2.y=src.at<float>(2,2);
p3.x=3;p3.y=src.at<float>(2,3);

PointOnCurve(out,t,p0,p1,p2,p3);
dst.at<float>(2,1)=out.y;

// diagonals

// 1
p0.x=0;p0.y=src.at<float>(0,0);
p1.x=1;p1.y=src.at<float>(1,1);
p2.x=2;p2.y=src.at<float>(2,2);
p3.x=3;p3.y=src.at<float>(3,3);


PointOnCurve(out,t,p0,p1,p2,p3);
float d1=out.y;

// 2
p0.x=0;p0.y=src.at<float>(3,0);
p1.x=1;p1.y=src.at<float>(2,1);
p2.x=2;p2.y=src.at<float>(1,2);
p3.x=3;p3.y=src.at<float>(0,3);

PointOnCurve(out,t,p0,p1,p2,p3);
float d2=out.y;

// averaging
dst.at<float>(1,1)=1.0/6.0*(d1+d2+dst.at<float>(0,1)+dst.at<float>(1,0)+dst.at<float>(1,2)+dst.at<float>(2,1));
}
//-----------------------------------------------------------------------------------------------------
//
//-----------------------------------------------------------------------------------------------------
//-----------------------------------------------------------------------------------------------------
void Scale2Times(Mat& src_img,Mat &dstImg)
{
    Mat imgf,img;
    Mat dst;
    Mat src;
    src_img.convertTo(imgf,CV_32FC1,1.0/255.0);

    cv::copyMakeBorder(imgf,img,1,1,1,1,cv::BORDER_REFLECT);

    dstImg=Mat(src_img.rows*2,src_img.cols*2,CV_32FC1);

    for(int i=0;i<img.rows-4;i++)
    {
        for(int j=0;j<img.cols-4;j++)
        {
            img(Rect(j,i,4,4)).copyTo(src);
            PointOnSurface(src,dst);
            dst.copyTo(dstImg(Rect(2*j+1,2*i+1,3,3)));
        }
    }
    dstImg=dstImg(Rect(0,0,dstImg.cols-2,dstImg.rows-2)).clone();
}
//-----------------------------------------------------------------------------------------------------
//
//-----------------------------------------------------------------------------------------------------
int main( int argc, char** argv )
{
    namedWindow("Src");
    namedWindow("cvResize");
    namedWindow("Catmul-Rom");
    Mat Img=imread("C:\\ImagesForTest\\1.tiff",0);
    imshow("Src",Img);
    Mat dstImg;
    Scale2Times(Img,dstImg);
    imshow("Catmul-Rom",dstImg);

    Mat ImgLin(Img.rows*2,Img.cols*2,CV_8UC1);
    cv::resize(Img,ImgLin,Size(Img.cols*2,Img.rows*2),INTER_CUBIC);
    imshow("cvResize",ImgLin);

    waitKey(0);
    //getchar();

    return 0;
}