An Integrated Fast Hough Transform for Multidimensional Data

Abstract

Line, plane and hyperplane detection in multidimensional data has many applications in computer vision and artificial intelligence. We propose Integrated Fast Hough Transform (IFHT), a highly-efficient multidimensional Hough transform algorithm based on a new mathematical model. The parameter space of IFHT can be represented with a single k-tree to support hierarchical storage and "coarse-to-fine" search strategy. IFHT essentially changes the least square data-fitting in Li's Fast Hough transform (FHT) to the total least squares data-fitting, in which observational errors across all dimensions are taken into account, thus more practical and more resistant to data noise. It has practically resolved the problem of decreased precision of FHT for target objects mapped to boundaries between accumulators in the parameter space. In addition, it enables a straightforward visualization of the parameter space which not only provides intuitive insight on the number of objects in the data, but also helps with tuning the parameters and combining multiple instances if needed. In all simulated data with different levels of noise and parameters, IFHT surpasses Li's Fast Hough transform in terms of robustness and precision significantly.

Analysis of Properties of Dyadic Patterns for the Fast Hough Transform

“…For a more detailed exploration of the algorithm itself, we refer the reader to [3] and [10]. It is important to note that our discussion here specifically pertains to the FHT algorithm introduced by Brady et al However, it is worth mentioning that other algorithms, also bearing the name FHT, have been developed by H. Li, Lavin, Le Master, and Y. Li, Gan, as documented in [7,8]. In this paper, we do not delve into the statistical analysis of these alternative algorithms, but we anticipate addressing them in future research.…”