Three-Dimensional Lineament Visualization Using Fuzzy B-Spline Algorithm from Multispectral Satellite Data

A lineament is a linear feature in a landscape which is an expression of an underlying geological structure such as a fault. Typically a lineament will comprise a fault-aligned valley, a series of fault or fold-aligned hills, a straight coastline or indeed a combination of these features. Fracture zones, shear zones and igneous intrusions such as dykes can also give rise to lineaments. Lineaments are often apparent in geological or topographic maps and can appear obvious on aerial or satellite photographs. The term 'megalineament' has been used to describe such features on a continental scale. The trace of the San Andreas Fault might be considered an example. The Trans Brazilian Lineament and the TransSaharan Belt, taken together, form perhaps the longest coherent shear zone on the Earth, extending for about 4,000 km. Lineaments have also been identified on other planets and their moons. Their origins may be radically different from those of terrestrial lineaments due to the differing tectonic processes involved (Mostafa and Bishta, 2005; Semere and Ghebreab, 2006).

groundwater storages (Semere and Ghebreab, 2006). Fortunately, the application of remotesensing technology from space is providing geologists with means of acquiring these synoptic data sets.

Satellite remote sensing and image processing for lineament features detection
Lineaments are any linear features that can be picked out as lines (appearing as such or evident because of contrasts in terrain or ground cover on either side) in aerial or space imagery. If geological these are usually faults, joints, or boundaries between stratigraphic formations. Other causes of lineaments include roads and railroads, contrast-emphasized contacts between natural or man-made geographic features (e.g., fence lines), or vague "false alarms" caused by unknown (unspecified) factors. The human eye tends to single out both genuine and spurious linear features, so that some thought to be geological may, in fact, be of other origins (Semere and Ghebreab, 2006).
In the early days of Landsat, perhaps the most commonly cited use of space imagery in Geology was to detect linear features (the terms "linear" or "photolinear" are also used instead of lineaments, but 'linear' is almost a slang word) that appeared as tonal discontinuities. Almost anything that showed as a roughly straight line in an image was suspected to be geological. Most of these lineaments were attributed either to faults or to fracture systems that were controlled by joints (fractures without relative offsets) (Wang et al. 1990;Vassilas et al. 2002;Robinson et al., 2007).
Lineaments are well-known phenomena in the Earth's crust. Rocks exposed as surfaces or in road cuts or stream outcrops typically show innumerable fractures in different orientations, commonly spaced fractions of a meter to a few meters apart. These lineaments tend to disappear locally as individual structures, but fracture trends persist. The orientations are often systematic meaning, that in a region, joint planes may lie in spatial positions having several limited directions relative to north and to horizontal (Mostafa and Bishta, 2005). Where continuous subsurface fracture planes that extend over large distances and intersect the land surface produce linear traces (lineaments). A linear feature in general can show up in an aerial photo or a space images as discontinuity that is either darker (lighter in the image) in the middle and lighter (darker in the images) on both sides; or, is lighter on one side and darker on the other side. Obviously, some of these features are not geological. Instead, these could be fence lines between crop fields, roads, or variations in land use. Others may be geo-topographical, such as ridge crests, set off by shadowing. But those that are structural (joints and faults) are visible in several ways (Semere and Ghebreab, 2006;Zaineldeen 2011).
Lineament commonly are opened up and enlarged by erosion. Some may even become small valleys. Being zones of weak structure, they may be scoured out by glacial action and then filled by water to become elongated lakes (the Great Lakes are the prime example). Ground water may invade and gouge the fragmented rock or seep into the joints, causing periodic dampness that we can detect optically, thermally, or by radar. Vegetation can then develop in this moisture-rich soil, so that at certain times of year linear features are enhanced. We can detect all of these conditions in aerial or space imagery (Majumdar and Bhattacharya 1998;Katsuaki et al., 1995;Walsh 2000;Mostafa and Bishta, 2005;Semere and Ghebreab, 2006).

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Consequently, optical remote sensing techniques over more than three decades have shown a great promise for mapping geological feature variations over wide scale (Mostafa and Bishta, 2005;Semere and Ghebreab, 2006;Marghany et al., 2009a). In referring to Katsuaki et al., (1995); Walsh (2000) lineament information extractions in satellite images can be divided broadly into three categories: (i) lineament enhancement and lineament extraction for characterization of geologic structure;(ii) image classification to perform geologic mapping or to locate spectrally anomalous zones attributable to mineralization (Mostafa et al., 1995;Süzen and Toprak 1998); and (iii) superposition of satellite images and multiple data such as geological, geochemical, and geophysical data in a geographical information system (Novak and Soulakellis 2000;Semere and Ghebreab 2006). Furthermore, remote sensing data assimilation in real time could be a bulk tool for geological features extraction and mapping. In this context, several investigations currently underway on the assimilation of both passive and active remotely sensed data into automatic detection of significant geological features i.e., lineament, curvilinear and fault.
Image processing tools have used for lineament feature detections are: (i) image enhancement techniques (Mah et al. 1995;Chang et al. 1998;Walsh 2000;Marghany et al., 2009b); and (ii) edge detection and segmentation (Wang et al. 1990;Vassilas et al. 2002;Mostafa and Bishta 2005). In practice, researchers have preferred to use the spatial domain filtering techniques in order to get ride of the artificial lineaments and to verify disjoint lineament pixels in satellite data (Süzen and Toprak 1998). Further, Leech et al., (2003) implemented the band-rationing, linear and Gaussian nonlinear stretching enhancement techniques to determine lineament populations. Won-In and Charusiri (2003) found that High Pass Filter enhancement technique provides accurate geological map. In fact, the High Pass filter selectively enhances the small scale features of an image (high frequency spatial components) while maintaining the larger-scale features (low frequency components) that constitute most of the information in the image. Majumdar and Bhattacharya (1998) and Vassilas et al. (2002), respectively have used Haar and Hough transforms as edge detection algorithms for lineament detection in Landsat-TM satellite data. Majumdar and Bhattacharya (1998) reported that Haar transform is proper in extraction of subtle features with finer details from satellite data. Vassilas et al. (2002), however, reported that Hough transform is appropriate for fault feature mapping. Consequently, Laplacian, Sobel, and Canny are the major algorithms for lineament feature detections in remotely sensed data (Mostafa and Bishta 2005;Semere and Ghebreab, 2006;Marghany 2005).Recently Marghany and Mazlan (2010) proposed a new approach for automatic detection of lineament features from RADARSAT-1 SAR data. This approach is based on modification of Lee adaptive algorithm using convolution of Gaussian algorithm.

Problems for geological features extraction from remote sensing data
Geological studies are requiring standard methods and procedures to acquire precisely information. However, traditional methods might be difficult to use due to highly earth complex topography. Regarding the previous prospective, the advantage of satellite remote sensing in its application to geology is the wide coverage over the area of interest, where much accurate and useful information such as structural patterns and spectral features can www.intechopen.com be extracted from the imagery. Yet, abundance of geological features are not be fully understood. Lineaments are considered the bulk geological features which are still unclear in spite of they are useful for geological analysis in oil exploration. In this sense, the lineament extraction is very important for the application of remote sensing to geology. However the real meaning of lineament is still vague. Lineaments should be discriminated from other line features that are not due to geological structures. In this context, the lineament extraction should be carefully interpreted by geologists.

Hypothesis of study
Concerning with above prospective, we address the question of uncertainties impact on modelling Digital Elevation Model (DEM) for 3-D lineament visualization from multispectral satellite data without needing to include digital elevation data. This is demonstrated with LANDSAT-ETM satellite data using fuzzy B-spline algorithm (Marghany andMazlan 2005 andMarghany et al., 2007). Three hypotheses are examined: Canny algorithm can be used as semiautomatic tool to discriminate between lineaments and surrounding geological features in optical remotely sensed satellite data; and  uncertainties of DEM model can be solved using Fuzzy B-spline algorithm to map spatial lineament variations in 3-D.

Study area
The study area is located in Sharjah Emirates about 70 Km fromSharjah city. It is considered in the alluvium plain for central area of UAE and covers an Area of 1800 Km 2 (60 km x 30 km) within boundaries of latitudes 24º 12′N to 24º.23'N and longitudes of 55º.51'E to 55º 59' E ( Fig. 1). The northern part of UAE is formed of the Oman mountains and the marginal hills extends from the base of the mountains and (alluvium plain) to the south western sand dunes (Figs 2 and 3) such features can be seen clearly in Wadi Bani Awf, Western Hajar ( Fig.2). Land geomorphology is consisted of structural form, fluvial, and Aeolian forms(sand dunes). According to Maged et al., (2009) structural form is broad of the Oman mountains and JabalFayah ( Fig.4) which are folded structure due collusion of oceanic crust and Arabian plate (continental plate). Furthermore, the mountain is raised higher than 400 m above sea level and exhibit parallel ridges and high-tilted beds. Many valleys are cut down the mountains, forming narrow clefts and there are also intermittent basins caused by differential erosion. In addition, the Valley bases are formed small caves. Stream channels have been diverted to the southwest and they deposited silt in the tongue -shaped which lies between the dunes. Further, Aeolian forms are extended westwards from the Bahada plain, where liner dunes run towards the southwest direction in parallel branching pattern ( Fig. 3) with relative heights of 50 meters. Nevertheless, the heights are decreased towards the southeast due to a decrease in sand supply and erosion caused by water occasionally flowing from the Oman mountains. Moreover, some of the linear dunes are quite complex due to the development of rows of star dunes along the top of their axes. Additionally, inter dunes areas are covered by fluvial material which are laid down in the playas formed at the margins of the Bahadas plain near the coastline. The dunes changes their forms to low flats of marine origin and their components are also dominated by bioclastics and quartz sands (Marghany and Mazlan 2010).

Data sets
In study, there are two sort of data have been used. A thermal infrared channel with 60 m spatial resolution (band 6).  Full aperture, 5% absolute radiometric calibration.

Fig. 5. LANDSAT satellite data used in this study
Second is ancillary data which are contained digital topographic, geological maps, well logs and finally ground water data. Furthermore, ancillary data such as topography map of scale 1: 122,293 used to generate Digital Elevation Model (DEM) of selected area. Bands 1,2,3,5 and 7 are selected to achieve the objective of this study. According to Marghany et al., (2009) these bands can provide accurate geological information. Finally, the Digital Elevation Model (DEM) is acquired from SRTM data (Fig.6).

Model for 3-D lineament visualization
The procedures have been used to extract lineaments and drainage pattern from LANDSAT ETM satellite image were involved image enhancement contrast, stretching and linear enhancement which were applied to acquire an excellent visualization. In addition, automatic detection algorithm Canny are performed to acquire excellent accuracy of lineament extraction (Mostafa et al., 1995). Two procedures have involved to extract lineaments from LANDSAT ETM data. First is automatic detection by using automatic edge detection algorithm of Canny algorithm. Prior to implementations of automatic edge detection processing, LANDSAT ETM data are enhanced and then geometrically corrected. Second is implementing fuzzy B-spline was adopted from  to reconstruct 3D geologic mapping visualization from LANDSAT ETM satellite data.

Histogram equalization
Following Marghany et al., (2009) histogram equalization is applied to LANDSAT TM image to obtain high quality image visualization. An image histogram is an analytic tool used to measure the amplitude distribution of pixels within an image. For example, a histogram can be used to provide a count of the number of pixels at amplitude 0, the number at amplitude 1, and so on. By analyzing the distribution of pixel amplitudes, you can gain some information about the visual appearance of an image. A high-contrast image contains a wide distribution of pixel counts covering the entire amplitude range. A low contrast image has most of the pixel amplitudes congregated in a relatively narrow range (Süzen et al., 1998 andGonzalez andWoods 1992).

Canny algorithm
According to Canny ( 1986),the Canny edge detector uses a filter based on the first derivative of a Gaussian, because it is susceptible to noise present on raw unprocessed image data, so to begin with, the raw image is convolved with a Gaussian filter. The result is a slightly blurred version of the original which is not affected by a single noisy pixel to any significant degree. According to Deriche (1987) The direction of the edge θ is computed using the gradient in the G x and G y directions. However, an error will be generated when sum X is equal to zero. So in the code, there has to be a restriction set whenever this takes place. Whenever the gradient (G) in the x direction is equal to zero, the edge direction has to be equal to 90 degrees or 0 degrees, depending on what the value of the gradient in the y-direction is equal to. If G y has a value of zero, the edge direction will equal 0 degrees. Otherwise the edge direction will equal 90 degrees (Deriche 1987).
According to Gonzalez and Woods (1992),three criteria are used to improve edge detection. The first and most obvious is low error rate. It is important that edges occurring in images should not be missed and that there be NO responses to non-edges. The second criterion is that the edge points be well localized. In other words, the distance between the edge pixels as found by the detector and the actual edge is to be at a minimum. A third criterion is to have only one response to a single edge. This was implemented because the first 2 were not substantial enough to completely eliminate the possibility of multiple responses to an edge (Canny 1986).

The fuzzy B-splines algorithm
The fuzzy B-splines (FBS) are introduced allowing fuzzy numbers instead of intervals in the definition of the B-splines. Typically, in computer graphics, two objective quality definitions for fuzzy B-splines are used: triangle-based criteria and edge-based criteria (Marghany et al., 2009). A fuzzy number is defined using interval analysis. There are two basic notions that we combine together: confidence interval and presumption level. A confidence interval is a real values interval which provides the sharpest enclosing range for current gradient values.
An assumption  -level is an estimated truth value in the [0, 1] interval on our knowledge level of the topography elevation gradients (Anile 1997). The 0 value corresponds to minimum knowledge of topography elevation gradients, and 1 to the maximum topography elevation gradients. A fuzzy number is then prearranged in the confidence interval set, each one related to an assumption level   [0, 1]. Moreover, the following must hold for each pair of confidence intervals which define a number: Let us consider a function ' : f dd  , of N fuzzy variables 12 , ,...., n dd d. Where n d are the global minimum and maximum values topography elevation gradients along the space. Based on the spatial variation of the topography elevation gradients, the fuzzy B-spline algorithm is used to compute the function f . Follow Marghany et al., (2010) d(i,j) is the topography elevation value at location i,j in the region D where i is the horizontal and j is the vertical coordinates of a grid of m times n rectangular cells. Let N be www.intechopen.com the set of eight neighbouring cells. The input variables of the fuzzy are the amplitude differences of water depth d defined by  Equations 5 and 6 represent topography elevation in 2-D, in order to reconstruct fuzzy values of topography elevation in 3-D, then fuzzy number of digital elevation in z coordinate is estimated by the following equation proposed by Russo (1998)  The fuzzy number of water depth O F then is defined by B-spline in order to reconstruct 3-D of digital elevation. In doing so, B-spline functions including the knot positions, and fuzzy set of control points are constructed. The requirements for B-spline surface are set of control points, set of weights and three sets of knot vectors and are parameterized in the p and q directions.
Following Marghany et al., (2009b) and , a fuzzy number is defined whose range is given by the minimum and maximum values of digital elevation along each kernel window size. Furthermore, the identification of a fuzzy number is acquired to summarize the estimated digital elevation data in a cell and it is characterized by a suitable membership function. The choice of the most appropriate membership is based on triangular numbers which are identified by minimum, maximum, and mean values of digital elevation estimated. Furthermore, the membership support is the range of digital elevation data in the cell and whose vertex is the median value of digital elevation data ). Fig. 4 shows the Digital Elevation Model is derived from SRTM data that covered area of approximately 11 km 2 . Clearly, DEM varies between 319-929 m and maximum elevation value of 929 m is found in northeast direction of UAE. Therefore, SRTM has promised to produce DEM with root mean square error of 16 m (Nikolakopoulos et al., 2006). In addition, Oman mountain is dominated by highest DEM value of 929 m which is shown parallel to coastal zone of Arabian Gulf. The DEM is dominated by spatial variation of the topography features such as ridges, sand dunes and steep slopes. As the steep slopes are clearly seen within DEM of 400 m (Fig,7). According to Zaineldeen (2011), the rocks are well bedded massive limestones with some replacement chert band sand nodules. The limestone has been locally dolomitized.  classification shows a great fault moves through a highland area. According to Robinson et al., (2007) , TM bands 7 (2.08-2.35 mm),4 (0.76-0.90 mm),and 2(0.50-0.60 mm)are appropriate for geological features detection because they have low-correlation and produce high-contrast. In this regard, band 2 is useful for rock discrimination, band 4 for land/water contrasts, and band 7 for discrimination of mineral and rock types. Further, TM bands 7 are also able to imagined crest dunes parallel with tens kilometres of length. This feature is clear in northern part of Fig.8 and located in high land of DEM of 900 m. This finding confirm the study of Robinson et al., (2007) .   Fig. 9 shows the output result mapping of lineaments using composite of bands 3,4 , 5 and 7 in LANDSAT TM satellite data. The appearance of lineaments in LANDSAT TM satellite image are clearly distinguished. In addition, area adjacent to the mountainous from Manamh (northward), Flili village in the (southward) has high density of lineaments due to the westward compressive force between the oceanic crust and Arabian plate, such as fractures and faults and drainage pattern that running in the buried fault plains (filled weathered materials coming from Oman mountains) (Fig. 9). The lineaments are associated with fractures and faults which are located in northern part of Fig. 9. In fact that Canny algorithm first is smoothed the image to eliminate and noise. It then finds the image gradient to highlight regions with high spatial derivatives. The algorithm then tracks along these regions and suppresses any pixel that is not at the maximum (non-maximum suppression). The gradient array is further reduced by hysteresis. According to Deriche (1987), hysteresis is used to track along the remaining pixels that have not been suppressed. Hysteresis uses two thresholds and if the magnitude is below the first threshold, it is set to zero (made a non-edge). Further, If the magnitude is above the high threshold, it is made an edge. And if the magnitude is between the 2 thresholds, then it is set to zero unless there is a path from this pixel to a pixel with a gradient above threshold. In order to implement the canny edge detector algorithm, a series of steps must be followed. The first step is to filter out any noise in the original image before trying to locate and detect any edges. In fact, the Gaussian filter can be computed using a simple mask, it is used exclusively in the Canny algorithm. Once a suitable mask has been calculated, the Gaussian smoothing can be performed using standard convolution methods. According to Marghany et al., (2009), LANDSAT TM data can be used to map geological features such as lineaments and faults. This could be contributed to that composite of bands 3,4,5 able and 7 in LANDSAT TM satellite data are appropriate for mapping of geologic structures (Katsuaki and Ohmi 1995;Novak and Soulakellis 2000;Marghany et al., 2009). Consequently, the ground resolution cell size of LANDSAT TM data is about 30 m. This confirms the study of Robinson et al., (2007) .   Fig. 10 shows the lineament distribution with 3D map reconstruction using SRTM and LANDSAT TM bands 3,4,5, and 7. It is clear that the 3D visualization discriminates between different geological features. It can be noticed the faults, lineament and infrastructures clearly (Figure 10b). This study agrees with Marghany et al., (2009). It can be confirmed that the lineament are associated with faults and it also obvious that heavy capacity of lineament occurrences within the Oman mountain. This type of lineament can be named as mountain lineament. According to Robinson et al., (2007) and Marghany et al., (2009) the mountain is raised higher than 400 m above sea level and exhibit parallel ridges and high-tilted beds. Many valleys are cut down the mountains, forming narrow clefts and small caves. The fluvial forms are consisted of streams channels which are flowed from Oman mountains have and spread out into several braided channels at the base of the mountains from the Bahada and Playa plains (Figure 11). Stream channels have been diverted to the southwest and they deposited silt in the tongue -shaped which lies between the dunes.

3-D lineament visulization using classical method
Further, Aeolian forms are extended westwards from the Bahada plain, where liner dunes run towards the southwest direction in parallel branching pattern (Fig. 11) with relative heights of 50 meters. Nevertheless, the heights are decreased towards the southeast due to a www.intechopen.com decrease in sand supply and erosion caused by water occasionally flowing from the Oman mountains. Moreover, some of the linear dunes are quite complex due to the development of rows of star dunes along the top of their axes. Additionally, inter dunes areas are covered by fluvial material which are laid down in the playas formed at the margins of the Bahadas plain near the coastline. The dunes changes their forms to low flats of marine origin and their components are also dominated by bioclastics and quartz sands (Marghany et al., 2009 and Zaineldeen 2011). Fig. 12 shows the result acquires by using fuzzy B-spline algorithm. It is clear that the 3D visualization discriminates between different geological features. It can be noticed the faults, lineament and infrastructures clearly (Fig. 12c). This is due to the fact that the fuzzy Bsplines considered as deterministic algorithms which are described here optimize a triangulation only locally between two different points (Fuchs et al., 1977;Anile et al., 1995;Anile, 1997;Marghany and Mazlan 2011). This corresponds to the feature of deterministic strategies of finding only sub-optimal solutions usually. The visualization of geological feature is sharp with the LANDSAT TM satellite image due to the fact that each operation on a fuzzy number becomes a sequence of corresponding operations on the respective µ-levels and the multiple occurrences of the same fuzzy parameters evaluated as a result of the function on fuzzy variables Keppel 1975;Anile et al., 1995;Magrghany and Mazlan 2011).

3-D lineament visulization using fuzzy B-spline technique
It is very easy to distinguish between smooth and jagged features. Typically, in computer graphics, two objective quality definitions for fuzzy B-splines were used: triangle-based criteria and edge-based criteria. Triangle-based criteria follow the rule of maximization or minimization, respectively, of the angles of each triangle (Fuchs et al., 1977). The so-called max-min angle criterion prefers short triangles with obtuse angles. This finding confirms those of Keppel 1975 andAnile 1997. Table 1 confirms the accurate of fuzzy B-spline to eliminate uncertainties of 3-D visualization. Consequently, the fuzzy B-spline shows higher performance with standard error of mean of 0.12 and bias of 0.23 than SRTM technique. In www.intechopen.com Approximation with FBS provides a fast way to obtain qualitatively reliable descriptions whenever the introduction of a precise probabilistic DEM is too costly or impossible. In this study, fuzzy B-spline algorithm produced 3-D lineament visulization without need to ground geological survey. In fact fuzzy B-spline algorithm is able to keep track of uncertainty and provide tool for representing spatially clustered geological features. This advantage of fuzzy B-spline is not provided in Canny algorithm and DEM produced by SRTM data.

Statistical Parameters 3-D Visualization
Fuzzy B-spline SRTM Bias 0.23 0.63 Standard error of the mean 0.12 0.56 Table 1. Statistical Comparison of 3-D computer visualization using Fuzzy-B-spline and SRTM.

Conclusions
This study has demonstrated a method to map lineament distributions in United Arab Emirates (UAE) using LANDSAT-TM satellite data. In doing so, 3D image reconstruction is produced using SRTM data. Then Canny algorithm is implemented for lineament automatic detection from LANDSAT TM bands of 3,4,5,and 7. The results show that the maximum DEM value of 929 m is found in the northeast direction of UAE. The vegetation covers are dominated feature in the highest DEM while highlands are located in lowest elevation of 660 m. In addition, Canny algorithm has detected automatically lineament and fracture features. Therefore, 3D visualization is discriminated between lineament and fault features.
The results show that the highest spatial distribution of lineaments are appeared in Oman mountain which are named by lineament mountain. In conclusion, the integration between Digital Elevation Model (DEM) and Canny algorithm can be used as geomatic tool for lineament automatic detection in 3D visualization. Further, a fuzzy B-spline algorithm is used to reconstruct Three Dimensional (3D) visualization of geologic feature spatial variations with standard error of mean of 0.12 and bias of 0.23. In conclusion, combination between Canny algorithm and DEM generated by using fuzzy B-spline could be used as an excellent tool for geologic mapping.