Mean-shift for Statistical Hough Transform
نویسنده
چکیده
The Hough Transform is a well known robust technique to infer shapes from a set of spatial points (Hough (1962); Duda and Hart (1972); Ballard (1981); Goldenshluger and Zeevi (2004); Dattner (2009)). Having a parametric form of the pattern of interest w.r.t. a latent variable Θ, the Hough transform computes an estimate of the density function of Θ using a histogram. Maxima of the histogram are then located to infer the instance(s) of the shape of interest. This generic approach has been successfully used in many domains such as image and video processing Bober and Kittler (1994), astronomy Ballester (1996) or geoscience Cooper and Cowan (2004). The problems of using multi-dimensional histograms are well-known. The trade off in between the number of bins in the histogram and the number of available observations is crucial. Too many bins for too few observations would lead to a memory consuming and sparse representation of the probability density pΘ(Θ). In addition, too few bins would reduce the resolution in the Θ−space and therefore limit the precision of the estimates. To overcome these limitations, we have introduced a kernel modelling of the Hough transform ( Dahyot (2008b,a)). We extend this formulation for inference of hyperplanes in multi-dimensional spatial domain R (Dahyot (2009)). The resulting density function of Θ is nonlinear and standard Mean Shift approach to find its maxima is not applicable (e.g. Comaniciu and Meer (2002); Carreira-Perpinan (2007)). Our approach is then taking advantage of recent advances on non-linear mean shift over riemannian manifolds Subbarao and Meer (2009). We illustrate this algorithm to infer lines in R and planes in R (Dahyot (2009)).
منابع مشابه
Comparison of Hough Transform and Mean Shift Algorithm for Estimation of the Orientation Angle of Industrial Data Matrix Codes
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