# TecLines: A MATLAB-Based Toolbox for Tectonic Lineament Analysis from Satellite Images and DEMs, Part 2: Line Segments Linking and Merging

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## Abstract

**:**

## 1. Introduction

## 2. Data

#### 2.1. Synthetic Dataset

**Figure 1.**The synthetic Digital Elevation Model (DEM) that is the result of landscape evolution algorithm created using set river incision and different uplift rates across tectonic faults. The drainage system adapts to the evolving surface conditions.

#### 2.2. Real Dataset

#### Study Area and Data

**Figure 2.**(

**A**) location of the study area in northeast Afghanistan; (

**B**) panchromatic band of the Quickbird-2 (1 m spatial resolution) for 2 March 2006 of the study area.

^{2}. In this study, we used panchromatic band of the Quickbird-2 (1 m spatial resolution) for 2 March 2006 (Figure 2B). This data is in UTM coordinate system, datum “WGS84” and zone 42 N.

## 3. Methodology

#### 3.1. Hough Transform (HT)

**Figure 3.**Overview of the essential components of linear image discontinuities extraction and grouping using TecLines.

#### 3.2. Grouping, Linking and Merging Line Segments

- (1)
- Define point (${x}_{G}$, ${y}_{G}$) as a pair coordinates of the centroid by using the two segment endpoints (four points) and segment lengths:$${x}_{G}=\frac{{l}_{i}\left({a}_{x}+{b}_{x}\right)+{l}_{j}({c}_{x}+{d}_{x})}{2({l}_{i}+{l}_{j})}$$$${y}_{G}=\frac{{l}_{i}\left({a}_{y}+{b}_{y}\right)+{l}_{j}({c}_{y}+{d}_{y})}{2({l}_{i}+{l}_{j})}$$
_{x}, a_{y}) and b = (b_{x}, b_{y}) are the endpoints of segment i, and c = (c_{x}, c_{y}) and d = (d_{x}, d_{y}) are the endpoints of segment j and ${l}_{i}and{l}_{j}$ are the lengths of segments i and j, respectively (Figure 6). The merged line will contain this centroid. - (2)
- The orientation of the merged line (θ
_{r}) is defined as the weighted sum of the orientations of the given segments. If $\left|{\text{\theta}}_{i}-{\text{\theta}}_{j}\right|\le \frac{\pi}{2}$ then$${\text{\theta}}_{r}=\frac{{l}_{i}{\text{\theta}}_{i}+{l}_{j}{\text{\theta}}_{j}}{{l}_{i}+{l}_{j}}$$$${\text{\theta}}_{r}=\frac{{l}_{i}{\text{\theta}}_{i}+{l}_{j}\left({\text{\theta}}_{j}-\pi \frac{{\text{\theta}}_{j}}{\left|{\text{\theta}}_{j}\right|}\right)}{{l}_{i}+{l}_{j}}$$ - (3)
- (X
_{G}, Y_{G}) coordinate system is defined on the centroid (x_{G}, y_{G}). The X_{G}axis is parallel to the direction θ_{r}of the merged line. - (4)
- Coordinates for the endpoints a, b, c and d of both segments in the (X
_{G}, Y_{G}) coordinate system are determined:$${\text{\delta}}_{XG}=({\text{\delta}}_{y}-{y}_{G})sin{\text{\theta}}_{r}+({\text{\delta}}_{x}-{x}_{G})cos{\text{\theta}}_{r}$$$${\text{\delta}}_{YG}=({\text{\delta}}_{y}-{y}_{G})cos{\text{\theta}}_{r}-({\text{\delta}}_{x}-{x}_{G})sin{\text{\theta}}_{r}$$_{G}, Y_{G}) coordinate system. The endpoints coordinates in the new coordinate system are ${\text{a}}_{(\text{X},\text{G})}$, = (${a}_{XG}$, ${a}_{YG}$), ${b}_{(X,G)}$ = (${b}_{XG}$, ${b}_{YG}$), ${\text{c}}_{(X,G)}$ = (${c}_{XG}$, ${c}_{YG}$) and ${\text{d}}_{(X,G)}$ = (${d}_{XG}$, ${d}_{YG}$). - (5)
- The two orthogonal projections over the axis X
_{G}of the four endpoints a, b, c and d, which are farther apart, define the endpoints of the merged line [39].

#### 3.3. Accuracy Measurements

**Figure 8.**(

**A**) The reference discontinuity map for real dataset that is based on manual extraction from panchromatic band of QuickBird-2; (

**B**) The reference map of the synthetic DEM consists in the digitized traces of the modeled discontinuities (black line).

## 4. Testing and Evaluating TecLines

#### 4.1. Performance Evaluation of the TecLines on a Synthetic Digital Elevation Model (DEM)

**Figure 9.**(

**A**–

**C**) the line segments extracted by Hough transform, Tavares-Padilha algorithm, and final resulting lineament map was obtained by B-spline method, respectively.

#### 4.1.1. Qualitative Accuracy Assessment

#### 4.1.2. Quantitative Accuracy Assessment

**Figure 10.**(

**A**–

**C**)

**:**Rose diagrams for discontinuities extracted by Hough transform, Tavares-Padilha algorithm and B-spline method, respectively. (

**D**): Rose diagram for reference lineament map.

**Table 1.**Quantitative measures obtained by Hough transform, Tavares-Padilha algorithm and B-spline method for synthetic dataset. True positive (TP) is the number of correctly extracted discontinuities. False positive (FP) is the number of line segments erroneously classified as discontinuities. False negative (FN) is the amount of line segments that were not classified as discontinuities.

Method | TP (m) | FP (m) | FN (m) | Length Accuracy (Matching Percentages) (%) | Overall Accuracy (%) |
---|---|---|---|---|---|

Hough Transform | 817 | 946 | 204 | 80 | 60 |

Tavares-Padilha | 868 | 452 | 153 | 85 | 72 |

B-spline | 970 | 223 | 51 | 95 | 90 |

#### 4.2. Experimental Results and Accuracy Assessment Using Real Dataset

**Figure 11.**(

**A**–

**C**) The binary edge datasets that are produced by Sobel, LOG and Canny edge detection methods and tensor voting, respectively. (

**D**–

**F**): Hough domains from Sobel, LOG and Canny binary edge maps, respectively. Points on (D–F) images show peak values in matrix H.

**Table 2.**Statistics of extracted image discontinuities lenghts, which are derived from the three binary edge map sources (Sobel, LOG, and Canny) using TecLines, reference discontinuity map (manual extraction) and extracted using LINE module of the PCI Geomatica.

Parameters | TecLines Toolbox | Manually | PCI | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Hough Transform | Tavares-Padilha | B-Spline | |||||||||

Sobel | LOG | Canny | Sobel | LOG | Canny | Sobel | LOG | Canny | |||

Mean (m) | 32 | 35 | 22 | 98 | 89 | 96 | 392 | 320 | 288 | 433 | 379 |

St deviation (m) | 45 | 31 | 30 | 112 | 97 | 105 | 145 | 120 | 113 | 275 | 285 |

Sum (km) | 75 | 84 | 88 | 56 | 43 | 58 | 42 | 35 | 47 | 44 | 32 |

Min (m) | 5 | 2 | 2 | 10 | 14 | 9 | 200 | 115 | 114 | 34 | 158 |

Max (m) | 353 | 256 | 281 | 540 | 372 | 511 | 895 | 695 | 781 | 1508 | 1762 |

Count | 2324 | 2362 | 4043 | 1481 | 1298 | 2725 | 892 | 875 | 1293 | 101 | 85 |

Range (m) | 348 | 254 | 279 | 530 | 358 | 502 | 695 | 580 | 667 | 85 | 1604 |

Median (m) | 11 | 23 | 10 | 180 | 134 | 173 | 365 | 319 | 275 | 12 | 271 |

**Figure 12.**(

**A**–

**C**): Extracted line segments using HT for binary edge data sources from Sobel, LOG method and Canny methods, respectively; (

**D**–

**F**): Intermediate discontinuity map after applying Tavares-Padilha algorithm; (

**G**–

**I**): Final lineament maps from polynomial interpolation using B-spline method for Sobel, LOG and Canny edge data sources, respectively. (

**J**): Extracted discontinuities using PCI.

#### 4.2.1. Qualitative Accuracy Assessment

#### 4.2.2. Quantitative Accuracy Assessment

**Figure 13.**(

**A**–

**C**): Rose diagram for extracted line segments by Hough transform from binary edge maps produced by Sobel, LOG and Canny methods, respectively; (

**D**–

**F**): Rose diagrams for intermediate discontinuities map extracted using Tavares-Padilha algorithm from three data sources (Sobel, LOG and Canny); (

**G**–

**I**): Rose diagrams for final discontinuities map extracted using B-spline method from three data sources (Sobel, LOG and Canny). (

**J**) and (

**K**): Rose diagrams for manually and automatically (PCI) extracted discontinuities, respectively.

**Figure 14.**(

**A**–

**C**): Frequency of extracted discontinuities length by polynomial interpolation method from Sobel, LOG and Canny data sources, respectively; (

**D-F1)**: Frequency of length for automatically (PCI) extracted discontinuities; (

**D-F2**): Enlarged image of (

**D**-

**F1**). (

**E-G1**): Frequency of length for manually extracted discontinuities; (

**E-G2**): Enlarge the image of (E-G1).

**Figure 15.**Superimposition of discontinuities extrapolated from Canny data sources (black lines) and the reference discontinuities, which are manually extracted (green lines), and automatically lineaments extracted by PCI Geomatica software (violet lines).

**Table 3.**Quantitative measures obtained by TecLines and PCI for panchromatic band of QuickBird-2. True positive (TP) is the number of correctly extracted discontinuities. False positive (FP) is the number of line segments erroneously classified as discontinuities. False negative (FN) is the amount of line segments that were not classified as discontinuities.

Method | TP (km) | FP (km) | FN (km) | Length Accuracy (Matching Percentages) (%) | Overall Accuracy (%) |
---|---|---|---|---|---|

Sobel | 31 | 11 | 13 | 70 | 62 |

LOG | 27 | 8 | 17 | 61 | 56 |

Canny | 36 | 9 | 8 | 81 | 73 |

PCI | 32 | 6 | 12 | 72 | 67 |

**Table 4.**Computational time for image discontinuities extraction using TecLines toolbox, and LINE module of the PCI Geomatica software.

Step | Time (Sec) | |
---|---|---|

TecLines (Canny) | PCI | |

Frequency filtering | 15 | -- |

Edge detection | 35 | 40 |

Morphological filtering | 20 | 18 |

Tensor voting framework | 65 | -- |

Hough transform | 50 | -- |

Grouping discontinuity | 20 | -- |

Linking discontinuity | 35 | 45 |

## 5. Concluding Remarks

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Rahnama, M.; Gloaguen, R.
TecLines: A MATLAB-Based Toolbox for Tectonic Lineament Analysis from Satellite Images and DEMs, Part 2: Line Segments Linking and Merging. *Remote Sens.* **2014**, *6*, 11468-11493.
https://doi.org/10.3390/rs61111468

**AMA Style**

Rahnama M, Gloaguen R.
TecLines: A MATLAB-Based Toolbox for Tectonic Lineament Analysis from Satellite Images and DEMs, Part 2: Line Segments Linking and Merging. *Remote Sensing*. 2014; 6(11):11468-11493.
https://doi.org/10.3390/rs61111468

**Chicago/Turabian Style**

Rahnama, Mehdi, and Richard Gloaguen.
2014. "TecLines: A MATLAB-Based Toolbox for Tectonic Lineament Analysis from Satellite Images and DEMs, Part 2: Line Segments Linking and Merging" *Remote Sensing* 6, no. 11: 11468-11493.
https://doi.org/10.3390/rs61111468