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L., +Nunez-Iglesias, J., Boulogne, F., Warner, J. D., Yager, N., Gouillart, +E., Yu, T., & contributors, the scikit-image. (2014). Scikit-image: +Image processing in Python. PeerJ, 2, e453. +https://doi.org/10.7717/peerj.453 + + + Spaghetti: Spatial network analysis in +PySAL + Gaboardi + Journal of Open Source +Software + 62 + 6 + 10.21105/joss.02826 + 2021 + Gaboardi, J. D., Rey, S., & +Lumnitz, S. (2021). 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+ + + + +Journal of Open Source Software +JOSS + +2475-9066 + +Open Journals + + + +6147 +10.21105/joss.06147 + +LinkingLines: Using the Hough Transform to Cluster Line +Segments and Mesoscale Feature Extraction + + + +https://orcid.org/0000-0002-1378-361X + +Hutchison +Allison Kubo + + + + +https://orcid.org/0000-0002-2197-2349 + +Karlstrom +Leif + + + + +https://orcid.org/0000-0002-8026-0018 + +Mittal +Tushar + + + + + +University of Oregon, Eugene, OR, USA + + + + +Pennsylvania State University, University Park, PA, +USA + + + + +5 +10 +2023 + +9 +98 +6147 + +Authors of papers retain copyright and release the +work under a Creative Commons Attribution 4.0 International License (CC +BY 4.0) +2022 +The article authors + +Authors of papers retain copyright and release the work under +a Creative Commons Attribution 4.0 International License (CC BY +4.0) + + + +python +hough transform +earth science +clustering + + + + + + Summary +

Linear feature analysis plays a fundamental role in geospatial + applications, from detecting infrastructure networks to characterizing + geological formations. In this paper, we introduce + linkinglines, an open-source Python package + tailored for the clustering and feature extraction of linear + structures in geospatial data. Our package leverages the Hough + Transform, commonly used in image processing, performs clustering of + line segments in the Hough Space, and then provides unique feature + extraction methods and visualization. + linkinglines empowers researchers, data + scientists, and analysts across diverse domains to efficiently + process, understand, and extract valuable insights from linear + features, contributing to more informed decision-making and enhanced + data-driven exploration. We have used + linkinglines to map dike swarms with thousands + of segments associated with Large Igneous Provinces in Kubo Hutchison + et al. + (2023).

+
+ + Statement of Need +

The linkinglines Python package addresses + the need for quantitative and automated line clustering and analysis + in geospatial data. In geology and related fields, there is a need to + analyze and extract patterns in overlapping and sometimes incomplete + datasets of linear features such as fractures, dikes, or roads.

+

The primary needs that the linkinglines + package fulfills include:

+ + +

Dissected Line Extraction or Data Reduction: In + areas where land cover or data availability affects the complete + mapping of linear features, this package can link together + similarly oriented segments into lines in a quantitative automated + way. This is also an data reduction technique.

+
+ +

Feature Extraction and Analysis: The + linkinglines package provides functions to + extract and then compute essential metrics and statistics on + extracted linear, radial or circumferential type features which + are commonly seen in dike swarms or fracture networks.

+
+ +

Custom Plotting and Visualization: Effective + visualization is critical for data interpretation. The package + offers custom plotting scripts, making it easier to visualize + results and communicate findings.

+
+
+ + State of the Field +

This package was originally developed to tackle the issue of + mapping dike segments. Rugged terrain, vegetation cover, and a large + area made it impossible to accurately map dikes. The length, + density, and structure of the dike swarm affects how magma is + transported and erupted. Scaling analysis indicated that for + segments of widths of 10 m, dikes could be tens to thousands of + kilometers long; however observed segments were two orders of + magnitude shorter + (Morriss + et al., 2020). Additionally, the complex overlapping + structure of the dike swarm was difficult to analyze. We designed + linkinglines to extract not only lines from + line segments but also help analyze the mesoscale structure of the + dike swarm. Using the unique properties of the Hough Transform we + can extract several unique mesoscale structures within a group of + lines.

+

Issues with data coverage, incompleteness, and complexity occur + in a wide range of Earth and Planetary science data products. As an + example we show in our documentation how this work can also be + applied to lineaments on Venus + (Grosfils + et al., 2011) and fracture networks + (Ovaskainen + et al., 2023). Clustering and machine learning methods are + commonly applied geosciences within the subdisciplines of + seismology, geochemistry, and planetary science + (Li + et al., 2023). There are currently available packages to work + with geospatial data clustering, examples are + geopandas, PySAL, and + others which perform the Hough Transform on images such as + scikit-image or + OpenCV. However this seems to be the first + union of the two methods and specific to geoscience data + applications + (Gaboardi + et al., 2021; + Jordahl + et al., 2020; + Walt + et al., 2014). Related packages which are specific to + geosciences, such as fractopo which focuses + on network analysis of fractures, could be utilized in parallel with + linkinglines for additional analysis + (Ovaskainen, + 2023).

+
+
+ + Algorithm +

linkinglines can read in any common + geospatial data format using geopandas such as + ESRI Shapefiles, GeoJSON, or Well Known Text + (Jordahl + et al., 2020). Preprocessing is applied to the dataset so that + only straight lines are considered in the algorithm. This is done by + loading in the points from each vector object and performing linear + regression, only considering those that yield a line with a + + 0.05]]> + p>0.05. + The data is then formatted into a pandas + DataFrame. This package heavily uses pandas as + the database structure for ease of use, data manipulation, and + integration with numpy and + scipy + (McKinney, + 2010).

+ +

Dike linking algorithm using the Hough Transform. First, + raw data in Cartesian space is converted into Hough space (a and b). + Agglomerative clustering is then performed on the data in Hough + coordinates (d). In this example, there are four dikes in total and + two (red and blue) clusters. The clusters are redrawn by connecting + the endpoints of the segments in the cluster (c).

+ +
+

The Hough Transform is an image processing technique used for + detecting straight lines and other patterns in images + (Ballard, + 1981; + Duda + & Hart, 1972). After loading in the data, it is assumed to + be already line structures, so the accumulator array of the Hough + Transform is skipped. First, the angle of the line segment is found. + In many methods, it is the left-hand corner of the image + (Ballard, + 1981), but we choose the average midpoint of the line segments + (Figure 1b). Other origins can be specified in certain functions using + the xc and yc arguments. + After the coordinate transform, + + ρ + and + + θ + become the basis for the next step, where we utilize Scipy’s + clustering algorithm + (Virtanen + et al., 2020).

+

After labels are assigned in the clustering portion of the + algorithm, new lines are drawn using the endpoints of the clustered + lines (Figure 1d). For each cluster, the nearest neighbors of the + segment midpoints are calculated in Cartesian space, allowing for an + analysis of the Cartesian spatial clustering of the lines. We also + introduce an optional filtering step, which analyzes the maximum + nearest neighbor difference of midpoints normalized by the total + cluster length. This filters out clusters with segments that are not + evenly clustered in Cartesian space.

+ + Feature Extraction +

Additionally, we leverage the unique properties of the Hough + Transform to combine clustering with feature extraction. In the + original usage case of overlapping complex dike swarms, two + potential end members of swarm types are linear and radial or + circumferential swarms (Figure 2). Using the equation of the Hough + Transform, we can apply curve-fitting to quantitatively fit the data + to a radial pattern.

+ +

Synthetic dike swarms in a Cartesian space (gray + background, uppercase label) and Hough Transform space (white + background, lowercase label). (A) Shows a simple linear swarm + oriented at 30°. (B) Shows three linear swarms at −30°, 30°, 75°. + (C) Shows three radial swarms aligned at a −45° angle. The angle + at which radial swarms intersect in the Hough space (HS) is the + angle of their relative orientation in Cartesian space. (D) Shows + a circumferential swarm with the lines extending to show how it + converges to a radial swarm. The radius of the circumferential + swarm is equal to the spacing of the parallel two curves in HS. + (E) Shows three circumferential swarms with the same radius + aligned at a -45° angle.

+ +
+

For extraction of linear features we can apply the Hough + accumulator array, a 2D histogram of + + θ + and + + ρ. + You set the size of bins in the histogram and if clusters fall + within those boxes they can be thought of as mesoscale clusters. We + allow for flexibility of cutoffs for these mesoscale feature + extraction, so it can be tailored to each research or engineering + application.

+
+
+ + Future Work +

This package takes geospatial or other types of line segment data + and clusters them based on their orientation. Currently, the + implementation only works with linear features, however it could be + generalized to arbitrary shapes for more flexibility + (Ballard, + 1981). Additionally, future work could incorporate other shapes + or patterns in the Hough Space and could extend the feature extraction + methods laid out here. We invite collaboration to increase the + capabilities of this code.

+
+ + Acknowledgements +

This paper was made possible by the “Crafting Quality Research + Software and Navigating Publication in Software Journals” held by the + Computational Infrastructure for Geodynamics in September 2023.

+
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