Beamlet pyramids: a new form of multiresolution analysis suited for extracting lines, curves, and objects from very noisy image data
David L. Donoho, Xiaoming Sharon Huo · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2000
We describe a multiscale pyramid of line segments and develop algorithms which exploit that pyramid to recover image features { lines, curves, and blobs { from very noisy data. The beamlet dictionary is a dyadically organized collection of line segments, occupying a range of dyadic locations and scales, and spanning a full range of orientations. It is an ecient substitute for the full dictionary of \\beams" (the collection of all possible line segments connecting pairs of pixels in an image). The beamlets dictionary has low cardinality (there are O(n 2 log(n)) beamlets as compared to O(n 4 ) beams). Despite the reduced cardinality, it takes at most 8 log 2 (n) beamlets to approximate any edgel to within distance 2=n. A wide range of polygonal curves can be built from chains of relatively few beamlets. The beamlet transform of a function f(x 1 ; x 2 ) is the collection of integrals of f over each segment in the beamlets dictionary. The resulting information is stored in an beamlet ...