Image Processing and Recognition

STRAIGHTNESS

When is a curve straight ?

Given a curve as a sequence of pixels C = P[i] for i=0,..,k its displacement is the (euclidean) distance between the endpoints

L{C} = d(P[0], P[k])

Its straightness is

S{C} = L{C} / ( 1 + 1/(k-1) Sum d(P[i], r) )

where r is the line between the endpoints, and d(P, r) denotes the (euclidean) distance from the point P to r,

r: x = P_x[0] + t ( P_x[k] - P_x[0] )
y = P_y[0] + t ( P_y[k] - P_y[0] )

that is

(x - P_x[0]) (P_y[k] - P_y[0] ) = (y - P_y[0]) (P_x[k] - P_x[0] )

The distance is

d(P, r) = (1/D) | (P_x - P_x[0]) (P_y[k] - P_y[0] ) - (P_y - P_y[0]) (P_x[k] - P_x[0] ) |

where D is

D = sqrt( (P_x[k] - P_x[0] )² + (P_y[k] - P_y[0] )² )

Marco Corvi - Page hosted by geocities.com.