Given pixels of a number m, a set of under-constrained equations specify a curve or manifold of a dimension = ? – m in R? if m < ?. E.g., from a line y=kx+b passing a given pixel in the image, we have a line b=y-kx in R2. This case is called diverging mapping because m pixels are mapped diversely to the R? space. On the other hand, if m = ?, a unique point in the R? space maybe determined by solving a set of joint equations or optimizing a cost when the joint equations are over-constrained, i.e., we have a converging mapping that maps m pixels into one point in R?.
Published in Chapter:
Randomized Hough Transform
Lei Xu (Chinese University of Hong Kong & Peking University, China) and Erkki Oja (Helsinki University of Technology, Finland)
Copyright: © 2009
|Pages: 8
DOI: 10.4018/978-1-59904-849-9.ch197
Abstract
Proposed in 1962, the Hough transform (HT) has been widely applied and investigated for detecting curves, shapes, and motions in the fields of image processing and computer vision. However, the HT has several shortcomings, including high computational cost, low detection accuracy, vulnerability to noise, and possibility of missing objects. Many efforts target at solving some of the problems for decades, while the key idea remains more or less the same. Proposed in 1989 and further developed thereafter, the Randomized Hough Transform (RHT) manages to considerably overcome these shortcomings via innovations on the fundamental mechanisms, with random sampling in place of pixel scanning, converging mapping in place of diverging mapping, and dynamic storage in place of accumulation array. This article will provides an overview on advances and applications of RHT in the past one and half decades.