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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Geological structures, such as faults and fractures, appear as image discontinuities or lineaments in remote sensing data. Geologic lineament mapping is a very important issue in geo-engineering, especially for construction site selection, seismic, and risk assessment, mineral exploration and hydrogeological research. Classical methods of lineaments extraction are based on semi-automated (or visual) interpretation of optical data and digital elevation models. We developed a freely available Matlab based toolbox TecLines (Tectonic Lineament Analysis) for locating and quantifying lineament patterns using satellite data and digital elevation models. TecLines consists of a set of functions including frequency filtering, spatial filtering, tensor voting, Hough transformation, and polynomial fitting. Due to differences in the mathematical background of the edge detection and edge linking procedure as well as the breadth of the methods, we introduce the approach in two-parts. In this first study, we present the steps that lead to edge detection. We introduce the data pre-processing using selected filters in spatial and frequency domains. We then describe the application of the tensor-voting framework to improve position and length accuracies of the detected lineaments. We demonstrate the robustness of the approach in a complex area in the northeast of Afghanistan using a panchromatic QUICKBIRD-2 image with 1-meter resolution. Finally, we compare the results of TecLines with manual lineament extraction, and other lineament extraction algorithms, as well as a published fault map of the study area.

Detection and extraction of lineaments are commonly used for construction site selection (dams, bridges, roads,

Traditionally, lineament mapping is based on a visual or semi-automatic interpretation (photo-geology). Lineaments are often extracted manually by digitizing, which is subjective, time consuming, expensive and requires expertise, training and adequate scientific skills. In addition, it cannot produce results for large scale areas [

Increasing spatial and radiometric resolution in satellite images favors the development of automatic, or criteria-based, lineament extraction algorithms [

The success of automatic lineament extraction procedures depends on the reliability and accuracy of edge detection mechanism [

The main goal of this study is to develop a new MATLAB based toolbox (TecLines) for automatic lineaments mapping from satellite images and digital elevation models (DEM). TecLines contains a set of functions for detecting and extracting potential edges with integration between image frequency and spatial filtering, Tensor voting framework, Hough transformation and polynomial fitting methodology.

The extraction of lineaments using the TecLines toolbox is performed in two main steps: edge detection and edge linking. Edge detection methods should ideally generate sets of pixels lying only on edges. In practice, these pixels seldom completely characterize edges because of unwanted noise and breaks. The general shape of the objects may be initially unknown, but in many cases they can be approximated by piecewise linear segments. It is not easily feasible to fit linear segments to all the edges in an image and discard false segments. These problems are addressed in the edge-linking step. The goal of edge linking is to describe an edge as a linear segment of specified shape and estimate the missing edge pixels from the assumed equation of the curvilinear segment. Due to differences in the mathematical background of the edge detection and edge linking procedure as well as the breadth of topics, we present the approach in a two-part paper. We chose MATLAB because it provides a multipurpose environment for mathematical processing based on a high-level programming language. Additionally, the functions provided in MATLAB are easy to modify and open for improvements.

The specific objective of the first part is to describe and assess the comprehensive edge detection procedure by integration of frequency domain filters, edge detection methods, and tensor voting framework. We introduce this part, with a focus on tectonic lineament extraction (binary edge maps with efficient thickness, length and pixel connectivity, and increased degree of accuracy of the edge detection). Finally, we validate this functionality using a synthetic image with known discontinuities and a high-resolution satellite image (QUICKBIRD-2) from an active tectonic area: the Andarab fault zone in NE Afghanistan.

In this paper, we demonstrate the performance of the TecLines for edge detection, where validation has been performed on a synthetic and a real dataset.

In recent decades, several approaches for performance evaluation of edge detection methods have been proposed according to the presence or absence of ground truth data [

We evaluated the performance of TecLines on satellite images of the active Andarab fault zone, northeastern part of Afghanistan (

TecLines is a new MATLAB based framework that contains various functions for automatic detection and extraction of tectonic lineaments from satellite images and digital elevation models (DEM). Besides import and export functions that support the raster and vectors in standard file formats, TecLines provides functions for image filtering in the frequency and spatial domains to produce primary binary edge maps. Final binary edge maps in TecLines are produced by performing the computation of the Tensor voting framework. In addition, TecLines extract line segments from final binary edge maps by employing standard Hough transformation functions. A set of functions serves the grouping and merging line segments, which will be resulted in final lineaments maps. Comparing results with published/non-published lineament maps and lineament analysis are also possible in TecLines. An overview of TecLines divisions can be found in

Image enhancement methods can contribute significantly to the automated extraction of linear features by using noise reduction and edges enhancement in the input images. There are two main categories for image enhancement methods: (1) spatial domain methods, such as Mean, Median, and Mode filters, and (2) frequency domain methods, such as Gaussian and Butterworth high, low, and band pass frequency filters. The main difference between both categories is that the spatial domain methods are usually applied locally, while the frequency domain methods are usually done in the global context. Unfortunately, there is no common principle for determining what is “good” image enhancement. However, when image enhancement methods are used as a pre-processing phase for other image processing methods, then quantitative measures can determine which methods are most appropriate.

In this study, we used Butterworth band-pass filter in the frequency domain _{L}_{H}

The principal physical edges correspond to significant variation in the reflectance, illumination, orientation and depth of scene surface [

In the Laplacian based methods such as LOG method, the gaussian smoothing filter is used for decreasing the sensitivity to noise in the input image, in other words to slightly blur the image. Then, Laplacian is applied to detect regions of rapid intensity change. The disadvantages of these edge detectors are their sensitivity to noise also producing two-pixel thick edges [

The Canny edge detection method is an optimum method and provides a multi-stage algorithm to detect a wide-range of edges in images. Those should be at a minimum distance to the actual edge in the real image. In addition, the detected edges should have minimal response. In other words, the discovered edges should have only one response to a single edge and completely eliminate the possibility of multiple responses to an edge by using adaptive thresholds with hysteresis.

Binary edge maps produced by Sobel, LOG, and Canny edge detection methods can have small-scale edges and isolated (or island) edge pixels. A common approach for improving these results is to use mathematical morphology methods to eliminate extra edge pixels. In this study, we used opening morphological filter using bwareaopen command in MATLAB. Morphological opening is an erosion followed by a dilation. Erosion eliminates small-scale details by removing outlying pixels and isolated pixels. Dilation restores all remained edges to their original size. The opening method presents many advantages because it relies only on the relative ordering of the pixel value, not on their numerical values. The opening is anti-extensive. In addition, opening is idempotent operation because it can be applied multiple times without changing the result beyond the initial application.

Tensor voting is a non-iterative methodology to the inference of statistically salient features from possibly sparse and noisy data. In the tensor voting framework [

The tensor can specify its preferred tangent, normal orientation, as well as saliency corresponding to its perceptual structures. In _{1} is the preferred normal orientation of a potential curve segment. The magnitude of the stick component (λ_{1}−λ_{2}) indicates curve saliency.

Tensor voting was implemented using tensor fields to pre-compute and store the votes from both stick and ball voters in receivers at various distances and angles (

In TecLines, we wrote and implemented a set of MATLAB based functions for tensor voting to compute the gradient vector and the tensor matrix at the edge pixels of the binary image, which were extracted by edge detection methods. Then, voting tensor field generated by casting votes on all the edge pixels of the image were used to construct the stick saliency map. Finally, we extracted the distinguished edge pixels based on the stick saliency map.

There are specific statistical measures that we can use to assess erroneous measures [_{IM}_{GTP}

Accuracy requires that edges should be detected as close as possible to their correct positions. In a given image, the edge positions and numbers can be vary according to resolution and procedures [

Accuracy assessment is based on 21 known lineaments, which have been shown by 1180 edge pixels in the synthetic DEM (

In the next step, we used a synthetic DEM preprocessed using a Butterworth band-pass filter in frequency domain. Due to local intensity changes in the image, edges are better detected in the west of the image (

As seen in

In the first step, we applied a Butterworth band-pass filter in the frequency domain. We used 0.2 as an upper-lower cutoffs frequency and 6 for order numbers of filter such that these preserved as many significant edges (tectonic linear features) present in the truth as possible (

We used opening morphological operation in order to thin the edges. This operation removes all pixels that are below a threshold of connected pixels. The minimum number of connected neighbors for each pixel was set to 4 pixels. The final binary edge maps are produced after removing all residual pixels.

We used the tensor-voting framework to improve edge detected map accuracy and merge neighboring edges with similar direction. This provides better results than other methods for detecting common edges. It should be noted that using tensor-voting framework could lead to loss of small edges surrounded by bigger ones. After the voting process, a saliency map is produced by assigning a second order symmetric tensor that estimates the structure of the feature type and the associated saliency (

The accuracy was computed by comparing the edges detected using TecLines to the set of edges in the reference dataset (ground truth), The reference dataset is based on visual image interpretation and manual extraction. We analyzed the results before and after tensor voting framework. The results are shown in

The aim of this work is to develop a MATLAB based toolbox (TecLines) in order to extract discontinuities from satellite images and digital elevation models. The high edge detection accuracy achieved by using TecLines shows that the proposed edge detection procedure can be used for geological purposes using high-resolution satellite images and DEM. The combined process of Butterworth band-pass filter in the frequency domain, edge detection methods in spatial domain and tensor voting framework slightly improves the edge detection accuracy. Consequently using the tensor-voting framework, the accuracy of edge detection is improved by 20% to 30%. We show that the combination of Sobel or LOG methods and tensor voting framework have similar overall accuracy for both the QuickBird and the synthetic images. However, the combination of the Canny and tensor-voting framework is considered more effective for edge detection. There are several important points that should be taken into account for further investigation. The percentage of achieved accuracy of edge detection methods largely depends on the gradient thresholds. The values of thresholds are still based on trial and error. For low thresholds, more edges will be detected but the resulting image will be increasingly susceptible to noise and trigger the detection of irrelevant features. A high threshold may miss subtle edges, or result in fragmented edges. Therefore, it is recommended to investigate further interactive thresholding in future edge detection methods. The outcome of this study is based on the panchromatic band of the QuickBird 2, which has a very high spatial resolution (1 m resolution). The proposed edge detection procedure is also adequate for medium resolution satellite images such as Landsat. The Landsat images have some advantages over QuickBird 2, such as free to availability, more coverage area, as well as shorter repeat intervals. While these results for edge detection procedures from satellite images are promising, the further mathematical approach presented in part 2 is still needed to extract linear segments from edges. In the second part of TecLines paper series, we describe the procedure of edge linking using the Hough transform and polynomial curve fitting using B-spline and Tavares methods. The quantitative representation of the binary edge maps can be exported as shape files, Geotiff and ENVI headers. Users can write their own MATLAB functions in order to expand the TecLines capabilities. The proposed toolbox is available from the TecLines website [

High resolution QuickBird image was freely obtained from the GeoEye Foundation. We would like to thanks Louis Andreani for review and editing of this manuscript. Thanks to two anonymous reviewers whose input improved this paper.

Mehdi Rahnama and Richard Gloaguen designed the research. Mehdi Rahnama wrote the manuscript and was responsible for the MATLAB programming, mathematical models and data analysis. Both authors contributed in editing and reviewing the manuscript.

The authors declare no conflict of interest.

The synthetic 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.

(

Overview of the essential components of lineament mapping using TecLines.

Tensor decomposition.

Second order vote casting by a stick tensor located at the origin [

(

(

(

Preliminary binary edge maps resulting from Sobel (

(

Elementary tensors in 2-D, where n and t represent the normal and tangent vector respectively and the geometric features extracted after 2-D tensor voting [

_{1}λ_{2} |
_{1}e_{2} |
|||||||
---|---|---|---|---|---|---|---|---|

Point | 1 | 1 | Any orthonormal basis | Ball | λ_{1} all_{2} > 1 |
None | Any orthonormal basis | None |

Curve | 1 | 0 | n t | Stick | λ_{1} − λ_{2} > λ_{2} |
e_{1} |
e_{2} |
e_{1} |

Quantitative measures and overall accuracy obtained by TecLines for synthetic digital elevation models (DEM). True positive (TP) is the number of correctly detected edge pixels. False positive (FP) is the number of pixels erroneously classified as edge pixels. False negative (FN) is the amount of pixels that were not classified as edge pixels.

Without Butterworth band-pass filtering | Canny | 360 | 26,370 | 820 | 15.9 |

Canny + TVF | 480 | 17,380 | 700 | 21.6 | |

With Butterworth band-pass filtering | Canny | 920 | 12,240 | 260 | 42.4 |

Canny + TVF | 1098 | 8339 | 82 | 52.3 |

Quantitative measures obtained by TecLines for panchromatic band of QuickBird-2. True positive (TP) is the number of correctly detected edge pixels. False positive (FP) is the number of pixels erroneously classified as edge pixels. False negative (FN) is the amount of pixels that were not classified as edge pixels.

Sobel | 3726 | 8657 | 2464 | 42.7 |

Sobel + TVF | 4333 | 1075 | 1857 | 64.8 |

LOG | 3838 | 9721 | 2352 | 43.1 |

LOG + TVF | 4271 | 1684 | 1919 | 60.62 |

Canny | 4147 | 6293 | 2043 | 46.5 |

Canny + TVF | 4891 | 795 | 1299 | 74.5 |