From fc674353775e936757f0cde9e474f427071b531a Mon Sep 17 00:00:00 2001 From: Tiger-The-Cat <70044734+Tiger-The-Cat@users.noreply.github.com> Date: Sun, 28 Jan 2024 14:54:32 -0800 Subject: [PATCH] Fix Latex & Footnotes render.githubusercontent has been replaced by mathjax. --- README.md | 21 ++++++++++----------- 1 file changed, 10 insertions(+), 11 deletions(-) diff --git a/README.md b/README.md index 3005187..efbb64b 100644 --- a/README.md +++ b/README.md @@ -13,7 +13,7 @@ Camera calibration computes the following parameters: * Rotation vector * Translation vector -Following is a brief description of the process [1]. +Following is a brief description of the process[^1]. #### Distortion Coefficients

@@ -23,10 +23,10 @@ Radial distortion causes straight lines to appear curved. Radial distortion beco

- +$x_{distorted} = x( 1 + k_1 r^2 + k_2 r^4 + k_3 r^6)$

- +$y_{distorted} = y( 1 + k_1 r^2 + k_2 r^4 + k_3 r^6)$

@@ -34,10 +34,10 @@ Similarly, tangential distortion occurs because the image-taking lense is not al

- +$x_{distorted} = x + [ 2p_1xy + p_2(r^2+2x^2)]$

- +$y_{distorted} = y + [ p_1(r^2+ 2y^2)+ 2p_2xy]$

@@ -45,23 +45,23 @@ In short, we need to find five parameters, known as distortion coefficients give

- +$dist = (k_1 \hspace{10pt} k_2 \hspace{10pt} p_1 \hspace{10pt} p_2 \hspace{10pt} k_3)$

#### Camera Intrinsic Parameters

-Intrinsic parameters are specific to a camera. They include information like focal length and optical center . The focal length and optical center can be used to create a camera matrix, which can be used to remove distortion due to the lens of a specific camera. The camera matrix is unique to a specific camera, so once calculated, it can be reused on other images captured by the same camera. It is expressed as a matrix: + Intrinsic parameters are specific to a camera. They include information like focal length $(f_x,f_y)$ and optical center $(c_x,c_y)$. The focal length and optical center can be used to create a camera matrix, which can be used to remove distortion due to the lens of a specific camera. The camera matrix is unique to a specific camera, so once calculated, it can be reused on other images captured by the same camera. It is expressed as a $3 \times 3$ matrix:

- + $$mtx=\left[\begin{matrix} f_x & 0 & c_x \\ 0 & f_y & c_y \\ 0 & 0 & 1 \end{matrix}\right]$$

#### Camera Extrinsic Parameters

-Extrinsic parameters correspond to rotation and translation vectors, and respectively, which transform 3D coordinates of a point in world frame to camera coordinate system. +Extrinsic parameters correspond to rotation and translation vectors, $r_{vecs}$ and $t_{vecs}$ respectively, which transform 3D coordinates of a point in world frame to camera coordinate system.

### Implementation: @@ -83,5 +83,4 @@ Once we get the `objpoints` and `imgpoints`, we can use them to calibrate the ca **Note:** To calibrate your own camera, you will need to print a suitable [calibration grid](https://github.com/Tinker-Twins/Camera-Calibration/tree/main/Calibration%20Grid) and use your own camera to take multiple pictures of the grid from various angles (similar to the sample [calibration images](https://github.com/Tinker-Twins/Camera-Calibration/tree/main/Calibration%20Images) in this repository). For better results, the distance between the camera and calibration grid should be approximately equal to the working distance that you intend to maintain in your application. Additionally, the resolution and focus of the camera should be maintained constant while taking pictures. ### References: - -[1] OpenCV, \"Camera Calibration,\" [Online]. Available: https://docs.opencv.org/master/dc/dbb/tutorial_py_calibration.html +[^1]: OpenCV, \"Camera Calibration,\" [Online]. Available: https://docs.opencv.org/master/dc/dbb/tutorial_py_calibration.html