On the Fréchet distance of a set of curves

A curve is a continuous mapping ! " #%$%&(' )+* with " #%$-,.) and "0/1$ . As a measure for the resemblance of curves, Alt and Godau have considered the so-called Frechet distance 243 . Definition 1 Let 5 6 " #%"879&:';) $?#@$A7BC)>* be two curves. The Frechet distance, denoted 2D3FEG # = H , is defined as 2 3 EG # = H! I JLK M NPO Q RTS U VBWXQ Y?S Y Z V [ O Q RTS U VBWXQ \]S \GZ V ^`_ a bdc Q RTS UdV e >Egf!Eih]HjH>kl= EgmnEih]HjH e #