Explanation of parameters for the Hough Transform

The Hough Transform needs many parameters to fine tune the application. The implementation does not depend on any unit of measurement. However, it is indispensible that the units of the parameters match with the units used for the input data.

General parameters:

PlaneDir Specifies the directory that the resulting planes are written to.
AccumulatorType The software offers different accumulator types:
1 the Accumulator Array with a linear discretization of the Hough Space
2 the Accumulator Ball with similar cell sizes when the Hough Space is mapped onto the unit sphere
3 the Accumulator Cube where the discretization is based on projecting a cube onto the unit sphere
4 the improved Accumulator Ball, where each of the two poles is represented by a single cell
The different Hough methods have various stopping rules. The following parameters are used to define the thresholds for these stopping rules:
MinSizeAllPoints Defines a threshold when to stop applying the Hough Transform. The number indicates the percentage of points from the input point cloud that have not been asigned to a plane.
MaxPlanes Defines a threshold for the maximum number of planes that are detected. The algorithms stops after this amount of planes has been reached.
TrashMax Threshold that defines after how many discarded planes the algorithm is stopped. If one cell in the accumulator receives enough votes, a plane is fitted through all points that belong to the represented plane. Planes are discarded if they are only represented by a small number of points, or if the planarity of the sample points is too low.
For practical applications the Hough Space is discretized. The following parameters define the discretization:
RhoMax Defines the maximum distance ρmax of a plane from the origin for discretization.
RhoNum Defines the number of cells ρN in direction of ρ. Each cell has the size ρmax/ρN.
ThetaNum Defines the number of cells θN in direction of θ.
PhiNum Defines the number of cells φN in direction of φ. Each cell has the size φmax/φN.

Plane parameters:

MaxPointPlaneDist Maximal distance between a point and the plane so that the point is still considered to belong to the plane. This parameter is used to compensate measurement noise and discretization.
MinPlanarity A detected plane is discarded if the planarity falls below this threshold. Each plane candidate is fitted through all points that are considered to belong to it using a least squares method based on the Jacobi eigenvalue algorithm. The planarity is given by the value of the smallest eigenvalue devided by the sum of all eigenvalues.

Additional parameters for certain algorithms:

PlaneRatio
For the SHT and the PHT the maxima in the accumulator are determined after the accumulation phase is completed. The PlaneRatio is a threshold r that determines which maxima from the accumulator are considered to be detected planes. Each cell in the accumulator with a count lower than r·maxc is discarded, where maxc is highest score in the accumulator
PeakWindow For the SHT and the PHT the maxima in the accumulator are determined after the accumulation phase is completed. If PeakWindow is set to false the raw maxima in the accumulator are used, otherwise a sliding window technique is used to filter out maxima in the accumulator that are close to each other.
WindowSize Sets the side lenght of the sliding window for peak detection.
MinDist Sets the minimum distance for the three points selected to calculate the model plane for the Randomized Hough Transform.
AccumulatorMax Sets the maximum distance for the three points selected to calculate the model plane for the Randomized Hough Transform.
Informatics VII - Robotics and Telematics, Prof. Dr Andreas Nüchter, andreas (at) nuechti.de, Tel. +49-177-7951270