I'm getting results I don't expect when I use OpenCV 3.0 calibrateCamera. Here is my algorithm:
Load in 30 image points
Load in 30 corresponding world points (coplanar in this case)
Use points to calibrate the camera, just for un-distorting
Un-distort the image points, but don't use the intrinsics (coplanar world points, so intrinsics are dodgy)
Use the undistorted points to find a homography, transforming to world points (can do this because they are all coplanar)
Use the homography and perspective transform to map the undistorted points to the world space
Compare the original world points to the mapped points
The points I have are noisy and only a small section of the image. There are 30 coplanar points from a single view so I can't get camera intrinsics, but should be able to get distortion coefficients and a homography to create a fronto-parallel view.
As expected, the error varies depending on the calibration flags. However, it varies opposite to what I expected. If I allow all variables to adjust, I would expect error to come down. I am not saying I expect a better model; I actually expect over-fitting, but that should still reduce error. What I see though is that the fewer variables I use, the lower my error. The best result is with a straight homography.
I have two suspected causes, but they seem unlikely and I'd like to hear an unadulterated answer before I air them. I have pulled out the code to just do what I'm talking about. It's a bit long, but it includes loading the points.
The code doesn't appear to have bugs; I've used "better" points and it works perfectly. I want to emphasize that the solution here can't be to use better points or perform a better calibration; the whole point of the exercise is to see how the various calibration models respond to different qualities of calibration data.
Any ideas?
Added
To be clear, I know the results will be bad and I expect that. I also understand that I may learn bad distortion parameters which leads to worse results when testing points that have not been used to train the model. What I don't understand is how the distortion model has more error when using the training set as the test set. That is, if the cv::calibrateCamera is supposed to choose parameters to reduce error over the training set of points provided, yet it is producing more error than if it had just selected 0s for K!, K2, ... K6, P1, P2. Bad data or not, it should at least do better on the training set. Before I can say the data is not appropriate for this model, I have to be sure I'm doing the best I can with the data available, and I can't say that at this stage.
Here an example image
The points with the green pins are marked. This is obviously just a test image.
Here is more example stuff
In the following the image is cropped from the big one above. The centre has not changed. This is what happens when I undistort with just the points marked manually from the green pins and allowing K1 (only K1) to vary from 0:
Before
After
I would put it down to a bug, but when I use a larger set of points that covers more of the screen, even from a single plane, it works reasonably well. This looks terrible. However, the error is not nearly as bad as you might think from looking at the picture.
// Load image points
std::vector<cv::Point2f> im_points;
im_points.push_back(cv::Point2f(1206, 1454));
im_points.push_back(cv::Point2f(1245, 1443));
im_points.push_back(cv::Point2f(1284, 1429));
im_points.push_back(cv::Point2f(1315, 1456));
im_points.push_back(cv::Point2f(1352, 1443));
im_points.push_back(cv::Point2f(1383, 1431));
im_points.push_back(cv::Point2f(1431, 1458));
im_points.push_back(cv::Point2f(1463, 1445));
im_points.push_back(cv::Point2f(1489, 1432));
im_points.push_back(cv::Point2f(1550, 1461));
im_points.push_back(cv::Point2f(1574, 1447));
im_points.push_back(cv::Point2f(1597, 1434));
im_points.push_back(cv::Point2f(1673, 1463));
im_points.push_back(cv::Point2f(1691, 1449));
im_points.push_back(cv::Point2f(1708, 1436));
im_points.push_back(cv::Point2f(1798, 1464));
im_points.push_back(cv::Point2f(1809, 1451));
im_points.push_back(cv::Point2f(1819, 1438));
im_points.push_back(cv::Point2f(1925, 1467));
im_points.push_back(cv::Point2f(1929, 1454));
im_points.push_back(cv::Point2f(1935, 1440));
im_points.push_back(cv::Point2f(2054, 1470));
im_points.push_back(cv::Point2f(2052, 1456));
im_points.push_back(cv::Point2f(2051, 1443));
im_points.push_back(cv::Point2f(2182, 1474));
im_points.push_back(cv::Point2f(2171, 1459));
im_points.push_back(cv::Point2f(2164, 1446));
im_points.push_back(cv::Point2f(2306, 1474));
im_points.push_back(cv::Point2f(2292, 1462));
im_points.push_back(cv::Point2f(2278, 1449));
// Create corresponding world / object points
std::vector<cv::Point3f> world_points;
for (int i = 0; i < 30; i++) {
world_points.push_back(cv::Point3f(5 * (i / 3), 4 * (i % 3), 0.0f));
}
// Perform calibration
// Flags are set out so they can be commented out and "freed" easily
int calibration_flags = 0
| cv::CALIB_FIX_K1
| cv::CALIB_FIX_K2
| cv::CALIB_FIX_K3
| cv::CALIB_FIX_K4
| cv::CALIB_FIX_K5
| cv::CALIB_FIX_K6
| cv::CALIB_ZERO_TANGENT_DIST
| 0;
// Initialise matrix
cv::Mat intrinsic_matrix = cv::Mat(3, 3, CV_64F);
intrinsic_matrix.ptr<float>(0)[0] = 1;
intrinsic_matrix.ptr<float>(1)[1] = 1;
cv::Mat distortion_coeffs = cv::Mat::zeros(5, 1, CV_64F);
// Rotation and translation vectors
std::vector<cv::Mat> undistort_rvecs;
std::vector<cv::Mat> undistort_tvecs;
// Wrap in an outer vector for calibration
std::vector<std::vector<cv::Point2f>>im_points_v(1, im_points);
std::vector<std::vector<cv::Point3f>>w_points_v(1, world_points);
// Calibrate; only 1 plane, so intrinsics can't be trusted
cv::Size image_size(4000, 3000);
calibrateCamera(w_points_v, im_points_v,
image_size, intrinsic_matrix, distortion_coeffs,
undistort_rvecs, undistort_tvecs, calibration_flags);
// Undistort im_points
std::vector<cv::Point2f> ud_points;
cv::undistortPoints(im_points, ud_points, intrinsic_matrix, distortion_coeffs);
// ud_points have been "unintrinsiced", but we don't know the intrinsics, so reverse that
double fx = intrinsic_matrix.at<double>(0, 0);
double fy = intrinsic_matrix.at<double>(1, 1);
double cx = intrinsic_matrix.at<double>(0, 2);
double cy = intrinsic_matrix.at<double>(1, 2);
for (std::vector<cv::Point2f>::iterator iter = ud_points.begin(); iter != ud_points.end(); iter++) {
iter->x = iter->x * fx + cx;
iter->y = iter->y * fy + cy;
}
// Find a homography mapping the undistorted points to the known world points, ground plane
cv::Mat homography = cv::findHomography(ud_points, world_points);
// Transform the undistorted image points to the world points (2d only, but z is constant)
std::vector<cv::Point2f> estimated_world_points;
std::cout << "homography" << homography << std::endl;
cv::perspectiveTransform(ud_points, estimated_world_points, homography);
// Work out error
double sum_sq_error = 0;
for (int i = 0; i < 30; i++) {
double err_x = estimated_world_points.at(i).x - world_points.at(i).x;
double err_y = estimated_world_points.at(i).y - world_points.at(i).y;
sum_sq_error += err_x*err_x + err_y*err_y;
}
std::cout << "Sum squared error is: " << sum_sq_error << std::endl;
I would take random samples of the 30 input points and compute the homography in each case along with the errors under the estimated homographies, a RANSAC scheme, and verify consensus between error levels and homography parameters, this can be just a verification of the global optimisation process. I know that might seem unnecessary, but it is just a sanity check for how sensitive the procedure is to the input (noise levels, location)
Also, it seems logical that fixing most of the variables gets you the least errors, as the degrees of freedom in the minimization process are less. I would try fixing different ones to establish another consensus. At least this would let you know which variables are the most sensitive to the noise levels of the input.
Hopefully, such a small section of the image would be close to the image centre as it will incur the least amount of lens distortion. Is using a different distortion model possible in your case? A more viable way is to adapt the number of distortion parameters given the position of the pattern with respect to the image centre.
Without knowing the constraints of the algorithm, I might have misunderstood the question, that's also an option too, in such case I can roll back.
I would like to have this as a comment rather, but I do not have enough points.
OpenCV runs Levenberg-Marquardt algorithm inside calibrate camera.
https://en.wikipedia.org/wiki/Levenberg%E2%80%93Marquardt_algorithm/
This algortihm works fine in problems with one minimum. In case of single image, points located close each other and many dimensional problem (n= number of coefficents) algorithm may be unstable (especially with wrong initial guess of camera matrix. Convergence of algorithm is well described here:
https://na.math.kit.edu/download/papers/levenberg.pdf/
As you wrote, error depends on calibration flags - number of flags changes dimension of a problem to be optimized.
Camera calibration also calculates pose of camera, which will be bad in models with wrong calibration matrix.
As a solution I suggest changing approach. You dont need to calculate camera matrix and pose in this step. Since you know, that points are located on a plane you can use 3d-2d plane projection equation to determine distribution type of points. By distribution I mean, that all points will be located equally on some kind of trapezoid.
Then you can use cv::undistort with different distCoeffs on your test image and calculate image point distribution and distribution error.
The last step will be to perform this steps as a target function for some optimization algorithm with distortion coefficents being optimized.
This is not the easiest solution, but i hope it will help you.
Related
I am totally new to OpenCV and I have started to dive into it. But I'd need a little bit of help.
So I want to combine these 2 images:
I would like the 2 images to match along their edges (ignoring the very right part of the image for now)
Can anyone please point me into the right direction? I have tried using the findTransformECC function. Here's my implementation:
cv::Mat im1 = [imageArray[1] CVMat3];
cv::Mat im2 = [imageArray[0] CVMat3];
// Convert images to gray scale;
cv::Mat im1_gray, im2_gray;
cvtColor(im1, im1_gray, CV_BGR2GRAY);
cvtColor(im2, im2_gray, CV_BGR2GRAY);
// Define the motion model
const int warp_mode = cv::MOTION_AFFINE;
// Set a 2x3 or 3x3 warp matrix depending on the motion model.
cv::Mat warp_matrix;
// Initialize the matrix to identity
if ( warp_mode == cv::MOTION_HOMOGRAPHY )
warp_matrix = cv::Mat::eye(3, 3, CV_32F);
else
warp_matrix = cv::Mat::eye(2, 3, CV_32F);
// Specify the number of iterations.
int number_of_iterations = 50;
// Specify the threshold of the increment
// in the correlation coefficient between two iterations
double termination_eps = 1e-10;
// Define termination criteria
cv::TermCriteria criteria (cv::TermCriteria::COUNT+cv::TermCriteria::EPS, number_of_iterations, termination_eps);
// Run the ECC algorithm. The results are stored in warp_matrix.
findTransformECC(
im1_gray,
im2_gray,
warp_matrix,
warp_mode,
criteria
);
// Storage for warped image.
cv::Mat im2_aligned;
if (warp_mode != cv::MOTION_HOMOGRAPHY)
// Use warpAffine for Translation, Euclidean and Affine
warpAffine(im2, im2_aligned, warp_matrix, im1.size(), cv::INTER_LINEAR + cv::WARP_INVERSE_MAP);
else
// Use warpPerspective for Homography
warpPerspective (im2, im2_aligned, warp_matrix, im1.size(),cv::INTER_LINEAR + cv::WARP_INVERSE_MAP);
UIImage* result = [UIImage imageWithCVMat:im2_aligned];
return result;
I have tried playing around with the termination_eps and number_of_iterations and increased/decreased those values, but they didn't really make a big difference.
So here's the result:
What can I do to improve my result?
EDIT: I have marked the problematic edges with red circles. The goal is to warp the bottom image and make it match with the lines from the image above:
I did a little bit of research and I'm afraid the findTransformECC function won't give me the result I'd like to have :-(
Something important to add:
I actually have an array of those image "stripes", 8 in this case, they all look similar to the images shown here and they all need to be processed to match the line. I have tried experimenting with the stitch function of OpenCV, but the results were horrible.
EDIT:
Here are the 3 source images:
The result should be something like this:
I transformed every image along the lines that should match. Lines that are too far away from each other can be ignored (the shadow and the piece of road on the right portion of the image)
By your images, it seems that they overlap. Since you said the stitch function didn't get you the desired results, implement your own stitching. I'm trying to do something close to that too. Here is a tutorial on how to implement it in c++: https://ramsrigoutham.com/2012/11/22/panorama-image-stitching-in-opencv/
You can use Hough algorithm with high threshold on two images and then compare the vertical lines on both of them - most of them should be shifted a bit, but keep the angle.
This is what I've got from running this algorithm on one of the pictures:
Filtering out horizontal lines should be easy(as they are represented as Vec4i), and then you can align the remaining lines together.
Here is the example of using it in OpenCV's documentation.
UPDATE: another thought. Aligning the lines together can be done with the concept similar to how cross-correlation function works. Doesn't matter if picture 1 has 10 lines, and picture 2 has 100 lines, position of shift with most lines aligned(which is, mostly, the maximum for CCF) should be pretty close to the answer, though this might require some tweaking - for example giving weight to every line based on its length, angle, etc. Computer vision never has a direct way, huh :)
UPDATE 2: I actually wonder if taking bottom pixels line of top image as an array 1 and top pixels line of bottom image as array 2 and running general CCF over them, then using its maximum as shift could work too... But I think it would be a known method if it worked good.
So, I'm taking over the work on an ortho-rectification algorithm that is intended to produce "accurate" results. I'm running into trouble trying to increase the accuracy and could use a little help.
Here is the basic approach.
Extract a calibration pattern from an image that was taken from a mobile phone.
Rectify the image based on a calibration pattern in the image
Scale the image to get the real world size of the scene around the pattern.
The calibration pattern is held against a flat surface, like a wall, counter, table, floor and the user takes a picture. With that picture, we want to measure artifacts on the same surface as the calibration pattern. We have tried this with calibration patterns ranging from the size of a credit card to a sheet of paper (8.5" x 11")
Here is an example input picture
With this resulting output image
Right now our measurements are usually within 1-2% of what we expect. This is sufficient for small areas (less than 25cm away from the calibration pattern. However, we'd like the algorithm to scale so that we can accurately measure a 2x2 meter area. However, at that size, the current error is too much (2-4 cm).
Here is the algorithm we are following.
// convert original image to grayscale and perform morphological dilation to reduce false matches when finding circle grid
Mat imgGray;
cvtColor(imgOriginal, imgGray, CV_BGR2GRAY);
// find calibration pattern in original image
Size patternSize(4, 11);
vector <Point2f> circleCenters_OriginalImage;
if (!findCirclesGrid(imgGray, patternSize, circleCenters_OriginalImage, CALIB_CB_ASYMMETRIC_GRID))
{
return false;
}
Point2f inputQuad[4];
inputQuad[0] = Point2f(circleCenters_OriginalImage[0].x, circleCenters_OriginalImage[0].y);
inputQuad[1] = Point2f(circleCenters_OriginalImage[3].x, circleCenters_OriginalImage[3].y);
inputQuad[2] = Point2f(circleCenters_OriginalImage[43].x, circleCenters_OriginalImage[43].y);
inputQuad[3] = Point2f(circleCenters_OriginalImage[40].x, circleCenters_OriginalImage[40].y);
// create model points for calibration pattern
vector <Point2f> circleCenters_ObjectSpace = GeneratePatternPointsInObjectSpace(circleCenters_OriginalImage[0], Distance(circleCenters_OriginalImage[0], circleCenters_OriginalImage[1]) / 2.0f, ioData.marker_up);
Point2f outputQuad[4];
outputQuad[0] = Point2f(circleCenters_ObjectSpace[0].x, circleCenters_ObjectSpace[0].y);
outputQuad[1] = Point2f(circleCenters_ObjectSpace[3].x, circleCenters_ObjectSpace[3].y);
outputQuad[2] = Point2f(circleCenters_ObjectSpace[43].x, circleCenters_ObjectSpace[43].y);
outputQuad[3] = Point2f(circleCenters_ObjectSpace[40].x, circleCenters_ObjectSpace[40].y);
Mat lambda(2,4,CV_32FC1);
lambda = Mat::zeros(imgOriginal.rows, imgOriginal.cols, imgOriginal.type());
lambda = getPerspectiveTransform(inputQuad, outputQuad);
warpPerspective(imgOriginal, imgOrthorectified, lambda, imgOrthorectified.size());
...
My Questions:
Is it reasonable to shoot for error < 0.25%? Is there a different algorithm that would yield more accurate results? What are the most valuable sources of error to identify and resolve?
As I've worked on this, I've also looked at removing pincushion / barrel distortions, and trying homographies to find the perspective transform. The best approaches I have found so far remain in the 1-2% error.
Any suggestions of where to go next would be really helpful
I'm trying to deskew an image that has an element of known size. Given this image:
I can use aruco:: estimatePoseBoard which returns rotation and translation vectors. Is there a way to use that information to deskew everything that's in the same plane as the marker board? (Unfortunately my linear algebra is rudimentary at best.)
Clarification
I know how to deskew the marker board. What I want to be able to do is deskew the other things (in this case, the cloud-shaped object) in the same plane as the marker board. I'm trying to determine whether or not that's possible and, if so, how to do it. I can already put four markers around the object I want to deskew and use the detected corners as input to getPerspectiveTransform along with the known distance between them. But for our real-world application it may be difficult for the user to place markers exactly. It would be much easier if they could place a single marker board in the frame and have the software deskew the other objects.
Since you tagged OpenCV:
From the image I can see that you have detected the corners of all the black box. So just get the most border for points in a way or another:
Then it is like this:
std::vector<cv::Point2f> src_points={/*Fill your 4 corners here*/};
std::vector<cv::Point2f> dst_points={cv:Point2f(0,0), cv::Point2f(width,0), cv::Point2f(width,height),cv::Point2f(0,height)};
auto H=v::getPerspectiveTransform(src_points,dst_points);
cv::Mat copped_image;
cv::warpPerspective(full_image,copped_image,H,cv::Size(width,height));
I was stuck on the assumption that the destination points in the call to getPerspectiveTransform had to be the corners of the output image (as they are in Humam's suggestion). Once it dawned on me that the destination points could be somewhere within the output image I had my answer.
float boardX = 1240;
float boardY = 1570;
float boardWidth = 1730;
float boardHeight = 1400;
vector<Point2f> destinationCorners;
destinationCorners(Point2f(boardX+boardWidth, boardY));
destinationCorners(Point2f(boardX+boardWidth, boardY+boardHeight));
destinationCorners(Point2f(boardX, boardY+boardHeight));
destinationCorners(Point2f(boardX, boardY));
Mat h = getPerspectiveTransform(detectedCorners, destinationCorners);
Mat bigImage(image.size() * 3, image.type(), Scalar(0, 50, 50));
warpPerspective(image, bigImage, h, bigImage.size());
This fixed the perspective of the board and everything in its plane. (The waviness of the board is due to the fact that the paper wasn't lying flat in the original photo.)
I want to create a Depth Map in order to obtain the 3D position of each pixels so that I can have 3D position of some selected Item on my picture. In order to see if my depth data is correct, I visualize it with MeshLab.
I use the stereo data of KITTI dataset so the images are rectified and the calibration for each camera is provided.
The process is the following:
Image left + image right --> Compute disparity using Stereo Semi Global Matching (SGBM) --> Compute the depth Map using cv::reprojectImageTo3D() with the Q initialized thanks to the parameters of the calibration and thanks to this function:
cv::stereoRectify(cameraMatrix1, distCoeffs1, cameraMatrix2, distCoeffs2, imgSize, R, T, R1, R2, P1, P2, Q);
My problem is the following:
The road is okey but the sign board have some distortion. I don't understand and I tried to change the parameters but without success. I always have this distortion. It's annoying because I cannot compute a good 3D position of the sign board.
I tried also with the classic block matching but It's the same and the results is not that good in comparison with the semi global one.
However my disparity looks like this (Which seems good to me) :
The parameters of the disparity computation is the following:
StereoSGBM sgbm;
sgbm.SADWindowSize = 3;
sgbm.numberOfDisparities = 128;
sgbm.preFilterCap = 10;
sgbm.minDisparity = 0;
sgbm.uniquenessRatio = 10.0;
sgbm.speckleWindowSize = 100;
sgbm.speckleRange = 32;
sgbm.disp12MaxDiff = 1;
sgbm.fullDP = 1;
sgbm.P1 = sgbm.SADWindowSize*sgbm.SADWindowSize*4;
sgbm.P2 = sgbm.SADWindowSize*sgbm.SADWindowSize*32;
sgbm(gray1, gray2, disp);
Do you have an idea why that's happened ? How I can solve that ? I would like to have a well planar surface of the sign board.
You could probably improve things slightly by playing with the SGBM parameters, but the reality is stereo data is noisy and you should not expect to get a perfectly planar sign in your point cloud.
If you are interested in finding the 3D location of the sign, segmenting the sign from the RGB image and averaging the corresponding points in the point cloud together should produce reasonable results.
For a group project, we are attempting to make a game, where functions are executed whenever a player forms a set of specific hand gestures in front of a camera. To process the images, we are using Open-CV 2.3.
During the image-processing we are trying to find the length between two points.
We already know this can be done very easily with Pythagoras law, though it is known that Pythagoras law requires much computer power, and we wish to do this as low-resource as possible.
We wish to know if there exist any build-in function within Open-CV or standard library for C++, which can handle low-resource calculations of the distance between two points.
We have the coordinates for the points, which are in pixel values (Of course).
Extra info:
Previous experience have taught us, that OpenCV and other libraries are heavily optimized. As an example, we attempted to change the RGB values of the live image feed from the camera with a for loop, going through each pixel. This provided with a low frame-rate output. Instead we decided to use an Open-CV build-in function instead, which instead gave us a high frame-rate output.
You should try this
cv::Point a(1, 3);
cv::Point b(5, 6);
double res = cv::norm(a-b);//Euclidian distance
As you correctly pointed out, there's an OpenCV function that does some of your work :)
(Also check the other way)
It is called magnitude() and it calculates the distance for you. And if you have a vector of more than 4 vectors to calculate distances, it will use SSE (i think) to make it faster.
Now, the problem is that it only calculate the square of the powers, and you have to do by hand differences. (check the documentation). But if you do them also using OpenCV functions it should be fast.
Mat pts1(nPts, 1, CV_8UC2), pts2(nPts, 1, CV_8UC2);
// populate them
Mat diffPts = pts1-pts2;
Mat ptsx, ptsy;
// split your points in x and y vectors. maybe separate them from start
Mat dist;
magnitude(ptsx, ptsy, dist); // voila!
The other way is to use a very fast sqrt:
// 15 times faster than the classical float sqrt.
// Reasonably accurate up to root(32500)
// Source: http://supp.iar.com/FilesPublic/SUPPORT/000419/AN-G-002.pdf
unsigned int root(unsigned int x){
unsigned int a,b;
b = x;
a = x = 0x3f;
x = b/x;
a = x = (x+a)>>1;
x = b/x;
a = x = (x+a)>>1;
x = b/x;
x = (x+a)>>1;
return(x);
}
This ought to a comment, but I haven't enough rep (50?) |-( so I post it as an answer.
What the guys are trying to tell you in the comments of your questions is that if it's only about comparing distances, then you can simply use
d=(dx*dx+dy*dy) = (x1-x2)(x1-x2) + (y1-y2)(y1-y2)
thus avoiding the square root. But you can't of course skip the square elevation.
Pythagoras is the fastest way, and it really isn't as expensive as you think. It used to be, because of the square-root. But modern processors can usually do this within a few cycles.
If you really need speed, use OpenCL on the graphics card for image processing.