On a Basic Consideration of the Warp Model of Hough Transform

fie Warp Model of Lhe Hough transform is pmposed la provide the ezlended Fiotigh lrawform functiow(EHT). The Warp Model is a skewed pammeler space (p, [), u~htch IS homeomofphic to the original (p,B) pornmeter spore. R i.7 imporfont tho! fo inlmduce the skewness of the pururneler space is io define [he ongular and posilional sensibiIily lo detecl lines. In this paper, the Hough transjormlunction is extended at firsi by introducing three Junctional conditions lo ensure the horn ~omorphic relation betuleen (p, ;I) and (p, 8) parameter spaces. APer proving lhese conditi0n.r to he feasible, a procedvre lo deritw ihe transfirm lunclion is pres~nled by using the Warp Mod~l so that the given angular and posiannl sensibility could be rrolrzed. The esscntiaI property of Rough transform is to ensure an unique one-to-one mapping, a hoeomorphic mapping, between a line in the pattern space and its parameter pair in the parameter space. If we could find other homeomorphic mapping functions, the functional expresion of E-lough transform would be extended. This new extended expression of Hough transform is cdled 'Extended Wough Transform (EIET)' in this paper.