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
-
+$dist = (k_1 \hspace{10pt} k_2 \hspace{10pt} p_1 \hspace{10pt} p_2 \hspace{10pt} k_3)$
-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:
-
+ $$mtx=\left[\begin{matrix} f_x & 0 & c_x \\ 0 & f_y & c_y \\ 0 & 0 & 1 \end{matrix}\right]$$
-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.