Editing Hough transform (section)

===3-D kernel-based Hough transform for plane detection (3DKHT)===
Limberger and Oliveira<ref>{{cite journal | last1 = Limberger | first1 = F.&nbsp;A. | last2 = Oliveira | first2 = M.&nbsp;M. | year = 2015 | title = Real-Time Detection of Planar Regions in Unorganized Point Clouds | doi = 10.1016/j.patcog.2014.12.020 | journal = Pattern Recognition | volume = 48 | issue = 6 | pages = 2043–2053 | bibcode = 2015PatRe..48.2043L | hdl = 10183/97001 | url = https://lume.ufrgs.br/bitstream/10183/97001/1/000919556.pdf | hdl-access = free }}</ref> suggested a deterministic technique for plane detection in unorganized point clouds whose cost is <math>n \log(n)</math> in the number of samples, achieving real-time performance for relatively large datasets (up to <math>10^5</math> points on a 3.4&nbsp;GHz CPU). It is based on a fast Hough-transform voting strategy for planar regions, inspired by the Kernel-based Hough transform (KHT). This 3D kernel-based Hough transform (3DKHT) uses a fast and robust algorithm to segment clusters of approximately co-planar samples, and casts votes for individual clusters (instead of for individual samples) on a (<math>\theta, \phi, \rho</math>) spherical accumulator using a trivariate Gaussian kernel. The approach is several orders of magnitude faster than existing (non-deterministic) techniques for plane detection in point clouds, such as [[Randomized Hough transform|RHT]] and [[RANSAC]], and scales better with the size of the datasets. It can be used with any application that requires fast detection of planar features on large datasets.