ICP algorithm implementation (MATLAB)

ICP Principle

The ICP (iterative closet point method) iterates through the nearest points method for registration between two sets of data, with the following specific steps to implement

For two sets of point clouds: p p, q q

Step1: Select control Point Pi→∈p \vec{p_{i}}\in{p}, set the initial value of T T t0=t0 t^{0}=t_{0}

Step2: Repeat the following steps until the convergence condition is met

Step2-1: For each control point, pi→\vec{p_{i}} in q Q for its nearest point Qj→\vec{q_{j}}, and as an imaginary corresponding point of pi→\vec{p_{i}}

Step2-2: For determining the corresponding relationship, solving the Tk t^k, and solving the loss function
Ek=∑tk|pi→−qj→|2> e^k=\sum{t^k|\vec{p_{i}}-\vec{q_{j}}|^{2}} >

Step2-3: Recalculate point of Control Point Pi→\vec{p_{i}} after the transformation of the Tk t_{k} and reassign it to Pi→\vec{p_{i}}

The convergence condition of the algorithm is δ=<