# Decomposing Projection Using OpenCV and C++

And the output is:

# 1) cv:: Mat_

You can create a matrix with cv:: Mat_

# 2) cv::Mat

or like this with cv::Mat

if you forgot the list of data types you use

more data types here

# Computing Fundamental Matrix and Drawing Epipolar Lines for Stereo Vision Cameras in OpenCV

Following my other post, you can extract the equation for epipolar lines. Basically choosing one point in one image and using fundamental matrix, we will get a line in the other image:

# Creating a Simulated Stereo Vision Cameras With OpenCV and C++

n this tutorial, I created an ellipsoid in 3D space and create two cameras in right and left and captured the image:​

Point cloud of 3D Ellipsoid

Image from right camera.

Image from left camera.

# Simulating A Virtual Camera With OpenCV and Reverse Projection From 2D to 3D

Projection of Points from 3D in the camera plane:

Computed rays from the camera origin in the direction of points:

points are stored in CSV file like this:

The content of “reverse_projection.hpp”

The content of “transformation.hpp

# Stereo Camera Calibration with ROS and OpenCV

In this tutorial, I’m gonna show you stereo camera calibration with ROS and OpenCV. So you need a pair of cameras, I bought a pair of this USB webcam which is okay for this task.

1)Save the following text under “stereo_usb_cam_stream_publisher.launch

2)Then run the following node to publish both cameras.

3)Now call the calibration node:

Super important:

If you have USB cam with some delays you should add the following “–no-service-check –approximate=0.1”

4)Pose the chess board in different position, and then click on the calibrate and save button.

5) The result gonna be store at /tmp/calibrationdata.tar.gz. Unzip the file and save it under “/home/<username>/.ros/stereo_camera_info

# How to use OpenCV 3 Contribution Modules

OpenCV Contribution Modules are developed code from the community of OpenCV and are not very stable but after they got stable they will be part f OpenCV. Anyhow, there are a lot of cool modules there (fuzzy logic, sfm, cnn, …) that made me have look at them and try them.

1)gflags

2)glog

3)ceres-solver

4)OpenCV

Add the following lines to the top of CMakeLists at root of OpenCV

Make a build directory in OpenCV3 and changed the current directory to that, then run the following command:

# Computing OpticalFlow with OpenCV

There are two main approaches for computing optical flow, computing optical flow for all pixel or computing optical flow for corners.

# Finding Homography Matrix using Singular-value Decomposition and RANSAC in OpenCV and Matlab



Solving a Homography problem leads to solving a set of homogeneous linear equations such below:

\left(
\begin{array}{ccccccccc}
-x1 & -y1 & -1 & 0 & 0 & 0 & x1*xp1 & y1*xp1 & xp1\\
0 & 0 & 0 & -x1 & -y1 & -1 & x1*yp1 & y1*yp1 &  yp1\\
-x2 & -y2 & -1 & 0 & 0 & 0 & x2*xp2 & y2*xp2 & xp2\\
0 & 0 & 0 & -x2 & -y2 & -1 & x2*yp2 & y2*yp2 & yp2\\
-x3 & -y3 & -1 & 0 & 0 & 0 & x3*xp3 & y3*xp3 & xp3\\
0 & 0 & 0 & -x3 & -y3 & -1 & x3*yp3 & y3*yp3 & yp3\\
-x4 & -y4 & -1 & 0 & 0 & 0 & x4*xp4 & y4*xp4 & xp4\\
0 & 0 & 0 & -x4 & -y4 & -1 & x4*yp4 & y4*yp4 & yp4\\
\end{array}
\right) *H=0

$$H^{*} \underset{H}{\mathrm{argmin}}= \|AH\|^{2}$$ subject to $$\|H\|=1$$

We can’t use least square since it’s a homogeneous linear equations (the other side of equation is 0 therfore we can’t just multyly it by the psudo inverse). To solve this problem we use Singular-value Decomposition (SVD).

For any given matrix $$A_{M{\times}N}$$

\underbrace{\mathbf{A}}_{M \times N} = \underbrace{\mathbf{U}}_{M \times M} \times \underbrace{\mathbf{\Sigma}}_{M\times N} \times \underbrace{\mathbf{V}^{\text{T}}}_{N \times N}

$$U$$ is an $${M\times M}$$ matrix with orthogonal matrix (columns are eigen vectors of A).
$$\Sigma$$ is an $${M\times N}$$ matrix with non-negative entries, termed the singular values  (diagonal entries are eigen values of A).
$$V$$ is an $${N\times N}$$ orthogonal matrix.

$$H^{*}$$ is the last column of $$V$$

# Peak Signal-to-Noise Ratio (PSNR) in Image using OpenCV and Matlab



Peak signal-to-noise ratio (PSNR) shows the ratio between the maximum possible power of a signal and the power of the same image with noise. PSNR is usually expressed in logarithmic decibel scale.

$$MSE =1/m*n \sum_{i=0}^{m-1} \sum_{j=0}^{n-1} [ Image( i,j) -NoisyImage( i,j) ] ^2$$
$$PSNR =10* \log_{10} \Bigg(MAXI^2/MSE\Bigg)$$

MSE is Mean Square Error and MAXI is the maximum possible pixel value of the image. For instance if the image is uint8, it will be 255.

Ref [1],[2], [3], 4