Rate Shape Identification Based on Particle Swarm Optimization

Abstract

When a near planar object is viewed from different directions with a camera placed sufficiently far away, its images can be mathematically related with the Affine Transformation as given by

$$ \label{eq1} \left[ {{\begin{array}{*{20}c} {d_{si} (x)} \hfill \\ {d_{si} (y)} \hfill \\ \end{array} }} \right]=\left[ {{\begin{array}{*{20}c} a \hfill & b \hfill \\ c \hfill & d \hfill \\ \end{array} }} \right]\left[ {{\begin{array}{*{20}c} {d_{ ri} (x)} \hfill \\ {d_{ri} (y)} \hfill \\ \end{array} }} \right]+\left[ {{\begin{array}{*{20}c} e \hfill \\ f \hfill \\ \end{array} }} \right] $$

((1))

where ($d_{si}(x), d_{si}(y))$ and ($d_{ri}(x), d_{ri}(y))$ are the co-ordinates of pixels in the scene $O_{scene}$ and reference $O_{ref}$ objects, respectively. The set of parameters $A$ = {a,b,c,d,e,f} are coefficients of the Affine Transformation relating the two images.