我正在徘徊在二维点数组中检测“数字”的最佳方法是什么。
在这个例子中，我有两个“模板”。图 1 是模板，图 2 是模板。这些模板中的每一个仅作为具有 x,y 坐标的点向量存在。
假设我们有第三个向量，其中的点具有 x,y 坐标
找出和隔离与第三个数组中的前两个数组之一匹配的点的最佳方法是什么。（包括缩放、旋转）？
我一直在尝试最近的邻居（FlannBasedMatcehr）甚至 SVM 实现，但它似乎没有给我任何结果，我认为模板匹配似乎也不是要走的路。我不是在处理图像，而是在内存中的 2D 点上工作......
特别是因为输入向量总是比要比较的原始数据集有更多的点。
它需要做的就是在数组中找到与模板匹配的点。
我不是机器学习或 opencv 的“专家”。我想我从一开始就忽略了一些东西......
非常感谢您的帮助/建议。
只是为了好玩，我尝试了这个：
这种方法非常幼稚，并且具有O(m*n²)n 个数据点和大小为 m（点）的单个模式的复杂性。对于一些最近邻搜索方法，这种复杂性可能会增加。所以你必须考虑它是否对你的应用程序不够有效。
一些改进可能包括一些不选择所有 n² 点组合的启发式方法，但是您需要最大模式缩放的背景信息或类似的东西。
为了评估，我首先创建了一个模式：
然后我创建随机点并在其中的某处添加模式（缩放、旋转和平移）：
经过一些计算后，此方法可以识别模式。红线显示了为转换计算选择的点。
这是代码：
// draw a set of points on a given destination image
void drawPoints(cv::Mat & image, std::vector<cv::Point2f> points, cv::Scalar color = cv::Scalar(255,255,255), float size=10)
{
for(unsigned int i=0; i<points.size(); ++i)
{
cv::circle(image, points[i], 0, color, size);
}
}
// assumes a 2x3 (affine) transformation (CV_32FC1). does not change the input points
std::vector<cv::Point2f> applyTransformation(std::vector<cv::Point2f> points, cv::Mat transformation)
{
for(unsigned int i=0; i<points.size(); ++i)
{
const cv::Point2f tmp = points[i];
points[i].x = tmp.x * transformation.at<float>(0,0) + tmp.y * transformation.at<float>(0,1) + transformation.at<float>(0,2) ;
points[i].y = tmp.x * transformation.at<float>(1,0) + tmp.y * transformation.at<float>(1,1) + transformation.at<float>(1,2) ;
}
return points;
}
const float PI = 3.14159265359;
// similarity transformation uses same scaling along both axes, rotation and a translation part
cv::Mat composeSimilarityTransformation(float s, float r, float tx, float ty)
{
cv::Mat transformation = cv::Mat::zeros(2,3,CV_32FC1);
// compute rotation matrix and scale entries
float rRad = PI*r/180.0f;
transformation.at<float>(0,0) = s*cosf(rRad);
transformation.at<float>(0,1) = s*sinf(rRad);
transformation.at<float>(1,0) = -s*sinf(rRad);
transformation.at<float>(1,1) = s*cosf(rRad);
// translation
transformation.at<float>(0,2) = tx;
transformation.at<float>(1,2) = ty;
return transformation;
}
// create random points
std::vector<cv::Point2f> createPointSet(cv::Size2i imageSize, std::vector<cv::Point2f> pointPattern, unsigned int nRandomDots = 50)
{
// subtract center of gravity to allow more intuitive rotation
cv::Point2f centerOfGravity(0,0);
for(unsigned int i=0; i<pointPattern.size(); ++i)
{
centerOfGravity.x += pointPattern[i].x;
centerOfGravity.y += pointPattern[i].y;
}
centerOfGravity.x /= (float)pointPattern.size();
centerOfGravity.y /= (float)pointPattern.size();
pointPattern = applyTransformation(pointPattern, composeSimilarityTransformation(1,0,-centerOfGravity.x, -centerOfGravity.y));
// create random points
//unsigned int nRandomDots = 0;
std::vector<cv::Point2f> pointset;
srand (time(NULL));
for(unsigned int i =0; i<nRandomDots; ++i)
{
pointset.push_back( cv::Point2f(rand()%imageSize.width, rand()%imageSize.height) );
}
cv::Mat image = cv::Mat::ones(imageSize,CV_8UC3);
image = cv::Scalar(255,255,255);
drawPoints(image, pointset, cv::Scalar(0,0,0));
cv::namedWindow("pointset"); cv::imshow("pointset", image);
// add point pattern to a random location
float scaleFactor = rand()%30 + 10.0f;
float translationX = rand()%(imageSize.width/2)+ imageSize.width/4;
float translationY = rand()%(imageSize.height/2)+ imageSize.height/4;
float rotationAngle = rand()%360;
std::cout << "s: " << scaleFactor << " r: " << rotationAngle << " t: " << translationX << "/" << translationY << std::endl;
std::vector<cv::Point2f> transformedPattern = applyTransformation(pointPattern,composeSimilarityTransformation(scaleFactor,rotationAngle,translationX,translationY));
//std::vector<cv::Point2f> transformedPattern = applyTransformation(pointPattern,trans);
drawPoints(image, transformedPattern, cv::Scalar(0,0,0));
drawPoints(image, transformedPattern, cv::Scalar(0,255,0),3);
cv::imwrite("dataPoints.png", image);
cv::namedWindow("pointset + pattern"); cv::imshow("pointset + pattern", image);
for(unsigned int i=0; i<transformedPattern.size(); ++i)
pointset.push_back(transformedPattern[i]);
return pointset;
}
void programDetectPointPattern()
{
cv::Size2i imageSize(640,480);
// create a point pattern, this can be in any scale and any relative location
std::vector<cv::Point2f> pointPattern;
pointPattern.push_back(cv::Point2f(0,0));
pointPattern.push_back(cv::Point2f(2,0));
pointPattern.push_back(cv::Point2f(4,0));
pointPattern.push_back(cv::Point2f(1,2));
pointPattern.push_back(cv::Point2f(3,2));
pointPattern.push_back(cv::Point2f(2,4));
// transform the pattern so it can be drawn
cv::Mat trans = cv::Mat::ones(2,3,CV_32FC1);
trans.at<float>(0,0) = 20.0f; // scale x
trans.at<float>(1,1) = 20.0f; // scale y
trans.at<float>(0,2) = 20.0f; // translation x
trans.at<float>(1,2) = 20.0f; // translation y
// draw the pattern
cv::Mat drawnPattern = cv::Mat::ones(cv::Size2i(128,128),CV_8U);
drawnPattern *= 255;
drawPoints(drawnPattern,applyTransformation(pointPattern, trans), cv::Scalar(0),5);
// display and save pattern
cv::imwrite("patternToDetect.png", drawnPattern);
cv::namedWindow("pattern"); cv::imshow("pattern", drawnPattern);
// draw the points and the included pattern
std::vector<cv::Point2f> pointset = createPointSet(imageSize, pointPattern);
cv::Mat image = cv::Mat(imageSize, CV_8UC3);
image = cv::Scalar(255,255,255);
drawPoints(image,pointset, cv::Scalar(0,0,0));
// normally we would have to use some nearest neighbor distance computation, but to make it easier here,
// we create a small area around every point, which allows to test for point existence in a small neighborhood very efficiently (for small images)
// in the real application this "inlier" check should be performed by k-nearest neighbor search and threshold the distance,
// efficiently evaluated by a kd-tree
cv::Mat pointImage = cv::Mat::zeros(imageSize,CV_8U);
float maxDist = 3.0f; // how exact must the pattern be recognized, can there be some "noise" in the position of the data points?
drawPoints(pointImage, pointset, cv::Scalar(255),maxDist);
cv::namedWindow("pointImage"); cv::imshow("pointImage", pointImage);
// choose two points from the pattern (can be arbitrary so just take the first two)
cv::Point2f referencePoint1 = pointPattern[0];
cv::Point2f referencePoint2 = pointPattern[1];
cv::Point2f diff1; // difference vector
diff1.x = referencePoint2.x - referencePoint1.x;
diff1.y = referencePoint2.y - referencePoint1.y;
float referenceLength = sqrt(diff1.x*diff1.x + diff1.y*diff1.y);
diff1.x = diff1.x/referenceLength; diff1.y = diff1.y/referenceLength;
std::cout << "reference: " << std::endl;
std::cout << referencePoint1 << std::endl;
// now try to find the pattern
for(unsigned int j=0; j<pointset.size(); ++j)
{
cv::Point2f targetPoint1 = pointset[j];
for(unsigned int i=0; i<pointset.size(); ++i)
{
cv::Point2f targetPoint2 = pointset[i];
cv::Point2f diff2;
diff2.x = targetPoint2.x - targetPoint1.x;
diff2.y = targetPoint2.y - targetPoint1.y;
float targetLength = sqrt(diff2.x*diff2.x + diff2.y*diff2.y);
diff2.x = diff2.x/targetLength; diff2.y = diff2.y/targetLength;
// with nearest-neighborhood search this line will be similar or the maximal neighbor distance must be relative to targetLength!
if(targetLength < maxDist) continue;
// scale:
float s = targetLength/referenceLength;
// rotation:
float r = -180.0f/PI*(atan2(diff2.y,diff2.x) + atan2(diff1.y,diff1.x));
// scale and rotate the reference point to compute the translation needed
std::vector<cv::Point2f> origin;
origin.push_back(referencePoint1);
origin = applyTransformation(origin, composeSimilarityTransformation(s,r,0,0));
// compute the translation which maps the two reference points on the two target points
float tx = targetPoint1.x - origin[0].x;
float ty = targetPoint1.y - origin[0].y;
std::vector<cv::Point2f> transformedPattern = applyTransformation(pointPattern,composeSimilarityTransformation(s,r,tx,ty));
// now test if all transformed pattern points can be found in the dataset
bool found = true;
for(unsigned int i=0; i<transformedPattern.size(); ++i)
{
cv::Point2f curr = transformedPattern[i];
// here we check whether there is a point drawn in the image. If you have no image you will have to perform a nearest neighbor search.
// this can be done with a balanced kd-tree in O(log n) time
// building such a balanced kd-tree has to be done once for the whole dataset and needs O(n*(log n)) afair
if((curr.x >= 0)&&(curr.x <= pointImage.cols-1)&&(curr.y>=0)&&(curr.y <= pointImage.rows-1))
{
if(pointImage.at<unsigned char>(curr.y, curr.x) == 0) found = false;
// if working with kd-tree: if nearest neighbor distance > maxDist => found = false;
}
else found = false;
}
if(found)
{
std::cout << composeSimilarityTransformation(s,r,tx,ty) << std::endl;
cv::Mat currentIteration;
image.copyTo(currentIteration);
cv::circle(currentIteration,targetPoint1,5, cv::Scalar(255,0,0),1);
cv::circle(currentIteration,targetPoint2,5, cv::Scalar(255,0,255),1);
cv::line(currentIteration,targetPoint1,targetPoint2,cv::Scalar(0,0,255));
drawPoints(currentIteration, transformedPattern, cv::Scalar(0,0,255),4);
cv::imwrite("detectedPattern.png", currentIteration);
cv::namedWindow("iteration"); cv::imshow("iteration", currentIteration); cv::waitKey(-1);
}
}
}
}