The Hough transform (HT) algorithm detects straight-line features in two-dimensional data. This correspondence extends the HT to N-dimensional data to efficiently combine multiple first-threshold crossings from moving targets. The data dimensions can be the target position, its range and range-rate, and/or the first-threshold crossing times. This multi-dimensional HT (MHT) technique can be applied to enhance the detection of targets in random clutter backgrounds through the application of track-before-detect (TBD) processing.

A Multi-Dimensional Hough Transform-Based Track-Before-Detect Technique for Detecting Weak Targets in Strong Clutter Backgrounds

For more than half a century, the Hough transform is everexpanding for new frontiers. Thousands of research papers and numerous applications have evolved over the decades. Carrying out an all-inclusive survey is hardly possible and enormously space-demanding. What we care about here is emphasizing some of the most crucial milestones of the transform. We describe its variations elaborating on the basic ones such as the line and circle Hough transforms. The high demand for storage and computation time is clarified with different solution approaches. Since most uses of the transform take place on binary images, we have been concerned with the work done directly on gray or color images. The myriad applications of the standard transform and its variations have been classified highlighting the up-to-date and the unconventional ones. Due to its merits such as noise-immunity and expandability, the transform has an excellent history, and a bright future as well.

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A Survey on Hough Transform, Theory, Techniques and Applications

We extend the wavelet transform to handle multidimensional signals that are smooth save for singularities along lower-dimensional manifolds. We first generalize the complex wavelet transform to higher dimensions using a multidimensional Hilbert transform. Then, using the resulting hypercomplex wavelet transform (HWT) as a building block, we construct new classes of nearly shift-invariant wavelet frames that are oriented along lower-dimensional subspaces. The HWT can be computed efficiently using a 1D dual-tree complex wavelet transform along each signal axis. We demonstrate how the HWT can be used for fast line detection in 3D.

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Directional hypercomplex wavelets for multidimensional signal analysis and processing

The ability of robots to meticulously cover large areas while gathering sensor data has widespread applications in precision agriculture. For autonomous operations in orchards, a suitable information management system is required, within which we can gather and process data relating to the state and performance of the crop over time, such as distinct yield count, canopy volume, and crop health. An efficient way to structure an information system is to discretize it to the individual tree, for which tree segmentation/detection is a key component. This paper presents a tree trunk detection pipeline for identifying individual trees in a trellis structured apple orchard, using ground-based lidar and image data. A coarse observation of trunk candidates is initially made using a Hough transformation on point cloud lidar data. These candidates are projected into the camera images, where pixelwise classification is used to update their likelihood of being a tree trunk. Detection is achieved by using a hidden semi-Markov model to leverage from contextual information provided by the repetitive structure of an orchard. By repeating this over individual orchard rows, we are able to build a tree map over the farm, which can be either GPS localized or represented topologically by the row and tree number. The pipeline was evaluated at a commercial apple orchard near Melbourne, Australia. Data were collected at different times of year, covering an area of 1.6 ha containing different apple varieties planted on two types of trellis systems: a vertical I-trellis structure and a Guttingen V-trellis structure. The results show good trunk detection performance for both apple varieties and trellis structures during the preharvest season 87-96% accuracy and near perfect trunk detection performance 99% accuracy during the flowering season.

A Pipeline for Trunk Detection in Trellis Structured Apple Orchards

[1] We propose a new pattern recognition method that is able to reconstruct the three-dimensional structure of the active part of a fault network using the spatial location of earthquakes. The method is a generalization of the so-called dynamic clustering (or k means) method, that partitions a set of data points into clusters, using a global minimization criterion of the variance of the hypocenters locations about their center of mass. The new method improves on the original k means method by taking into account the full spatial covariance tensor of each cluster in order to partition the data set into fault-like, anisotropic clusters. Given a catalog of seismic events, the output is the optimal set of plane segments that fits the spatial structure of the data. Each plane segment is fully characterized by its location, size, and orientation. The main tunable parameter is the accuracy of the earthquake locations, which fixes the resolution, i.e., the residual variance of the fit. The resolution determines the number of fault segments needed to describe the earthquake catalog: the better the resolution, the finer the structure of the reconstructed fault segments. The algorithm successfully reconstructs the fault segments of synthetic earthquake catalogs. Applied to the real catalog constituted of a subset of the aftershock sequence of the 28 June 1992 Landers earthquake in southern California, the reconstructed plane segments fully agree with faults already known on geological maps or with blind faults that appear quite obvious in longer-term catalogs. Future improvements of the method are discussed, as well as its potential use in the multiscale study of the inner structure of fault zones.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2007JB005032

Haiying Liu

Papers

Hough-transform detection of lines in 3-D space