SLAM Introduction

the sparse map of SLAM
sparse

the dense map of SLAM
dense

Cylinder Block Model

Cylinderblockmodel

a Cylinder block model has six degree of freedom, rotation has three and translation has three. which can be described as follow.

Pinhole Camera Model

pinhole a pinhole camera coordinate can be described as follow

${\begin{bmatrix}u \\ u \end{bmatrix}} = {\begin{bmatrix} fx & 0 & cx\\ 0 & fy & cy\\ 0 & 0 & 1\\ \end{bmatrix}} {\begin{bmatrix} {R_{3*3}}&{t_{3*1}}\\ {0_{1*3}}&{1_{1*1}}\\ \end{bmatrix}} * {P_w}$

${{P_c} = {\begin{bmatrix} {R_{3*3}}&{t_{3*1}}\\ {0_{1*3}}&{1_{1*1}}\\ \end{bmatrix}} * {P_w}}$

${R_{3*3}}{\text{ is a Orthogonal matrix}}\\ P_w{\text{ is point} (X, Y, Z, 1) \text{in world coordinate}}\\ P_c{\text{ is point} (X_c, Y_c, Z_c, 1) \text{in camera coordinate}}$