I have an unorganized point cloud of the scene. Below is a screenshot of the point cloud-
I want to compose an image from this point cloud. Below is the code snippet-
#include <iostream>
#include <pcl/io/pcd_io.h>
#include <pcl/point_types.h>
#include <opencv2/opencv.hpp>
int main(int argc, char** argv)
{
pcl::PointCloud<pcl::PointXYZRGBA>::Ptr cloud(new pcl::PointCloud<pcl::PointXYZRGBA>);
pcl::io::loadPCDFile("file.pcd", *cloud);
cv::Mat image = cv::Mat(cloud->height, cloud->width, CV_8UC3);
for (int i = 0; i < image.rows; i++)
{
for (int j = 0; j < image.cols; j++)
{
pcl::PointXYZRGBA point = cloud->at(j, i);
image.at<cv::Vec3b>(i, j)[0] = point.b;
image.at<cv::Vec3b>(i, j)[1] = point.g;
image.at<cv::Vec3b>(i, j)[2] = point.r;
}
}
cv::imwrite("image.png", image);
return (0);
}
The PCD file can be found here. The above code throws following error at runtime-
terminate called after throwing an instance of 'pcl::IsNotDenseException'
what(): : Can't use 2D indexing with a unorganized point cloud
Since the cloud is unorganized, the HEIGHT field is 1. This makes me confused while defining the dimensions of the image.
Questions
How to compose an image from an unorganized point cloud?
How to convert pixels located in composed image back to point cloud (3D space)?
PS: I am using PCL 1.7 in Ubuntu 14.04 LTS OS.
What Unorganized point cloud means is that the points are NOT assigned to a fixed (organized) grid, therefore ->at(j, i) can't be used (height is always 1, and the width is just the size of the cloud.
If you want to generate an image from your cloud, I suggest the following process:
Project the point cloud to a plane.
Generate a grid (organized point cloud) on that plane.
Interpolate the colors from the unorganized cloud to the grid (organized cloud).
Generate image from your organized grid (your initial attempt).
To be able to convert back to 3D:
When projecting to the plane save the "projection vectors" (vector from original point to the projected point).
Interpolate that as well to the grid.
methods for creating the grid:
Project the point cloud to a plane (unorganized cloud), and optionally save the reconstruction information in the normals:
pcl::PointCloud<pcl::PointXYZINormal>::Ptr ProjectToPlane(pcl::PointCloud<pcl::PointXYZINormal>::Ptr cloud, Eigen::Vector3f origin, Eigen::Vector3f axis_x, Eigen::Vector3f axis_y)
{
PointCloud<PointXYZINormal>::Ptr aux_cloud(new PointCloud<PointXYZINormal>);
copyPointCloud(*cloud, *aux_cloud);
auto normal = axis_x.cross(axis_y);
Eigen::Hyperplane<float, 3> plane(normal, origin);
for (auto itPoint = aux_cloud->begin(); itPoint != aux_cloud->end(); itPoint++)
{
// project point to plane
auto proj = plane.projection(itPoint->getVector3fMap());
itPoint->getVector3fMap() = proj;
// optional: save the reconstruction information as normals in the projected cloud
itPoint->getNormalVector3fMap() = itPoint->getVector3fMap() - proj;
}
return aux_cloud;
}
Generate a grid based on an origin point and two axis vectors (length and image_size can either be predetermined as calculated from your cloud):
pcl::PointCloud<pcl::PointXYZINormal>::Ptr GenerateGrid(Eigen::Vector3f origin, Eigen::Vector3f axis_x , Eigen::Vector3f axis_y, float length, int image_size)
{
auto step = length / image_size;
pcl::PointCloud<pcl::PointXYZINormal>::Ptr image_cloud(new pcl::PointCloud<pcl::PointXYZINormal>(image_size, image_size));
for (auto i = 0; i < image_size; i++)
for (auto j = 0; j < image_size; j++)
{
int x = i - int(image_size / 2);
int y = j - int(image_size / 2);
image_cloud->at(i, j).getVector3fMap() = center + (x * step * axisx) + (y * step * axisy);
}
return image_cloud;
}
Interpolate to an organized grid (where the normals store reconstruction information and the curvature is used as a flag to indicate empty pixel (no corresponding point):
void InterpolateToGrid(pcl::PointCloud<pcl::PointXYZINormal>::Ptr cloud, pcl::PointCloud<pcl::PointXYZINormal>::Ptr grid, float max_resolution, int max_nn_to_consider)
{
pcl::search::KdTree<pcl::PointXYZINormal>::Ptr tree(new pcl::search::KdTree<pcl::PointXYZINormal>);
tree->setInputCloud(cloud);
for (auto idx = 0; idx < grid->points.size(); idx++)
{
std::vector<int> indices;
std::vector<float> distances;
if (tree->radiusSearch(grid->points[idx], max_resolution, indices, distances, max_nn_to_consider) > 0)
{
// Linear Interpolation of:
// Intensity
// Normals- residual vector to inflate(recondtruct) the surface
float intensity(0);
Eigen::Vector3f n(0, 0, 0);
float weight_factor = 1.0F / accumulate(distances.begin(), distances.end(), 0.0F);
for (auto i = 0; i < indices.size(); i++)
{
float w = weight_factor * distances[i];
intensity += w * cloud->points[indices[i]].intensity;
auto res = cloud->points[indices[i]].getVector3fMap() - grid->points[idx].getVector3fMap();
n += w * res;
}
grid->points[idx].intensity = intensity;
grid->points[idx].getNormalVector3fMap() = n;
grid->points[idx].curvature = 1;
}
else
{
grid->points[idx].intensity = 0;
grid->points[idx].curvature = 0;
grid->points[idx].getNormalVector3fMap() = Eigen::Vector3f(0, 0, 0);
}
}
}
Now you have a grid (an organized cloud), which you can easily map to an image. Any changes you make to the images, you can map back to the grid, and use the normals to project back to your original point cloud.
usage example for creating the grid:
pcl::PointCloud<pcl::PointXYZINormal>::Ptr original_cloud = ...;
// reference frame for the projection
// e.g. take XZ plane around 0,0,0 of length 100 and map to 128*128 image
Eigen::Vector3f origin = Eigen::Vector3f(0,0,0);
Eigen::Vector3f axis_x = Eigen::Vector3f(1,0,0);
Eigen::Vector3f axis_y = Eigen::Vector3f(0,0,1);
float length = 100
int image_size = 128
auto aux_cloud = ProjectToPlane(original_cloud, origin, axis_x, axis_y);
// aux_cloud now contains the points of original_cloud, with:
// xyz coordinates projected to XZ plane
// color (intensity) of the original_cloud (remains unchanged)
// normals - we lose the normal information, as we use this field to save the projection information. if you wish to keep the normal data, you should define a custom PointType.
// note: for the sake of projection, the origin is only used to define the plane, so any arbitrary point on the plane can be used
auto grid = GenerateGrid(origin, axis_x , axis_y, length, image_size)
// organized cloud that can be trivially mapped to an image
float max_resolution = 2 * length / image_size;
int max_nn_to_consider = 16;
InterpolateToGrid(aux_cloud, grid, max_resolution, max_nn_to_consider);
// Now you have a grid (an organized cloud), which you can easily map to an image. Any changes you make to the images, you can map back to the grid, and use the normals to project back to your original point cloud.
additional helper methods for how I use the grid:
// Convert an Organized cloud to cv::Mat (an image and a mask)
// point Intensity is used for the image
// if as_float is true => take the raw intensity (image is CV_32F)
// if as_float is false => assume intensity is in range [0, 255] and round it (image is CV_8U)
// point Curvature is used for the mask (assume 1 or 0)
std::pair<cv::Mat, cv::Mat> ConvertGridToImage(pcl::PointCloud<pcl::PointXYZINormal>::Ptr grid, bool as_float)
{
int rows = grid->height;
int cols = grid->width;
if ((rows <= 0) || (cols <= 0))
return pair<Mat, Mat>(Mat(), Mat());
// Initialize
Mat image = Mat(rows, cols, as_float? CV_32F : CV_8U);
Mat mask = Mat(rows, cols, CV_8U);
if (as_float)
{
for (int y = 0; y < image.rows; y++)
{
for (int x = 0; x < image.cols; x++)
{
image.at<float>(y, x) = grid->at(x, image.rows - y - 1).intensity;
mask.at<uchar>(y, x) = 255 * grid->at(x, image.rows - y - 1).curvature;
}
}
}
else
{
for (int y = 0; y < image.rows; y++)
{
for (int x = 0; x < image.cols; x++)
{
image.at<uchar>(y, x) = (int)round(grid->at(x, image.rows - y - 1).intensity);
mask.at<uchar>(y, x) = 255 * grid->at(x, image.rows - y - 1).curvature;
}
}
}
return pair<Mat, Mat>(image, mask);
}
// project image to cloud (using the grid data)
// organized - whether the resulting cloud should be an organized cloud
pcl::PointCloud<pcl::PointXYZI>::Ptr BackProjectImage(cv::Mat image, pcl::PointCloud<pcl::PointXYZINormal>::Ptr grid, bool organized)
{
if ((image.size().height != grid->height) || (image.size().width != grid->width))
{
assert(false);
throw;
}
PointCloud<PointXYZI>::Ptr cloud(new PointCloud<PointXYZI>);
cloud->reserve(grid->height * grid->width);
// order of iteration is critical for organized target cloud
for (auto r = image.size().height - 1; r >= 0; r--)
{
for (auto c = 0; c < image.size().width; c++)
{
PointXYZI point;
auto mask_value = mask.at<uchar>(image.rows - r - 1, c);
if (mask_value > 0) // valid pixel
{
point.intensity = mask_value;
point.getVector3fMap() = grid->at(c, r).getVector3fMap() + grid->at(c, r).getNormalVector3fMap();
}
else // invalid pixel
{
if (organized)
{
point.intensity = 0;
point.x = numeric_limits<float>::quiet_NaN();
point.y = numeric_limits<float>::quiet_NaN();
point.z = numeric_limits<float>::quiet_NaN();
}
else
{
continue;
}
}
cloud->push_back(point);
}
}
if (organized)
{
cloud->width = grid->width;
cloud->height = grid->height;
}
return cloud;
}
usage example for working with the grid:
// image_mask is std::pair<cv::Mat, cv::Mat>
auto image_mask = ConvertGridToImage(grid, false);
...
do some work with the image/mask
...
auto new_cloud = BackProjectImage(image_mask.first, grid, false);
For an unorganized point cloud, height and width have different meanings as you may have noticed. http://pointclouds.org/documentation/tutorials/basic_structures.php
It is not as simple to convert an unorganized point cloud to an image, as the points are represented as floats and there is no defined perspective. However, you can work around that by determining a perspective and creating discrete bins for the points. A similar question and answer can be found here: Converting a pointcloud to a depth/multi channel image
Let's say I initialize a point-cloud. I want to store its RGB channels in opencv's Mat data-type. How can I do that?
pcl::PointCloud<pcl::PointXYZRGBA>::Ptr cloud (new pcl::PointCloud<pcl::PointXYZRGBA>); //Create a new cloud
pcl::io::loadPCDFile<pcl::PointXYZRGBA> ("cloud.pcd", *cloud);
Do I understand it right, that you are only interested in the RGB-values of the point-cloud and don't care about its XYZ-values?
Then you can do:
pcl::PointCloud<pcl::PointXYZRGBA>::Ptr cloud (new pcl::PointCloud<pcl::PointXYZRGBA>);
//Create a new cloud
pcl::io::loadPCDFile<pcl::PointXYZRGBA> ("cloud.pcd", *cloud);
cv::Mat result;
if (cloud->isOrganized()) {
result = cv::Mat(cloud->height, cloud->width, CV_8UC3);
if (!cloud->empty()) {
for (int h=0; h<result.rows; h++) {
for (int w=0; w<result.cols; w++) {
pcl::PointXYZRGBA point = cloud->at(w, h);
Eigen::Vector3i rgb = point.getRGBVector3i();
result.at<cv::Vec3b>(h,w)[0] = rgb[2];
result.at<cv::Vec3b>(h,w)[1] = rgb[1];
result.at<cv::Vec3b>(h,w)[2] = rgb[0];
}
}
}
}
I think it's enough to show the basic idea.
BUT this only works, if your point-cloud is organized:
An organized point cloud dataset is the name given to point clouds
that resemble an organized image (or matrix) like structure, where the
data is split into rows and columns. Examples of such point clouds
include data coming from stereo cameras or Time Of Flight cameras. The
advantages of a organized dataset is that by knowing the relationship
between adjacent points (e.g. pixels), nearest neighbor operations are
much more efficient, thus speeding up the computation and lowering the
costs of certain algorithms in PCL. (Source)
I know how to convert from Mat(3D Image) to XYZRGB. I think you can figure out the other way. Here Q is disparity to depth Matrix.
pcl::PointCloud<pcl::PointXYZRGB>::Ptr point_cloud_ptr (new pcl::PointCloud<pcl::PointXYZRGB>);
double px, py, pz;
uchar pr, pg, pb;
for (int i = 0; i < img_rgb.rows; i++)
{
uchar* rgb_ptr = img_rgb.ptr<uchar>(i);
uchar* disp_ptr = img_disparity.ptr<uchar>(i);
double* recons_ptr = recons3D.ptr<double>(i);
for (int j = 0; j < img_rgb.cols; j++)
{
//Get 3D coordinates
uchar d = disp_ptr[j];
if ( d == 0 ) continue; //Discard bad pixels
double pw = -1.0 * static_cast<double>(d) * Q32 + Q33;
px = static_cast<double>(j) + Q03;
py = static_cast<double>(i) + Q13;
pz = Q23;
// Normalize the points
px = px/pw;
py = py/pw;
pz = pz/pw;
//Get RGB info
pb = rgb_ptr[3*j];
pg = rgb_ptr[3*j+1];
pr = rgb_ptr[3*j+2];
//Insert info into point cloud structure
pcl::PointXYZRGB point;
point.x = px;
point.y = py;
point.z = pz;
uint32_t rgb = (static_cast<uint32_t>(pr) << 16 |
static_cast<uint32_t>(pg) << 8 | static_cast<uint32_t>(pb));
point.rgb = *reinterpret_cast<float*>(&rgb);
point_cloud_ptr->points.push_back (point);
}
}
point_cloud_ptr->width = (int) point_cloud_ptr->points.size();
point_cloud_ptr->height = 1;
I have the same problem and I succeed to solve it!
You should firstly transform the coordinate so that your 'ground plane' is the X-O-Y plane.
The core api is pcl::getTransformationFromTwoUnitVectorsAndOrigin
You can have a look at my question:
good luck!
I have searched internet and stackoverflow thoroughly, but I haven't found answer to my question:
How can I get/set (both) RGB value of certain (given by x,y coordinates) pixel in OpenCV? What's important-I'm writing in C++, the image is stored in cv::Mat variable. I know there is an IplImage() operator, but IplImage is not very comfortable in use-as far as I know it comes from C API.
Yes, I'm aware that there was already this Pixel access in OpenCV 2.2 thread, but it was only about black and white bitmaps.
EDIT:
Thank you very much for all your answers. I see there are many ways to get/set RGB value of pixel. I got one more idea from my close friend-thanks Benny! It's very simple and effective. I think it's a matter of taste which one you choose.
Mat image;
(...)
Point3_<uchar>* p = image.ptr<Point3_<uchar> >(y,x);
And then you can read/write RGB values with:
p->x //B
p->y //G
p->z //R
Try the following:
cv::Mat image = ...do some stuff...;
image.at<cv::Vec3b>(y,x); gives you the RGB (it might be ordered as BGR) vector of type cv::Vec3b
image.at<cv::Vec3b>(y,x)[0] = newval[0];
image.at<cv::Vec3b>(y,x)[1] = newval[1];
image.at<cv::Vec3b>(y,x)[2] = newval[2];
The low-level way would be to access the matrix data directly. In an RGB image (which I believe OpenCV typically stores as BGR), and assuming your cv::Mat variable is called frame, you could get the blue value at location (x, y) (from the top left) this way:
frame.data[frame.channels()*(frame.cols*y + x)];
Likewise, to get B, G, and R:
uchar b = frame.data[frame.channels()*(frame.cols*y + x) + 0];
uchar g = frame.data[frame.channels()*(frame.cols*y + x) + 1];
uchar r = frame.data[frame.channels()*(frame.cols*y + x) + 2];
Note that this code assumes the stride is equal to the width of the image.
A piece of code is easier for people who have such problem. I share my code and you can use it directly. Please note that OpenCV store pixels as BGR.
cv::Mat vImage_;
if(src_)
{
cv::Vec3f vec_;
for(int i = 0; i < vHeight_; i++)
for(int j = 0; j < vWidth_; j++)
{
vec_ = cv::Vec3f((*src_)[0]/255.0, (*src_)[1]/255.0, (*src_)[2]/255.0);//Please note that OpenCV store pixels as BGR.
vImage_.at<cv::Vec3f>(vHeight_-1-i, j) = vec_;
++src_;
}
}
if(! vImage_.data ) // Check for invalid input
printf("failed to read image by OpenCV.");
else
{
cv::namedWindow( windowName_, CV_WINDOW_AUTOSIZE);
cv::imshow( windowName_, vImage_); // Show the image.
}
The current version allows the cv::Mat::at function to handle 3 dimensions. So for a Mat object m, m.at<uchar>(0,0,0) should work.
uchar * value = img2.data; //Pointer to the first pixel data ,it's return array in all values
int r = 2;
for (size_t i = 0; i < img2.cols* (img2.rows * img2.channels()); i++)
{
if (r > 2) r = 0;
if (r == 0) value[i] = 0;
if (r == 1)value[i] = 0;
if (r == 2)value[i] = 255;
r++;
}
const double pi = boost::math::constants::pi<double>();
cv::Mat distance2ellipse(cv::Mat image, cv::RotatedRect ellipse){
float distance = 2.0f;
float angle = ellipse.angle;
cv::Point ellipse_center = ellipse.center;
float major_axis = ellipse.size.width/2;
float minor_axis = ellipse.size.height/2;
cv::Point pixel;
float a,b,c,d;
for(int x = 0; x < image.cols; x++)
{
for(int y = 0; y < image.rows; y++)
{
auto u = cos(angle*pi/180)*(x-ellipse_center.x) + sin(angle*pi/180)*(y-ellipse_center.y);
auto v = -sin(angle*pi/180)*(x-ellipse_center.x) + cos(angle*pi/180)*(y-ellipse_center.y);
distance = (u/major_axis)*(u/major_axis) + (v/minor_axis)*(v/minor_axis);
if(distance<=1)
{
image.at<cv::Vec3b>(y,x)[1] = 255;
}
}
}
return image;
}
I am wondering if there is an easy way to match (register) 2 clouds of 2d points.
Let's say I have an object represented by points and an cluttered 2nd image with the object points and noise (noise in a way of points that are useless).
Basically the object can be 2d rotated as well as translated and scaled.
I know there is the ICP - Algorithm but I think that this is not a good approach due to high noise.
I hope that you understand what i mean. please ask if (im sure it is) anything is unclear.
cheers
Here is the function that finds translation and rotation. Generalization to scaling, weighted points, and RANSAC are straight forward. I used openCV library for visualization and SVD. The function below combines data generation, Unit Test , and actual solution.
// rotation and translation in 2D from point correspondences
void rigidTransform2D(const int N) {
// Algorithm: http://igl.ethz.ch/projects/ARAP/svd_rot.pdf
const bool debug = false; // print more debug info
const bool add_noise = true; // add noise to imput and output
srand(time(NULL)); // randomize each time
/*********************************
* Creat data with some noise
**********************************/
// Simulated transformation
Point2f T(1.0f, -2.0f);
float a = 30.0; // [-180, 180], see atan2(y, x)
float noise_level = 0.1f;
cout<<"True parameters: rot = "<<a<<"deg., T = "<<T<<
"; noise level = "<<noise_level<<endl;
// noise
vector<Point2f> noise_src(N), noise_dst(N);
for (int i=0; i<N; i++) {
noise_src[i] = Point2f(randf(noise_level), randf(noise_level));
noise_dst[i] = Point2f(randf(noise_level), randf(noise_level));
}
// create data with noise
vector<Point2f> src(N), dst(N);
float Rdata = 10.0f; // radius of data
float cosa = cos(a*DEG2RAD);
float sina = sin(a*DEG2RAD);
for (int i=0; i<N; i++) {
// src
float x1 = randf(Rdata);
float y1 = randf(Rdata);
src[i] = Point2f(x1,y1);
if (add_noise)
src[i] += noise_src[i];
// dst
float x2 = x1*cosa - y1*sina;
float y2 = x1*sina + y1*cosa;
dst[i] = Point2f(x2,y2) + T;
if (add_noise)
dst[i] += noise_dst[i];
if (debug)
cout<<i<<": "<<src[i]<<"---"<<dst[i]<<endl;
}
// Calculate data centroids
Scalar centroid_src = mean(src);
Scalar centroid_dst = mean(dst);
Point2f center_src(centroid_src[0], centroid_src[1]);
Point2f center_dst(centroid_dst[0], centroid_dst[1]);
if (debug)
cout<<"Centers: "<<center_src<<", "<<center_dst<<endl;
/*********************************
* Visualize data
**********************************/
// Visualization
namedWindow("data", 1);
float w = 400, h = 400;
Mat Mdata(w, h, CV_8UC3); Mdata = Scalar(0);
Point2f center_img(w/2, h/2);
float scl = 0.4*min(w/Rdata, h/Rdata); // compensate for noise
scl/=sqrt(2); // compensate for rotation effect
Point2f dT = (center_src+center_dst)*0.5; // compensate for translation
for (int i=0; i<N; i++) {
Point2f p1(scl*(src[i] - dT));
Point2f p2(scl*(dst[i] - dT));
// invert Y axis
p1.y = -p1.y; p2.y = -p2.y;
// add image center
p1+=center_img; p2+=center_img;
circle(Mdata, p1, 1, Scalar(0, 255, 0));
circle(Mdata, p2, 1, Scalar(0, 0, 255));
line(Mdata, p1, p2, Scalar(100, 100, 100));
}
/*********************************
* Get 2D rotation and translation
**********************************/
markTime();
// subtract centroids from data
for (int i=0; i<N; i++) {
src[i] -= center_src;
dst[i] -= center_dst;
}
// compute a covariance matrix
float Cxx = 0.0, Cxy = 0.0, Cyx = 0.0, Cyy = 0.0;
for (int i=0; i<N; i++) {
Cxx += src[i].x*dst[i].x;
Cxy += src[i].x*dst[i].y;
Cyx += src[i].y*dst[i].x;
Cyy += src[i].y*dst[i].y;
}
Mat Mcov = (Mat_<float>(2, 2)<<Cxx, Cxy, Cyx, Cyy);
if (debug)
cout<<"Covariance Matrix "<<Mcov<<endl;
// SVD
cv::SVD svd;
svd = SVD(Mcov, SVD::FULL_UV);
if (debug) {
cout<<"U = "<<svd.u<<endl;
cout<<"W = "<<svd.w<<endl;
cout<<"V transposed = "<<svd.vt<<endl;
}
// rotation = V*Ut
Mat V = svd.vt.t();
Mat Ut = svd.u.t();
float det_VUt = determinant(V*Ut);
Mat W = (Mat_<float>(2, 2)<<1.0, 0.0, 0.0, det_VUt);
float rot[4];
Mat R_est(2, 2, CV_32F, rot);
R_est = V*W*Ut;
if (debug)
cout<<"Rotation matrix: "<<R_est<<endl;
float cos_est = rot[0];
float sin_est = rot[2];
float ang = atan2(sin_est, cos_est);
// translation = mean_dst - R*mean_src
Point2f center_srcRot = Point2f(
cos_est*center_src.x - sin_est*center_src.y,
sin_est*center_src.x + cos_est*center_src.y);
Point2f T_est = center_dst - center_srcRot;
// RMSE
double RMSE = 0.0;
for (int i=0; i<N; i++) {
Point2f dst_est(
cos_est*src[i].x - sin_est*src[i].y,
sin_est*src[i].x + cos_est*src[i].y);
RMSE += SQR(dst[i].x - dst_est.x) + SQR(dst[i].y - dst_est.y);
}
if (N>0)
RMSE = sqrt(RMSE/N);
// Final estimate msg
cout<<"Estimate = "<<ang*RAD2DEG<<"deg., T = "<<T_est<<"; RMSE = "<<RMSE<<endl;
// show image
printTime(1);
imshow("data", Mdata);
waitKey(-1);
return;
} // rigidTransform2D()
// --------------------------- 3DOF
// calculates squared error from two point mapping; assumes rotation around Origin.
inline float sqErr_3Dof(Point2f p1, Point2f p2,
float cos_alpha, float sin_alpha, Point2f T) {
float x2_est = T.x + cos_alpha * p1.x - sin_alpha * p1.y;
float y2_est = T.y + sin_alpha * p1.x + cos_alpha * p1.y;
Point2f p2_est(x2_est, y2_est);
Point2f dp = p2_est-p2;
float sq_er = dp.dot(dp); // squared distance
//cout<<dp<<endl;
return sq_er;
}
// calculate RMSE for point-to-point metrics
float RMSE_3Dof(const vector<Point2f>& src, const vector<Point2f>& dst,
const float* param, const bool* inliers, const Point2f center) {
const bool all_inliers = (inliers==NULL); // handy when we run QUADRTATIC will all inliers
unsigned int n = src.size();
assert(n>0 && n==dst.size());
float ang_rad = param[0];
Point2f T(param[1], param[2]);
float cos_alpha = cos(ang_rad);
float sin_alpha = sin(ang_rad);
double RMSE = 0.0;
int ninliers = 0;
for (unsigned int i=0; i<n; i++) {
if (all_inliers || inliers[i]) {
RMSE += sqErr_3Dof(src[i]-center, dst[i]-center, cos_alpha, sin_alpha, T);
ninliers++;
}
}
//cout<<"RMSE = "<<RMSE<<endl;
if (ninliers>0)
return sqrt(RMSE/ninliers);
else
return LARGE_NUMBER;
}
// Sets inliers and returns their count
inline int setInliers3Dof(const vector<Point2f>& src, const vector <Point2f>& dst,
bool* inliers,
const float* param,
const float max_er,
const Point2f center) {
float ang_rad = param[0];
Point2f T(param[1], param[2]);
// set inliers
unsigned int ninliers = 0;
unsigned int n = src.size();
assert(n>0 && n==dst.size());
float cos_ang = cos(ang_rad);
float sin_ang = sin(ang_rad);
float max_sqErr = max_er*max_er; // comparing squared values
if (inliers==NULL) {
// just get the number of inliers (e.g. after QUADRATIC fit only)
for (unsigned int i=0; i<n; i++) {
float sqErr = sqErr_3Dof(src[i]-center, dst[i]-center, cos_ang, sin_ang, T);
if ( sqErr < max_sqErr)
ninliers++;
}
} else {
// get the number of inliers and set them (e.g. for RANSAC)
for (unsigned int i=0; i<n; i++) {
float sqErr = sqErr_3Dof(src[i]-center, dst[i]-center, cos_ang, sin_ang, T);
if ( sqErr < max_sqErr) {
inliers[i] = 1;
ninliers++;
} else {
inliers[i] = 0;
}
}
}
return ninliers;
}
// fits 3DOF (rotation and translation in 2D) with least squares.
float fit3DofQUADRATICold(const vector<Point2f>& src, const vector<Point2f>& dst,
float* param, const bool* inliers, const Point2f center) {
const bool all_inliers = (inliers==NULL); // handy when we run QUADRTATIC will all inliers
unsigned int n = src.size();
assert(dst.size() == n);
// count inliers
int ninliers;
if (all_inliers) {
ninliers = n;
} else {
ninliers = 0;
for (unsigned int i=0; i<n; i++){
if (inliers[i])
ninliers++;
}
}
// under-dermined system
if (ninliers<2) {
// param[0] = 0.0f; // ?
// param[1] = 0.0f;
// param[2] = 0.0f;
return LARGE_NUMBER;
}
/*
* x1*cosx(a)-y1*sin(a) + Tx = X1
* x1*sin(a)+y1*cos(a) + Ty = Y1
*
* approximation for small angle a (radians) sin(a)=a, cos(a)=1;
*
* x1*1 - y1*a + Tx = X1
* x1*a + y1*1 + Ty = Y1
*
* in matrix form M1*h=M2
*
* 2n x 4 4 x 1 2n x 1
*
* -y1 1 0 x1 * a = X1
* x1 0 1 y1 Tx Y1
* Ty
* 1=Z
* ----------------------------
* src1 res src2
*/
// 4 x 1
float res_ar[4]; // alpha, Tx, Ty, 1
Mat res(4, 1, CV_32F, res_ar); // 4 x 1
// 2n x 4
Mat src1(2*ninliers, 4, CV_32F); // 2n x 4
// 2n x 1
Mat src2(2*ninliers, 1, CV_32F); // 2n x 1: [X1, Y1, X2, Y2, X3, Y3]'
for (unsigned int i=0, row_cnt = 0; i<n; i++) {
// use inliers only
if (all_inliers || inliers[i]) {
float x = src[i].x - center.x;
float y = src[i].y - center.y;
// first row
// src1
float* rowPtr = src1.ptr<float>(row_cnt);
rowPtr[0] = -y;
rowPtr[1] = 1.0f;
rowPtr[2] = 0.0f;
rowPtr[3] = x;
// src2
src2.at<float> (0, row_cnt) = dst[i].x - center.x;
// second row
row_cnt++;
// src1
rowPtr = src1.ptr<float>(row_cnt);
rowPtr[0] = x;
rowPtr[1] = 0.0f;
rowPtr[2] = 1.0f;
rowPtr[3] = y;
// src2
src2.at<float> (0, row_cnt) = dst[i].y - center.y;
}
}
cv::solve(src1, src2, res, DECOMP_SVD);
// estimators
float alpha_est;
Point2f T_est;
// original
alpha_est = res.at<float>(0, 0);
T_est = Point2f(res.at<float>(1, 0), res.at<float>(2, 0));
float Z = res.at<float>(3, 0);
if (abs(Z-1.0) > 0.1) {
//cout<<"Bad Z in fit3DOF(), Z should be close to 1.0 = "<<Z<<endl;
//return LARGE_NUMBER;
}
param[0] = alpha_est; // rad
param[1] = T_est.x;
param[2] = T_est.y;
// calculate RMSE
float RMSE = RMSE_3Dof(src, dst, param, inliers, center);
return RMSE;
} // fit3DofQUADRATICOLd()
// fits 3DOF (rotation and translation in 2D) with least squares.
float fit3DofQUADRATIC(const vector<Point2f>& src_, const vector<Point2f>& dst_,
float* param, const bool* inliers, const Point2f center) {
const bool debug = false; // print more debug info
const bool all_inliers = (inliers==NULL); // handy when we run QUADRTATIC will all inliers
assert(dst_.size() == src_.size());
int N = src_.size();
// collect inliers
vector<Point2f> src, dst;
int ninliers;
if (all_inliers) {
ninliers = N;
src = src_; // copy constructor
dst = dst_;
} else {
ninliers = 0;
for (int i=0; i<N; i++){
if (inliers[i]) {
ninliers++;
src.push_back(src_[i]);
dst.push_back(dst_[i]);
}
}
}
if (ninliers<2) {
param[0] = 0.0f; // default return when there is not enough points
param[1] = 0.0f;
param[2] = 0.0f;
return LARGE_NUMBER;
}
/* Algorithm: Least-Square Rigid Motion Using SVD by Olga Sorkine
* http://igl.ethz.ch/projects/ARAP/svd_rot.pdf
*
* Subtract centroids, calculate SVD(cov),
* R = V[1, det(VU')]'U', T = mean_q-R*mean_p
*/
// Calculate data centroids
Scalar centroid_src = mean(src);
Scalar centroid_dst = mean(dst);
Point2f center_src(centroid_src[0], centroid_src[1]);
Point2f center_dst(centroid_dst[0], centroid_dst[1]);
if (debug)
cout<<"Centers: "<<center_src<<", "<<center_dst<<endl;
// subtract centroids from data
for (int i=0; i<ninliers; i++) {
src[i] -= center_src;
dst[i] -= center_dst;
}
// compute a covariance matrix
float Cxx = 0.0, Cxy = 0.0, Cyx = 0.0, Cyy = 0.0;
for (int i=0; i<ninliers; i++) {
Cxx += src[i].x*dst[i].x;
Cxy += src[i].x*dst[i].y;
Cyx += src[i].y*dst[i].x;
Cyy += src[i].y*dst[i].y;
}
Mat Mcov = (Mat_<float>(2, 2)<<Cxx, Cxy, Cyx, Cyy);
Mcov /= (ninliers-1);
if (debug)
cout<<"Covariance-like Matrix "<<Mcov<<endl;
// SVD of covariance
cv::SVD svd;
svd = SVD(Mcov, SVD::FULL_UV);
if (debug) {
cout<<"U = "<<svd.u<<endl;
cout<<"W = "<<svd.w<<endl;
cout<<"V transposed = "<<svd.vt<<endl;
}
// rotation (V*Ut)
Mat V = svd.vt.t();
Mat Ut = svd.u.t();
float det_VUt = determinant(V*Ut);
Mat W = (Mat_<float>(2, 2)<<1.0, 0.0, 0.0, det_VUt);
float rot[4];
Mat R_est(2, 2, CV_32F, rot);
R_est = V*W*Ut;
if (debug)
cout<<"Rotation matrix: "<<R_est<<endl;
float cos_est = rot[0];
float sin_est = rot[2];
float ang = atan2(sin_est, cos_est);
// translation (mean_dst - R*mean_src)
Point2f center_srcRot = Point2f(
cos_est*center_src.x - sin_est*center_src.y,
sin_est*center_src.x + cos_est*center_src.y);
Point2f T_est = center_dst - center_srcRot;
// Final estimate msg
if (debug)
cout<<"Estimate = "<<ang*RAD2DEG<<"deg., T = "<<T_est<<endl;
param[0] = ang; // rad
param[1] = T_est.x;
param[2] = T_est.y;
// calculate RMSE
float RMSE = RMSE_3Dof(src_, dst_, param, inliers, center);
return RMSE;
} // fit3DofQUADRATIC()
// RANSAC fit in 3DOF: 1D rot and 2D translation (maximizes the number of inliers)
// NOTE: no data normalization is currently performed
float fit3DofRANSAC(const vector<Point2f>& src, const vector<Point2f>& dst,
float* best_param, bool* inliers,
const Point2f center ,
const float inlierMaxEr,
const int niter) {
const int ITERATION_TO_SETTLE = 2; // iterations to settle inliers and param
const float INLIERS_RATIO_OK = 0.95f; // stopping criterion
// size of data vector
unsigned int N = src.size();
assert(N==dst.size());
// unrealistic case
if(N<2) {
best_param[0] = 0.0f; // ?
best_param[1] = 0.0f;
best_param[2] = 0.0f;
return LARGE_NUMBER;
}
unsigned int ninliers; // current number of inliers
unsigned int best_ninliers = 0; // number of inliers
float best_rmse = LARGE_NUMBER; // error
float cur_rmse; // current distance error
float param[3]; // rad, Tx, Ty
vector <Point2f> src_2pt(2), dst_2pt(2);// min set of 2 points (1 correspondence generates 2 equations)
srand (time(NULL));
// iterations
for (int iter = 0; iter<niter; iter++) {
#ifdef DEBUG_RANSAC
cout<<"iteration "<<iter<<": ";
#endif
// 1. Select a random set of 2 points (not obligatory inliers but valid)
int i1, i2;
i1 = rand() % N; // [0, N[
i2 = i1;
while (i2==i1) {
i2 = rand() % N;
}
src_2pt[0] = src[i1]; // corresponding points
src_2pt[1] = src[i2];
dst_2pt[0] = dst[i1];
dst_2pt[1] = dst[i2];
bool two_inliers[] = {true, true};
// 2. Quadratic fit for 2 points
cur_rmse = fit3DofQUADRATIC(src_2pt, dst_2pt, param, two_inliers, center);
// 3. Recalculate to settle params and inliers using a larger set
for (int iter2=0; iter2<ITERATION_TO_SETTLE; iter2++) {
ninliers = setInliers3Dof(src, dst, inliers, param, inlierMaxEr, center); // changes inliers
cur_rmse = fit3DofQUADRATIC(src, dst, param, inliers, center); // changes cur_param
}
// potential ill-condition or large error
if (ninliers<2) {
#ifdef DEBUG_RANSAC
cout<<" !!! less than 2 inliers "<<endl;
#endif
continue;
} else {
#ifdef DEBUG_RANSAC
cout<<" "<<ninliers<<" inliers; ";
#endif
}
#ifdef DEBUG_RANSAC
cout<<"; recalculate: RMSE = "<<cur_rmse<<", "<<ninliers <<" inliers";
#endif
// 4. found a better solution?
if (ninliers > best_ninliers) {
best_ninliers = ninliers;
best_param[0] = param[0];
best_param[1] = param[1];
best_param[2] = param[2];
best_rmse = cur_rmse;
#ifdef DEBUG_RANSAC
cout<<" --- Solution improved: "<<
best_param[0]<<", "<<best_param[1]<<", "<<param[2]<<endl;
#endif
// exit condition
float inlier_ratio = (float)best_ninliers/N;
if (inlier_ratio > INLIERS_RATIO_OK) {
#ifdef DEBUG_RANSAC
cout<<"Breaking early after "<< iter+1<<
" iterations; inlier ratio = "<<inlier_ratio<<endl;
#endif
break;
}
} else {
#ifdef DEBUG_RANSAC
cout<<endl;
#endif
}
} // iterations
// 5. recreate inliers for the best parameters
ninliers = setInliers3Dof(src, dst, inliers, best_param, inlierMaxEr, center);
return best_rmse;
} // fit3DofRANSAC()
Let me first make sure I'm interpreting your question correctly. You have two sets of 2D points, one of which contains all "good" points corresponding to some object of interest, and one of which contains those points under an affine transformation with noisy points added. Right?
If that's correct, then there is a fairly reliable and efficient way to both reject noisy points and determine the transformation between your points of interest. The algorithm that is usually used to reject noisy points ("outliers") is known as RANSAC, and the algorithm used to determine the transformation can take several forms, but the most current state of the art is known as the five-point algorithm and can be found here -- a MATLAB implementation can be found here.
Unfortunately I don't know of a mature implementation of both of those combined; you'll probably have to do some work of your own to implement RANSAC and integrate it with the five point algorithm.
Edit:
Actually, OpenCV has an implementation that is overkill for your task (meaning it will work but will take more time than necessary) but is ready to work out of the box. The function of interest is called cv::findFundamentalMat.
I believe you are looking for something like David Lowe's SIFT (Scale Invariant Feature Transform). Other option is SURF (SIFT is patent protected). The OpenCV computer library presents a SURF implementation
I would try and use distance geometry (http://en.wikipedia.org/wiki/Distance_geometry) for this
Generate a scalar for each point by summing its distances to all neighbors within a certain radius. Though not perfect, this will be good discriminator for each point.
Then put all the scalars in a map that allows a point (p) to be retrieve by its scalar (s) plus/minus some delta
M(s+delta) = p (e.g K-D Tree) (http://en.wikipedia.org/wiki/Kd-tree)
Put all the reference set of 2D points in the map
On the other (test) set of 2D points:
foreach test scaling (esp if you have a good idea what typical scaling values are)
...scale each point by S
...recompute the scalars of the test set of points
......for each point P in test set (or perhaps a sample for faster method)
.........lookup point in reference scalar map within some delta
.........discard P if no mapping found
.........else foreach P' point found
............examine neighbors of P and see if they have corresponding scalars in the reference map within some delta (i.e reference point has neighbors with approx same value)
......... if all points tested have a mapping in the reference set, you have found a mapping of test point P onto reference point P' -> record mapping of test point to reference point
......discard scaling if no mappings recorded
Note this is trivially parallelized in several different places
This is off the top of my head, drawing from research I did years ago. It lacks fine details but the general idea is clear: find points in the noisy (test) graph whose distances to their closest neighbors are roughly the same as the reference set. Noisy graphs will have to measure the distances with a larger allowed error that less noisy graphs.
The algorithm works perfectly for graphs with no noise.
Edit: there is a refinement for the algorithm that doesn't require looking at different scalings. When computing the scalar for each point, use a relative distance measure instead. This will be invariant of transform
From C++, you could use ITK to do the image registration. It includes many registration functions that will work in the presence of noise.
The KLT (Kanade Lucas Tomasi) Feature Tracker makes a Affine Consistency Check of tracked features. The Affine Consistency Check takes into account translation, rotation and scaling. I don't know if it is of help to you, because you can't use the function (which calculates the affine transformation of a rectangular region) directly. But maybe you can learn from the documentation and source-code, how the affine transformation can be calculated and adapt it to your problem (clouds of points instead of a rectangular region).
You want want the Denton-Beveridge point matching algorithm. Source code at the bottom of the page linked below, and there is also a paper that explain the algorithm and why Ransac is a bad choice for this problem.
http://jasondenton.me/pntmatch.html