【OpenCV入门之三】光流跟踪

光流（optical flow）法是目前分析运动图像比较重要的方法，用来指时变图像的运动速度，是根据运动的物体，对应到图像中亮度模式也在运动得到的。

基本流程

• 读取图像
• 角点提取
• 光流计算
• 跟踪流程
• 输出跟踪图像

读取图像

常用的一些读取文件操作，通常驱动会把相机映射为一个文件。
- fopen
- fseek
- fread
- fclose
- fwrite

角点提取

角点是计算机视觉中获取图像特征的一种方法，广泛应用于运动检测、图像匹配、视觉跟踪、三维重建等领域。
角点定义方法有多种，我们这里以两条边的交点，常见的方法有Harris算子、Shi-Tomasi算子等。
Shi-Tomasi算子是1994年在《Good Features to Track》论文中被提出，OpenCV对应的算法函数命名为 goodFeaturesToTrack，下面我们就来看看该函数的实现原理。

函数定义及实现如下：

 `goodFeaturesToTrack()`
***********************************************************
C++: void goodFeaturesToTrack(
                                InputArray image, 
                                OutputArray corners, 
                                int maxCorners, 
                                double qualityLevel, 
                                double minDistance, 
                                InputArray mask=noArray(), 
                                int blockSize=3, 
                                bool useHarrisDetector=false, 
                                double k=0.04 )

Parameters:

image – 输入 8-bit or floating-point 32-bit, single-channel 图像.
corners – 输出 vector of detected 角点.
maxCorners – 返回最大值 of corners. If there are more corners than are found, the strongest of them is returned.
qualityLevel – Parameter characterizing the 最小特征值 of 图像角点. 例如, if the best corner has the quality measure = 1500, and the qualityLevel=0.01 , then all the corners with the quality measure less than 15 are rejected.
minDistance – 最小 possible 欧拉距离 between the returned 角点.
mask – Optional 感兴趣区域. If the image is not empty (it needs to have the type CV_8UC1 and the same size as image ), it specifies the region in which the corners are detected.
blockSize – Size of an average block for computing a 导数自相关矩阵 over each pixel neighborhood. See cornerEigenValsAndVecs() .
useHarrisDetector – Parameter indicating 是否使用 Harris detector (see cornerHarris()) or cornerMinEigenVal().
k – Free parameter of the Harris detector.

关键一点，在该项目中，该 goodFeaturesToTrack 被用来初始化光流跟踪的特征点。goodFeaturesToTrack具体实现代码如下：

void cv::goodFeaturesToTrack(   InputArray _image, 
                                OutputArray _corners,
                                int maxCorners, 
                                double minDistance,
                                InputArray _mask, 
                                int blockSize,
                                bool useHarrisDetector, 
                                double harrisK )
{
    Mat image = _image.getMat(), mask = _mask.getMat();

    CV_Assert( qualityLevel > 0 && minDistance >= 0 && maxCorners >= 0 );
    CV_Assert( mask.empty() || (mask.type() == CV_8UC1 && mask.size() == image.size()) );

    Mat eig, tmp;
    // 默认采用 cornerMinEigenVal
    if( useHarrisDetector )
        cornerHarris( image, eig, blockSize, 3, harrisK );
    else
        cornerMinEigenVal( image, eig, blockSize, 3 );

    double maxVal = 0;
    minMaxLoc( eig, 0, &maxVal, 0, 0, mask );
    threshold( eig, eig, maxVal*qualityLevel, 0, THRESH_TOZERO );
    dilate( eig, tmp, Mat());

    Size imgsize = image.size();

    vector<const float*> tmpCorners;

    // collect list of pointers to features - put them into temporary image
    for( int y = 1; y < imgsize.height - 1; y++ )
    {
        const float* eig_data = (const float*)eig.ptr(y);
        const float* tmp_data = (const float*)tmp.ptr(y);
        const uchar* mask_data = mask.data ? mask.ptr(y) : 0;

        for( int x = 1; x < imgsize.width - 1; x++ )
        {
            float val = eig_data[x];
            if( val != 0 && val == tmp_data[x] && (!mask_data || mask_data[x]) )
                tmpCorners.push_back(eig_data + x);
        }
    }

    sort( tmpCorners, greaterThanPtr<float>() );
    vector corners;
    size_t i, j, total = tmpCorners.size(), ncorners = 0;

    if(minDistance >= 1)
    {
         // Partition the image into larger grids
        int w = image.cols;
        int h = image.rows;

        const int cell_size = cvRound(minDistance);
        const int grid_width = (w + cell_size - 1) / cell_size;
        const int grid_height = (h + cell_size - 1) / cell_size;

        std::vector > grid(grid_width*grid_height);

        minDistance *= minDistance;

        for( i = 0; i < total; i++ )
        {
            int ofs = (int)((const uchar*)tmpCorners[i] - eig.data);
            int y = (int)(ofs / eig.step);
            int x = (int)((ofs - y*eig.step)/sizeof(float));

            bool good = true;

            int x_cell = x / cell_size;
            int y_cell = y / cell_size;

            int x1 = x_cell - 1;
            int y1 = y_cell - 1;
            int x2 = x_cell + 1;
            int y2 = y_cell + 1;

            // boundary check
            x1 = std::max(0, x1);
            y1 = std::max(0, y1);
            x2 = std::min(grid_width-1, x2);
            y2 = std::min(grid_height-1, y2);

            for( int yy = y1; yy <= y2; yy++ )
            {
                for( int xx = x1; xx <= x2; xx++ )
                {
                    vector  &m = grid[yy*grid_width + xx];

                    if( m.size() )
                    {
                        for(j = 0; j < m.size(); j++)
                        {
                            float dx = x - m[j].x;
                            float dy = y - m[j].y;

                            if( dx*dx + dy*dy < minDistance )
                            {
                                good = false;
                                goto break_out;
                            }
                        }
                    }
                }
            }

            break_out:

            if(good)
            {
                // printf("%d: %d %d -> %d %d, %d, %d -- %d %d %d %d, %d %d, c=%d\n",
                //    i,x, y, x_cell, y_cell, (int)minDistance, cell_size,x1,y1,x2,y2, grid_width,grid_height,c);
                grid[y_cell*grid_width + x_cell].push_back(Point2f((float)x, (float)y));

                corners.push_back(Point2f((float)x, (float)y));
                ++ncorners;

                if( maxCorners > 0 && (int)ncorners == maxCorners )
                    break;
            }
        }
    }
    else
    {
        for( i = 0; i < total; i++ )
        {
            int ofs = (int)((const uchar*)tmpCorners[i] - eig.data);
            int y = (int)(ofs / eig.step);
            int x = (int)((ofs - y*eig.step)/sizeof(float));

            corners.push_back(Point2f((float)x, (float)y));
            ++ncorners;
            if( maxCorners > 0 && (int)ncorners == maxCorners )
                break;
        }
    }

    Mat(corners).convertTo(_corners, _corners.fixedType() ? _corners.type() : CV_32F);

    /*
    for( i = 0; i < total; i++ )
    {
        int ofs = (int)((const uchar*)tmpCorners[i] - eig.data);
        int y = (int)(ofs / eig.step);
        int x = (int)((ofs - y*eig.step)/sizeof(float));

        if( minDistance > 0 )
        {
            for( j = 0; j < ncorners; j++ )
            {
                float dx = x - corners[j].x;
                float dy = y - corners[j].y;
                if( dx*dx + dy*dy < minDistance )
                    break;
            }
            if( j < ncorners )
                continue;
        }

        corners.push_back(Point2f((float)x, (float)y));
        ++ncorners;
        if( maxCorners > 0 && (int)ncorners == maxCorners )
            break;
    }
    */
}

---

中间函数，关键看这个 cornerEigenValsVecs 函数：

// 后面会用到
enum { MINEIGENVAL=0, HARRIS=1, EIGENVALSVECS=2 };
// 自相关函数
void cv::cornerMinEigenVal( InputArray _src, 
                            OutputArray _dst, 
                            int blockSize, 
                            int ksize, 
                            int borderType )
{
    Mat src = _src.getMat();
    _dst.create( src.size(), CV_32F );
    Mat dst = _dst.getMat();
    cornerEigenValsVecs( src, dst, blockSize, ksize, MINEIGENVAL, 0, borderType );
}

---

通过 cornerEigenValsVecs 计算图像二阶导数的自相关矩阵：

static void cornerEigenValsVecs(    const Mat& src, 
                                    Mat& eigenv, 
                                    int block_size,
                                    int aperture_size, 
                                    double k=0.,
                                    int borderType=BORDER_DEFAULT )
{
#ifdef HAVE_TEGRA_OPTIMIZATION
    if (tegra::cornerEigenValsVecs(src, eigenv, block_size, aperture_size, op_type, k, borderType))
        return;
#endif

    int depth = src.depth();
    double scale = (double)(1 << ((aperture_size > 0 ? aperture_size : 3) - 1)) * block_size;
    if( aperture_size < 0 )
        scale *= 2.;
    if( depth == CV_8U )
        scale *= 255.;
    scale = 1./scale;

    CV_Assert( src.type() == CV_8UC1 || src.type() == CV_32FC1 );

    Mat Dx, Dy;
    // 孔径尺寸大于零
    if( aperture_size > 0 )
    {
        Sobel( src, Dx, CV_32F, 1, 0, aperture_size, scale, 0, borderType );
        Sobel( src, Dy, CV_32F, 0, 1, aperture_size, scale, 0, borderType );
    }
    else
    {
        Scharr( src, Dx, CV_32F, 1, 0, scale, 0, borderType );
        Scharr( src, Dy, CV_32F, 0, 1, scale, 0, borderType );
    }

    Size size = src.size();
    Mat cov( size, CV_32FC3 );
    int i, j;

    for( i = 0; i < size.height; i++ )
    {
        float* cov_data = (float*)(cov.data + i*cov.step);
        const float* dxdata = (const float*)(Dx.data + i*Dx.step);
        const float* dydata = (const float*)(Dy.data + i*Dy.step);

        for( j = 0; j < size.width; j++ )
        {
            float dx = dxdata[j];
            float dy = dydata[j];

            cov_data[j*3] = dx*dx;
            cov_data[j*3+1] = dx*dy;
            cov_data[j*3+2] = dy*dy;
        }
    }
    // 滤波操作
    boxFilter(cov, cov, cov.depth(), Size(block_size, block_size),
        Point(-1,-1), false, borderType );

    if( op_type == MINEIGENVAL )
        calcMinEigenVal( cov, eigenv );
    else if( op_type == HARRIS )
        calcHarris( cov, eigenv, k );
    else if( op_type == EIGENVALSVECS )
        calcEigenValsVecs( cov, eigenv );
}

按照规定的参数设置，特征点提取到此完成，我们可以通过 imshow 函数验证结果。

---

光流计算

计算一个稀疏特征光流使用Lucas Kanade迭代法与金字塔。OpenCV 函数为 calcOpticalFlowPyrLK 。这里通过prevImg定位特征点和 nextImg对物体的跟踪那么处理第二帧的时候这两个参数都会有了，可以进行跟踪了。

该函数实现的原理来自于Jean-Yves Bouguet的论文“Pyramidal Implementation of the Lucas Kanade Feature Tracker Description of the algorithm”中提出的基于金字塔Lucas Kanade光流法。
该算法基于三个假设条件：
- 亮度恒定
- 时间连续或者运动是“小运动”
- 空间一致
接下来就是通过这三点假设构建一个有效的跟踪算法。

具体实现代码如下所示：

//! computes sparse optical flow using multi-scale Lucas-Kanade algorithm
CV_EXPORTS_W void calcOpticalFlowPyrLK( InputArray prevImg, 
                            InputArray nextImg,
                            InputArray prevPts, 
                            CV_OUT InputOutputArray nextPts,
                            OutputArray status,
                            OutputArray err,
                            Size winSize=Size(21,21), 
                            int maxLevel=3,
                            TermCriteria criteria=TermCriteria(TermCriteria::COUNT+TermCriteria::EPS, 30, 0.01),
                            double minEigThreshold=1e-4);

Parameters: 
prevImg – first 8-bit 输入图像 or 金字塔.
nextImg – second 输入图像 or pyramid of the same size and the same type as prevImg.
prevPts – vector of 2D 角点 for which the flow needs to be found; 
nextPts – output vector of 2D 角点 containing the calculated new positions of input features in the second image;
status – output 状态 vector (of unsigned chars); 
err – output vector of 错误;
winSize – size of the 搜索窗口 at each pyramid level.
maxLevel – 0-based maximal pyramid level number; if set to 0, pyramids are not used (single level), if set to 1, two levels are used, and so on; 
criteria – parameter, specifying the termination criteria of the iterative search algorithm
flags – 操作标志：
OPTFLOW_USE_INITIAL_FLOW uses initial estimations, stored in nextPts; 
OPTFLOW_LK_GET_MIN_EIGENVALS use minimum eigen values as an error measure ;
minEigThreshold – the algorithm calculates the minimum eigen value of a 2x2 normal matrix of optical flow equations.

---

void cv::calcOpticalFlowPyrLK( InputArray _prevImg, 
                           InputArray _nextImg,
                           InputArray _prevPts,
                           InputOutputArray _nextPts,
                           OutputArray _status, 
                           OutputArray _err,
                           Size winSize, 
                           int maxLevel,
                           TermCriteria criteria,
                           int flags, 
                           double minEigThreshold )
{
    Mat prevPtsMat = _prevPts.getMat();
    const int derivDepth = DataType::depth;

    CV_Assert( maxLevel >= 0 && winSize.width > 2 && winSize.height > 2 );

    int level=0, i, npoints;
    CV_Assert( (npoints = prevPtsMat.checkVector(2, CV_32F, true)) >= 0 );

    if( npoints == 0 )
    {
        _nextPts.release();
        _status.release();
        _err.release();
        return;
    }

    if( !(flags & OPTFLOW_USE_INITIAL_FLOW) )
        _nextPts.create(prevPtsMat.size(), prevPtsMat.type(), -1, true);

    Mat nextPtsMat = _nextPts.getMat();
    CV_Assert( nextPtsMat.checkVector(2, CV_32F, true) == npoints );

    const Point2f* prevPts = (const Point2f*)prevPtsMat.data;
    Point2f* nextPts = (Point2f*)nextPtsMat.data;

    _status.create((int)npoints, 1, CV_8U, -1, true);
    Mat statusMat = _status.getMat(), errMat;
    CV_Assert( statusMat.isContinuous() );
    uchar* status = statusMat.data;
    float* err = 0;

    for( i = 0; i < npoints; i++ )
        status[i] = true;

    if( _err.needed() )
    {
        _err.create((int)npoints, 1, CV_32F, -1, true);
        errMat = _err.getMat();
        CV_Assert( errMat.isContinuous() );
        err = (float*)errMat.data;
    }

    vector prevPyr, nextPyr;
    int levels1 = -1;
    int lvlStep1 = 1;
    int levels2 = -1;
    int lvlStep2 = 1;

    if(_prevImg.kind() == _InputArray::STD_VECTOR_MAT)
    {
        _prevImg.getMatVector(prevPyr);

        levels1 = int(prevPyr.size()) - 1;
        CV_Assert(levels1 >= 0);

        if (levels1 % 2 == 1 && prevPyr[0].channels() * 2 == prevPyr[1].channels() && prevPyr[1].depth() == derivDepth)
        {
            lvlStep1 = 2;
            levels1 /= 2;
        }

        // ensure that pyramid has reqired padding
        if(levels1 > 0)
        {
            Size fullSize;
            Point ofs;
            prevPyr[lvlStep1].locateROI(fullSize, ofs);
            CV_Assert(ofs.x >= winSize.width && ofs.y >= winSize.height
                && ofs.x + prevPyr[lvlStep1].cols + winSize.width <= fullSize.width
                && ofs.y + prevPyr[lvlStep1].rows + winSize.height <= fullSize.height);
        }

        if(levels1 < maxLevel)
            maxLevel = levels1;
    }

    if(_nextImg.kind() == _InputArray::STD_VECTOR_MAT)
    {
        _nextImg.getMatVector(nextPyr);

        levels2 = int(nextPyr.size()) - 1;
        CV_Assert(levels2 >= 0);

        if (levels2 % 2 == 1 && nextPyr[0].channels() * 2 == nextPyr[1].channels() && nextPyr[1].depth() == derivDepth)
        {
            lvlStep2 = 2;
            levels2 /= 2;
        }

        // ensure that pyramid has reqired padding
        if(levels2 > 0)
        {
            Size fullSize;
            Point ofs;
            nextPyr[lvlStep2].locateROI(fullSize, ofs);
            CV_Assert(ofs.x >= winSize.width && ofs.y >= winSize.height
                && ofs.x + nextPyr[lvlStep2].cols + winSize.width <= fullSize.width
                && ofs.y + nextPyr[lvlStep2].rows + winSize.height <= fullSize.height);
        }

        if(levels2 < maxLevel)
            maxLevel = levels2;
    }

    if (levels1 < 0)
        maxLevel = buildOpticalFlowPyramid(_prevImg, prevPyr, winSize, maxLevel, false);

    if (levels2 < 0)
        maxLevel = buildOpticalFlowPyramid(_nextImg, nextPyr, winSize, maxLevel, false);

    if( (criteria.type & TermCriteria::COUNT) == 0 )
        criteria.maxCount = 30;
    else
        criteria.maxCount = std::min(std::max(criteria.maxCount, 0), 100);
    if( (criteria.type & TermCriteria::EPS) == 0 )
        criteria.epsilon = 0.01;
    else
        criteria.epsilon = std::min(std::max(criteria.epsilon, 0.), 10.);
    criteria.epsilon *= criteria.epsilon;

    // dI/dx ~ Ix, dI/dy ~ Iy
    Mat derivIBuf;
    if(lvlStep1 == 1)
        derivIBuf.create(prevPyr[0].rows + winSize.height*2, prevPyr[0].cols + winSize.width*2, CV_MAKETYPE(derivDepth, prevPyr[0].channels() * 2));

    for( level = maxLevel; level >= 0; level-- )
    {
        Mat derivI;
        if(lvlStep1 == 1)
        {
            Size imgSize = prevPyr[level * lvlStep1].size();
            Mat _derivI( imgSize.height + winSize.height*2,
                imgSize.width + winSize.width*2, derivIBuf.type(), derivIBuf.data );
            derivI = _derivI(Rect(winSize.width, winSize.height, imgSize.width, imgSize.height));
            calcSharrDeriv(prevPyr[level * lvlStep1], derivI);
            copyMakeBorder(derivI, _derivI, winSize.height, winSize.height, winSize.width, winSize.width, BORDER_CONSTANT|BORDER_ISOLATED);
        }
        else
            derivI = prevPyr[level * lvlStep1 + 1];

        CV_Assert(prevPyr[level * lvlStep1].size() == nextPyr[level * lvlStep2].size());
        CV_Assert(prevPyr[level * lvlStep1].type() == nextPyr[level * lvlStep2].type());

#ifdef HAVE_TEGRA_OPTIMIZATION
        typedef tegra::LKTrackerInvoker LKTrackerInvoker;
#else
        typedef cv::detail::LKTrackerInvoker LKTrackerInvoker;
#endif

        parallel_for_(Range(0, npoints), LKTrackerInvoker(prevPyr[level * lvlStep1], derivI,
                                                          nextPyr[level * lvlStep2], prevPts, nextPts,
                                                          status, err,
                                                          winSize, criteria, level, maxLevel,
                                                          flags, (float)minEigThreshold));
    }
}

---

//! constructs a pyramid which can be used as input for calcOpticalFlowPyrLK
CV_EXPORTS_W int buildOpticalFlowPyramid(InputArray img, 
                                        OutputArrayOfArrays pyramid,
                                        Size winSize, 
                                        int maxLevel, 
                                        bool withDerivatives = true,
                                        int pyrBorder = BORDER_REFLECT_101, 
                                        int derivBorder = BORDER_CONSTANT,
                                        bool tryReuseInputImage = true);

---

int cv::buildOpticalFlowPyramid(InputArray _img, OutputArrayOfArrays pyramid, Size winSize, int maxLevel, bool withDerivatives,
                                int pyrBorder, int derivBorder, bool tryReuseInputImage)
{
    Mat img = _img.getMat();
    CV_Assert(img.depth() == CV_8U && winSize.width > 2 && winSize.height > 2 );
    int pyrstep = withDerivatives ? 2 : 1;

    pyramid.create(1, (maxLevel + 1) * pyrstep, 0 /*type*/, -1, true, 0);

    int derivType = CV_MAKETYPE(DataType::depth, img.channels() * 2);

    //level 0
    bool lvl0IsSet = false;
    if(tryReuseInputImage && img.isSubmatrix() && (pyrBorder & BORDER_ISOLATED) == 0)
    {
        Size wholeSize;
        Point ofs;
        img.locateROI(wholeSize, ofs);
        if (ofs.x >= winSize.width && ofs.y >= winSize.height
              && ofs.x + img.cols + winSize.width <= wholeSize.width
              && ofs.y + img.rows + winSize.height <= wholeSize.height)
        {
            pyramid.getMatRef(0) = img;
            lvl0IsSet = true;
        }
    }

    if(!lvl0IsSet)
    {
        Mat& temp = pyramid.getMatRef(0);

        if(!temp.empty())
            temp.adjustROI(winSize.height, winSize.height, winSize.width, winSize.width);
        if(temp.type() != img.type() || temp.cols != winSize.width*2 + img.cols || temp.rows != winSize.height * 2 + img.rows)
            temp.create(img.rows + winSize.height*2, img.cols + winSize.width*2, img.type());

        if(pyrBorder == BORDER_TRANSPARENT)
            img.copyTo(temp(Rect(winSize.width, winSize.height, img.cols, img.rows)));
        else
            copyMakeBorder(img, temp, winSize.height, winSize.height, winSize.width, winSize.width, pyrBorder);
        temp.adjustROI(-winSize.height, -winSize.height, -winSize.width, -winSize.width);
    }

    Size sz = img.size();
    Mat prevLevel = pyramid.getMatRef(0);
    Mat thisLevel = prevLevel;

    for(int level = 0; level <= maxLevel; ++level)
    {
        if (level != 0)
        {
            Mat& temp = pyramid.getMatRef(level * pyrstep);

            if(!temp.empty())
                temp.adjustROI(winSize.height, winSize.height, winSize.width, winSize.width);
            if(temp.type() != img.type() || temp.cols != winSize.width*2 + sz.width || temp.rows != winSize.height * 2 + sz.height)
                temp.create(sz.height + winSize.height*2, sz.width + winSize.width*2, img.type());

            thisLevel = temp(Rect(winSize.width, winSize.height, sz.width, sz.height));
            pyrDown(prevLevel, thisLevel, sz);

            if(pyrBorder != BORDER_TRANSPARENT)
                copyMakeBorder(thisLevel, temp, winSize.height, winSize.height, winSize.width, winSize.width, pyrBorder|BORDER_ISOLATED);
            temp.adjustROI(-winSize.height, -winSize.height, -winSize.width, -winSize.width);
        }

        if(withDerivatives)
        {
            Mat& deriv = pyramid.getMatRef(level * pyrstep + 1);

            if(!deriv.empty())
                deriv.adjustROI(winSize.height, winSize.height, winSize.width, winSize.width);
            if(deriv.type() != derivType || deriv.cols != winSize.width*2 + sz.width || deriv.rows != winSize.height * 2 + sz.height)
                deriv.create(sz.height + winSize.height*2, sz.width + winSize.width*2, derivType);

            Mat derivI = deriv(Rect(winSize.width, winSize.height, sz.width, sz.height));
            calcSharrDeriv(thisLevel, derivI);

            if(derivBorder != BORDER_TRANSPARENT)
                copyMakeBorder(derivI, deriv, winSize.height, winSize.height, winSize.width, winSize.width, derivBorder|BORDER_ISOLATED);
            deriv.adjustROI(-winSize.height, -winSize.height, -winSize.width, -winSize.width);
        }

        sz = Size((sz.width+1)/2, (sz.height+1)/2);
        if( sz.width <= winSize.width || sz.height <= winSize.height )
        {
            pyramid.create(1, (level + 1) * pyrstep, 0 /*type*/, -1, true, 0);//check this
            return level;
        }

        prevLevel = thisLevel;
    }

    return maxLevel;
}

---

函数 calcOpticalFlowPyrLK实现了金字塔中 Lucas-Kanade 光流计算的稀疏迭代版本。 它根据给出的前一帧特征点坐标计算当前视频帧上的特征点坐标（函数寻找具有子象素精度的坐标值）。

跟踪流程

prew_pts = cur_pts;

跟踪流程如上图所示，具体就不做介绍。

输出跟踪图像

通过以下可视化功能，输出图像移动的位置信息。
-circle
-imwrite
-imshow

上述就是基于OpenCV光流跟踪的实现过程，至此，我们学习了如何读取文件，如何调用OpenCV提供的库函数，更重要的是我们掌握了对应库函数实现原理，提高了我们的理论基础。
最后，通过一整套流程，完成了光流的顺利结项。