From Hough Transform to Integral Geometry
Jean-Marie Becker, Stéphane Grousson, Daniela Colţuc, Paul Michelon · 2002
Hough Transform (H.T.) is a classical tool for multiple alignment detection in image processing, based on the property that Aligned Points are transformed into Inter- secting Curves (APIC). Among the alternative transforms which possess the APIC property, one of the most interest- ing is Polar Transform (P.T.) which exchanges a point (a,b) and the straight line with equation ax + by = 1. This trans- form represents classical duality between a pole and its polar line w.r. to the unit circle. Another property common to both H.T. and P.T. is the correspondence between shapes' Boundary Length and connected Areas (BLA property), ei- ther direct or compensated by a weight function, allowing an efficient measure of these lengthes on a digital screen. P.T. is shown to be connected to Projective and Integral (or Stochastic) Geometry with an important role given to a weight function 1/d 3 .