Cumulative Homography Wrongly Scaling - c++

I'm to build a panorama image of the ground covered by a downward facing camera (at a fixed height, around 1 metre above ground). This could potentially run to thousands of frames, so the Stitcher class' built in panorama method isn't really suitable - it's far too slow and memory hungry.
Instead I'm assuming the floor and motion is planar (not unreasonable here) and trying to build up a cumulative homography as I see each frame. That is, for each frame, I calculate the homography from the previous one to the new one. I then get the cumulative homography by multiplying that with the product of all previous homographies.
Let's say I get H01 between frames 0 and 1, then H12 between frames 1 and 2. To get the transformation to place frame 2 onto the mosaic, I need to get H01*H12. This continues as the frame count increases, such that I get H01*H12*H23*H34*H45*....
In code, this is something akin to:
cv::Mat previous, current;
// Init cumulative homography
cv::Mat cumulative_homography = cv::Mat::eye(3);
video_stream >> previous;
for(;;) {
video_stream >> current;
// Here I do some checking of the frame, etc
// Get the homography using my DenseMosaic class (using Farneback to get OF)
cv::Mat tmp_H = DenseMosaic::get_homography(previous,current);
// Now normalise the homography by its bottom right corner
tmp_H /= tmp_H.at<double>(2, 2);
cumulative_homography *= tmp_H;
previous = current.clone( );
}
It works pretty well, except that as the camera moves "up" in the viewpoint, the homography scale decreases. As it moves down, the scale increases again. This gives my panoramas a perspective type effect that I really don't want.
For example, this is taken on a few seconds of video moving forward then backward. The first frame looks ok:
The problem comes as we move forward a few frames:
Then when we come back again, you can see the frame gets bigger again:
I'm at a loss as to where this is coming from.
I'm using Farneback dense optical flow to calculate pixel-pixel correspondences as below (sparse feature matching doesn't work well on this data) and I've checked my flow vectors - they're generally very good, so it's not a tracking problem. I also tried switching the order of the inputs to find homography (in case I'd mixed up the frame numbers), still no better.
cv::calcOpticalFlowFarneback(grey_1, grey_2, flow_mat, 0.5, 6,50, 5, 7, 1.5, flags);
// Using the flow_mat optical flow map, populate grid point correspondences between images
std::vector<cv::Point2f> points_1, points_2;
median_motion = DenseMosaic::dense_flow_to_corresp(flow_mat, points_1, points_2);
cv::Mat H = cv::findHomography(cv::Mat(points_2), cv::Mat(points_1), CV_RANSAC, 1);
Another thing I thought it could be was the translation I include in the transformation to ensure my panorama is centred within the scene:
cv::warpPerspective(init.clone(), warped, translation*homography, init.size());
But having checked the values in the homography before the translation is applied, the scaling issue I mention is still present.
Any hints are gratefully received. There's a lot of code I could put in but it seems irrelevant, please do let me know if there's something missing
UPDATE
I've tried switching out the *= operator for the full multiplication and tried reversing the order the homographies are multiplied in, but no luck. Below is my code for calculating the homography:
/**
\brief Calculates the homography between the current and previous frames
*/
cv::Mat DenseMosaic::get_homography()
{
cv::Mat grey_1, grey_2; // Grayscale versions of frames
cv::cvtColor(prev, grey_1, CV_BGR2GRAY);
cv::cvtColor(cur, grey_2, CV_BGR2GRAY);
// Calculate the dense flow
int flags = cv::OPTFLOW_FARNEBACK_GAUSSIAN;
if (frame_number > 2) {
flags = flags | cv::OPTFLOW_USE_INITIAL_FLOW;
}
cv::calcOpticalFlowFarneback(grey_1, grey_2, flow_mat, 0.5, 6,50, 5, 7, 1.5, flags);
// Convert the flow map to point correspondences
std::vector<cv::Point2f> points_1, points_2;
median_motion = DenseMosaic::dense_flow_to_corresp(flow_mat, points_1, points_2);
// Use the correspondences to get the homography
cv::Mat H = cv::findHomography(cv::Mat(points_2), cv::Mat(points_1), CV_RANSAC, 1);
return H;
}
And this is the function I use to find the correspondences from the flow map:
/**
\brief Calculate pixel->pixel correspondences given a map of the optical flow across the image
\param[in] flow_mat Map of the optical flow across the image
\param[out] points_1 The set of points from #cur
\param[out] points_2 The set of points from #prev
\param[in] step_size The size of spaces between the grid lines
\return The median motion as a point
Uses a dense flow map (such as that created by cv::calcOpticalFlowFarneback) to obtain a set of point correspondences across a grid.
*/
cv::Point2f DenseMosaic::dense_flow_to_corresp(const cv::Mat &flow_mat, std::vector<cv::Point2f> &points_1, std::vector<cv::Point2f> &points_2, int step_size)
{
std::vector<double> tx, ty;
for (int y = 0; y < flow_mat.rows; y += step_size) {
for (int x = 0; x < flow_mat.cols; x += step_size) {
/* Flow is basically the delta between left and right points */
cv::Point2f flow = flow_mat.at<cv::Point2f>(y, x);
tx.push_back(flow.x);
ty.push_back(flow.y);
/* There's no need to calculate for every single point,
if there's not much change, just ignore it
*/
if (fabs(flow.x) < 0.1 && fabs(flow.y) < 0.1)
continue;
points_1.push_back(cv::Point2f(x, y));
points_2.push_back(cv::Point2f(x + flow.x, y + flow.y));
}
}
// I know this should be median, not mean, but it's only used for plotting the
// general motion direction so it's unimportant.
cv::Point2f t_median;
cv::Scalar mtx = cv::mean(tx);
t_median.x = mtx[0];
cv::Scalar mty = cv::mean(ty);
t_median.y = mty[0];
return t_median;
}

It turns out this was because my viewpoint was close to the features, meaning that the non-planarity of the tracked features was causing skew to the homography. I managed to prevent this (it's more of a hack than a method...) by using estimateRigidTransform instead of findHomography, as this does not estimate for perspective variations.
In this particular case, it makes sense to do so, as the view does only ever undergo rigid transformations.

Related

What is the correct way to average several ARUCO rotation vectors

I am writing a Eye On Hand Calibration Program.
To do that, I am moving the camera mounted on the robot arm to 20 different positions, looking at a single aruco marker.
The translation vector is very stable, but the rotation axes flicker, introducing an error into the resulting calibration matrix.
Therefore, I would like to average X number of frames' rotation vectors (The aruco library does return rotation vectors and translation vectors separately).
Here is the important part of the code
cv::aruco::detectMarkers(image, dictionary, markerCorners, markerIds, parameters, rejectedCandidates);
outputImage = image.clone();
cv::aruco::drawDetectedMarkers(outputImage, markerCorners, markerIds);
cv::aruco::estimatePoseSingleMarkers(markerCorners, 0.05, camMatrix, distCoeffs, rvecs, tvecs);
rvecs is actualy a vector of rotation vectors, with only one member because there is only one aruco marker.
If a marker is found in the frame then,
if (rvecs.size() == 1) { // There is one marker good frame
framesFound++;
for (int i = 0; i < 3; i++) {
avgRvecs[i] =+ rvecs[0][i];
avgTvecs[i] =+ tvecs[0][i];
}
}
And after all the desired frames to average have been processed,
if (framesFound == 0 ) { // No frames with markers...
} else {
for (int i = 0; i < 3; i++) {
avgRvecs[i] = avgRvecs[i] / framesFound;
avgTvecs[i] = avgTvecs[i] / framesFound;
}
cv::drawFrameAxes(outputImage, camMatrix, distCoeffs, avgRvecs, avgTvecs, 0.1);
With a single frame I get
With 10 averaged frames I get
Because the pose estimation of Aruco markers is usually done with IPPE (the algorithm under the hood of solvePnP), you might have some "singularities" in the rotation results.
Averaging the rotations can be a good solution as it works as a low-pass filter, though you need to remember that if you are seeking precision, this might not be the most appropriate filter to use.
Most of the time, we like to manipulate Euler angles, Direct Cosine Matrix, or Rodriguez angles. Unfortunately, none of those is the ideal solution to average angular values. If you want to manipulate angles without mathematical errors, I definitely recommend having a look at quaternions.
Some existing posts suggest interesting approaches with quaternions :
"Average" of multiple quaternions?
https://math.stackexchange.com/questions/1984608/average-of-3d-rotations
Math can be a little scary but the posts come with well written code examples.

Is it possible to obtain distance scaling in Monocular ORB-SLAM2?

I am trying to find the real world distance from camera to ORB feature points using Monocular ORB SLAM2.
I calculated the Euclidean distance between world coordinates of each ORB feature point and the world coordinate of the current key frame's camera location. This process is repeated for all the frames. So a distance is obtained for each ORB point in the current frame.
In Viewer.cc
std::vector<MapPoint*> MP = mpTracker->mCurrentFrame.mvpMapPoints;
cv::Mat CC = mpTracker->mCurrentFrame.GetCameraCenter();
mpFrameDrawer->DrawFrame(MP,CC);
In FrameDrawer.cc
cv::Mat FrameDrawer::DrawFrame(std::vector<MapPoint*> DistMapPt, cv::Mat CameraPt)
{
.
.
.
else if(state==Tracking::OK) //TRACKING
{
mnTracked=0;
mnTrackedVO=0;
const float r = 5;
for(int i=0;i<n;i++)
{
if(vbVO[i] || vbMap[i])
{
cv::Point2f pt1,pt2;
pt1.x=vCurrentKeys[i].pt.x-r;
pt1.y=vCurrentKeys[i].pt.y-r;
pt2.x=vCurrentKeys[i].pt.x+r;
pt2.y=vCurrentKeys[i].pt.y+r;
float MapPointDist;
MapPointDist = sqrt(pow((DistMapPt[i]->GetWorldPos().at<float>(0)-CameraPt.at<float>(0)),2)+pow((DistMapPt[i]->GetWorldPos().at<float>(1)-CameraPt.at<float>(1)),2)+pow((DistMapPt[i]->GetWorldPos().at<float>(2)-CameraPt.at<float>(2)),2));
}
.
.
.
}
}
}
How ever this calculated distance is neither equal to nor can be scaled to the real distance. The same method gives relatively accurate distances in RGBD ORB SLAM2.
Is there any method to scale distances in Monocular ORB SLAM?
Please look at this post: "ORB-SLAM2 arbitrarily define scale at initialization, as the median scene depth. In practice, scale is different every time you initialize orb-slam2." It is impossible to obtain correct scale in monocular SLAM as you cannot estimate real world depth from sequence of images. You need another source of data such as second camera, IMU, Lidar, robot odometry or a marker with known real-world dimensions. In RGBD case the depth is known from the depth sensor so the coordinates are scaled correctly.

Hausdorff Distance Object Detection

I have been struggling trying to implement the outlining algorithm described here and here.
The general idea of the paper is determining the Hausdorff distance of binary images and using it to find the template image from a test image.
For template matching, it is recommended to construct image pyramids along with sliding windows which you'll use to slide over your test image for detection. I was able to do both of these as well.
I am stuck on how to move forward from here on. Do I slide my template over the test image from different pyramid layers? Or is it the test image over the template? And with regards to the sliding window, is/are they meant to be a ROI of the test or template image?
In a nutshell, I have pieces to the puzzle but no idea of which direction to take to solve the puzzle
int distance(vector<Point>const& image, vector<Point>const& tempImage)
{
int maxDistance = 0;
for(Point imagePoint: image)
{
int minDistance = numeric_limits<int>::max();
for(Point tempPoint: tempImage)
{
Point diff = imagePoint - tempPoint;
int length = (diff.x * diff.x) + (diff.y * diff.y);
if(length < minDistance) minDistance = length;
if(length == 0) break;
}
maxDistance += minDistance;
}
return maxDistance;
}
double hausdorffDistance(vector<Point>const& image, vector<Point>const& tempImage)
{
double maxDistImage = distance(image, tempImage);
double maxDistTemp = distance(tempImage, image);
return sqrt(max(maxDistImage, maxDistTemp));
}
vector<Mat> buildPyramids(Mat& frame)
{
vector<Mat> pyramids;
int count = 6;
Mat prevFrame = frame, nextFrame;
while(count > 0)
{
resize(prevFrame, nextFrame, Size(), .85, .85);
prevFrame = nextFrame;
pyramids.push_back(nextFrame);
--count;
}
return pyramids;
}
vector<Rect> slidingWindows(Mat& image, int stepSize, int width, int height)
{
vector<Rect> windows;
for(size_t row = 0; row < image.rows; row += stepSize)
{
if((row + height) > image.rows) break;
for(size_t col = 0; col < image.cols; col += stepSize)
{
if((col + width) > image.cols) break;
windows.push_back(Rect(col, row, width, height));
}
}
return windows;
}
Edit I: More analysis on my solution can be found here
This is a bi-directional task.
Forward Direction
1. Translation
For each contour, calculate its moment. Then for each point in that contour, translate it about the moment i.e. contour.point[i] = contour.point[i] - contour.moment[i]. This moves all of the contour points to the origin.
PS: You need to keep track of each contour's produced moment because it will be used in the next section
2. Rotation
With the newly translated points, calculate their rotated rect. This will give you the angle of rotation. Depending on this angle, you would want to calculate the new angle which you want to rotate this contour by; this answer would be helpful.
After attaining the new angle, calculate the rotation matrix. Remember that your center here will be the origin i.e. (0, 0). I did not take scaling into account (that's where the pyramids come into play) when calculating the rotation matrix hence I passed 1.
PS: You need to keep track of each contour's produced matrix because it will be used in the next section
Using this matrix, you can go ahead and rotate each point in the contour by it as shown here*.
Once all of this is done, you can go ahead and calculate the Hausdorff distance and find contours which pass your set threshold.
Back Direction
Everything done in the first section, has to be undone in order for us to draw the valid contours onto our camera feed.
1. Rotation
Recall that each detected contour produced a rotation matrix. You want to undo the rotation of the valid contours. Just perform the same rotation but using the inverse matrix.
For each valid contour and corresponding matrix
inverse_matrix = matrix[i].inv(cv2.DECOMP_SVD)
Use * to rotate the points but with inverse_matrix as parameter
PS: When calculating the inverse, if the produced matrix was not a square one, it would fail. cv2.DECOMP_SVD will produce an inverse matrix even if the original matrix was a non-square.
2. Translation
With the valid contours' points rotated back, you just have to undo the previously performed translation. Instead of subtracting, just add the moment to each point.
You can now go ahead and draw these contours to your camera feed.
Scaling
This is were image pyramids come into play.
All you have to do is resize your template image by a fixed size/ratio upto your desired number of times (called layers). The tutorial found here does a good job of explaining how to do this in OpenCV.
It goes without saying that the values you choose to resize your image by and number of layers will and do play a huge role in how robust your program will be.
Put it all together
Template Image Operations
Create a pyramid consisting of n layers
For each layer in n
Find contours
Translate the contour points
Rotate the contour points
This operation should only be performed once and only store the results of the rotated points.
Camera Feed Operations
Assumptions
Let the rotated contours of the template image at each level be stored in templ_contours. So if I say templ_contours[0], this is going to give me the rotated contours at pyramid level 0.
Let the image's translated, rotated contours and moments be stored in transCont, rotCont and moment respectively.
image_contours = Find Contours
for each contour detected in image
moment = calculate moment
for each point in image_contours
transCont.thisPoint = forward_translate(image_contours.thisPoint)
rotCont.thisPoint = forward_rotate(transCont.thisPoint)
for each contour_layer in templ_contours
for each contour in rotCont
calculate Hausdorff Distance
valid_contours = contours_passing_distance_threshold
for each point in valid_contours
valid_point = backward_rotate(valid_point)
for each point in valid_contours
valid_point = backward_translate(valid_point)
drawContours(valid_contours, image)

OpenCV Dense feature detector

I am using openCV to do some dense feature extraction. For example, The code
DenseFeatureDetector detector(12.f, 1, 0.1f, 10);
I don't really understand the parameters in the above constructor. What does it mean ? Reading the opencv documentation about it does not help much either. In the documentation the arguments are:
DenseFeatureDetector( float initFeatureScale=1.f, int featureScaleLevels=1,
float featureScaleMul=0.1f,
int initXyStep=6, int initImgBound=0,
bool varyXyStepWithScale=true,
bool varyImgBoundWithScale=false );
What are they supposed to do ? i.e. what is the meaning of scale, initFeatureScale, featureScaleLevels etc ? How do you know the grid or grid spacing etc for the dense sampling.
I'm using opencv with dense detector too and I think I can help you with something. I'm not sure about what I'm going to say but the experience learnt me that.
When I use Dense detector I pass there the gray scale image. The detector makes some threshold filters where opencv uses a gray minimum value with is used to transform the image. The píxels where have a more gray level than the threshold will be made like black points and the others are white point. This action is repeated in a loop where the threshold will be bigger and bigger. So the parameter initFeatureScale determine the first threshold you put to do this loop, the featureScaleLevels parameter indicates how much this threshold is bigger between one loop iteration and the next one and featureScaleMul is a multiply factor to calculate the next threshold.
Anyway if you are looking for a your optimal parameters to use Dense detector to detect any particular points You would offer a program I made for that. It is liberated in github. This is a program where you can test some detectors (Dense detector is one of them) and check how it works if you change their parameters thanks to a user interface that let you change the detectors parameters as long as you are executing the program. You will see how the detected points will be change. For try it just click on the link, and download the files. You might need almost all the files to execute the program.
Apologies in advance, i'm predominantly using Python so i'll avoid embarressing myself by referring to C++.
DenseFeatureDetector populates a vector with KeyPoints to pass to compute feature descriptors. These keypoints have a point vector and their scale set. In the documentation, scale is the pixel radius of the keypoint.
KeyPoints are evenly spaced across the width and height of the image matrix passed to DenseFeatureVector.
Now to the arguments:
initFeatureScale
Set the initial KeyPoint feature radius in pixels (as far as I am aware this has no effect)
featureScaleLevels
Number of scales overwhich we wish to make keypoints
featureScaleMuliplier
Scale adjustment for initFeatureScale over featureScaleLevels, this scale adjustment can also be applied to the border (initImgBound) and the step size (initxystep). So when we set featureScaleLevels>1 then this multiplier will be applied to successive scales, to adjust feature scale, step and the boundary around the image.
initXyStep
moving column and row step in pixels. Self explanatory I hope.
initImgBound
row/col bounding region to ignore around the image (pixels), So a 100x100 image, with an initImgBound of 10, would create keypoints in the central 80x80 portion of the image.
varyXyStepWithScale
Boolean, if we have multiple featureScaleLevels do we want to adjust the step size using featureScaleMultiplier.
varyImgBoundWithScale
Boolean,as varyXyStepWithScale, but applied to the border.
Here is the DenseFeatureDetector source code from detectors.cpp in the OpenCV 2.4.3 source, which will probably explain better than my words:
DenseFeatureDetector::DenseFeatureDetector( float _initFeatureScale, int _featureScaleLevels,
float _featureScaleMul, int _initXyStep,
int _initImgBound, bool _varyXyStepWithScale,
bool _varyImgBoundWithScale ) :
initFeatureScale(_initFeatureScale), featureScaleLevels(_featureScaleLevels),
featureScaleMul(_featureScaleMul), initXyStep(_initXyStep), initImgBound(_initImgBound),
varyXyStepWithScale(_varyXyStepWithScale), varyImgBoundWithScale(_varyImgBoundWithScale)
{}
void DenseFeatureDetector::detectImpl( const Mat& image, vector<KeyPoint>& keypoints, const Mat& mask ) const
{
float curScale = static_cast<float>(initFeatureScale);
int curStep = initXyStep;
int curBound = initImgBound;
for( int curLevel = 0; curLevel < featureScaleLevels; curLevel++ )
{
for( int x = curBound; x < image.cols - curBound; x += curStep )
{
for( int y = curBound; y < image.rows - curBound; y += curStep )
{
keypoints.push_back( KeyPoint(static_cast<float>(x), static_cast<float>(y), curScale) );
}
}
curScale = static_cast<float>(curScale * featureScaleMul);
if( varyXyStepWithScale ) curStep = static_cast<int>( curStep * featureScaleMul + 0.5f );
if( varyImgBoundWithScale ) curBound = static_cast<int>( curBound * featureScaleMul + 0.5f );
}
KeyPointsFilter::runByPixelsMask( keypoints, mask );
}
You might expect a call to compute would calculate additional KeyPoint characteristics using the relevant keypoint detection algorithm (e.g. angle), based on the KeyPoints generated by DenseFeatureDetector. Unfortunately this isn't the case for SIFT under Python - i've not looked at at the other feature detectors, nor looked at the behaviour in C++.
Also note that DenseFeatureDetector is not in OpenCV 3.2 (unsure at which release it was removed).

Matching small grayscale images

I want to test whether two images match. Partial matches also interest me.
The problem is that the images suffer from strong noise. Another problem is that the images might be rotated with an unknown angle. The objects shown in the images will roughly always have the same scale!
The images show area scans from a top-shot perspective. "Lines" are mostly walls and other objects are mostly trees and different kinds of plants.
Another problem was, that the left image was very blurry and the right one's lines were very thin.
To compensate for this difference I used dilation. The resulting images are the ones I uploaded.
Although It can easily be seen that these images match almost perfectly I cannot convince my algorithm of this fact.
My first idea was a feature based matching, but the matches are horrible. It only worked for a rotation angle of -90°, 0° and 90°. Although most descriptors are rotation invariant (in past projects they really were), the rotation invariance seems to fail for this example.
My second idea was to split the images into several smaller segments and to use template matching. So I segmented the images and, again, for the human eye they are pretty easy to match. The goal of this step was to segment the different walls and trees/plants.
The upper row are parts of the left, and the lower are parts of the right image. After the segmentation the segments were dilated again.
As already mentioned: Template matching failed, as did contour based template matching and contour matching.
I think the dilation of the images was very important, because it was nearly impossible for the human eye to match the segments without dilation before the segmentation. Another dilation after the segmentation made this even less difficult.
Your first job should be to fix the orientation. I am not sure what is the best algorithm to do that but here is an approach I would use: fix one of the images and start rotating the other. For each rotation compute a histogram for the color intense on each of the rows/columns. Compute some distance between the resulting vectors(e.g. use cross product). Choose the rotation that results in smallest cross product. It may be good idea to combine this approach with hill climbing.
Once you have the images aligned in approximately the same direction, I believe matching should be easier. As the two images are supposed to be at the same scale, compute something analogous to the geometrical center for both images: compute weighted sum of all pixels - a completely white pixel would have a weight of 1, and a completely black - weight 0, the sum should be a vector of size 2(x and y coordinate). After that divide those values by the dimensions of the image and call this "geometrical center of the image". Overlay the two images in a way that the two centers coincide and then once more compute cross product for the difference between the images. I would say this should be their difference.
You can also try following methods to find rotation and similarity.
Use image moments to get the rotation as shown here.
Once you rotate the image, use cross-correlation to evaluate the similarity.
EDIT
I tried this with OpenCV and C++ for the two sample images. I'm posting the code and results below as it seems to work well at least for the given samples.
Here's the function to calculate the orientation vector using image moments:
Mat orientVec(Mat& im)
{
Moments m = moments(im);
double cov[4] = {m.mu20/m.m00, m.mu11/m.m00, m.mu11/m.m00, m.mu02/m.m00};
Mat covMat(2, 2, CV_64F, cov);
Mat evals, evecs;
eigen(covMat, evals, evecs);
return evecs.row(0);
}
Rotate and match sample images:
Mat im1 = imread(INPUT_FOLDER_PATH + string("WojUi.png"), 0);
Mat im2 = imread(INPUT_FOLDER_PATH + string("XbrsV.png"), 0);
// get the orientation vector
Mat v1 = orientVec(im1);
Mat v2 = orientVec(im2);
double angle = acos(v1.dot(v2))*180/CV_PI;
// rotate im2. try rotating with -angle and +angle. here using -angle
Mat rot = getRotationMatrix2D(Point(im2.cols/2, im2.rows/2), -angle, 1.0);
Mat im2Rot;
warpAffine(im2, im2Rot, rot, Size(im2.rows, im2.cols));
// add a border to rotated image
int borderSize = im1.rows > im2.cols ? im1.rows/2 + 1 : im1.cols/2 + 1;
Mat im2RotBorder;
copyMakeBorder(im2Rot, im2RotBorder, borderSize, borderSize, borderSize, borderSize,
BORDER_CONSTANT, Scalar(0, 0, 0));
// normalized cross-correlation
Mat& image = im2RotBorder;
Mat& templ = im1;
Mat nxcor;
matchTemplate(image, templ, nxcor, CV_TM_CCOEFF_NORMED);
// take the max
double max;
Point maxPt;
minMaxLoc(nxcor, NULL, &max, NULL, &maxPt);
// draw the match
Mat rgb;
cvtColor(image, rgb, CV_GRAY2BGR);
rectangle(rgb, maxPt, Point(maxPt.x+templ.cols-1, maxPt.y+templ.rows-1), Scalar(0, 255, 255), 2);
cout << "max: " << max << endl;
With -angle rotation in code, I get max = 0.758. Below is the rotated image in this case with the matching region.
Otherwise max = 0.293