INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)  
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025  
Extraction of Edge-type and Anomaly-type Lineaments Based on  
Directional Continuous Wavelet Transform  
Man Hyok Song*, Song Lyu, Chol Yong O  
Faculty of Earth Science and Technology, Kim Chaek University of Technology, City-Pyongyang, State-  
DPR of Korea  
DOI: https://dx.doi.org/10.51244/IJRSI.2025.1210000340  
Received: 02 November 2025; Accepted: 10 November 2025; Published: 22 November 2025  
ABSTRACT  
Background  
Lineaments can be expressed as linear features which are notably brighter or darker than background (anomaly-  
type) and suddenly changed in brightness (edge-type) in the remote sensing (RS) and digital elevation model  
(DEM) images. A new method is proposed to extract both types of lineaments from RS and DEM images based  
on directional continuous wavelet transform (CWT).  
The method consists of three steps: (i) determination of omni-directional CWT coefficient concerned with image  
gradient magnitude and omni-direction image reflecting image gradient direction using multi-directional CWT  
coefficients, (ii) extraction of image features such as extrema and edges using CWT modulus maxima line and  
(iii) detection of lineaments through segmentation and linkage of image features and linearization of image  
feature segments. The omni-directional CWT and omni-direction image determined from multi-directional CWT  
coefficients are associated with image gradient to be applied to image feature extraction, segmentation and  
linkage. The positive and negative lineaments can also be detected by the method.  
The proposed method is tested using a simple example image and compared with the Hough transform (HT)  
method and applied to real RS and DEM images to extract both types of lineaments, which are compared with  
real geological structures including faults. The results show the proposed method is superior to the HT method  
and effective in detection of lineaments reflecting geological structures which are roughly rectilinear and  
expressed at multiple scales and directions.  
Keywords: Directional continuous wavelet transform, Omni-direction, Lineament extraction, Digital elevation  
model, Image gradient  
INTRODUCTION  
Lineaments are closely associated with geological features including geological structures, lithological  
boundaries and stream networks. Therefore, lineament extraction is important in geological studies (1~3).  
Lineaments have been differently defined by many researchers for many decades, but their definition can be  
classified into two types: linear features which are abnormally brighter and darker than background (4,5) and  
those associated with sudden changes in brightness. In the view of image process, the sudden changes in image  
intensity correspond to image edge and lighter or darker pixels correspond to anomalies.  
Most studies in lineament detection have been based on image edges (2, 6, 7). These methods generally consist  
of two steps: edge detection and lineament extraction. Image edges have been mainly detected using the  
convolution with derivative masks including the Roberts, Sobel, Prewitt, and Canny methods. In special, the  
Canny method has been widely applied to edge detection as it can detect edges more exactly using image  
gradients than other methods. Image gradients are determined by horizontal and vertical derivatives based on  
Gaussian filters. However, both derivatives can lead exact gradients about continuous and differentiable images  
which do not always agree with real images. Although images are smoothed, there can exist some line  
Page 3945  
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)  
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025  
singularities like corners where images are not continuous and differentiable. Some researchers have used  
directional first derivative operators to overcome these shortcomings (8). Such methods can determine directly  
image gradients from multi-directional convolutions of images with directional derivative masks. These masks  
are usually constructed at specific scales and can hardly possible at any scales. Moreover, some researchers used  
four directional masks, which cannot provide exact image gradients. Other researchers used two-dimensional  
continuous wavelet transform (2D CWT) and its multi-directional characters to detect image edges more exactly  
near line singularities such as corners (9,10). However, their methods have not been applied to lineament  
extraction.  
Another important issue in detecting and mapping lineaments is to enhance linearity of edges. Lineaments have  
to be image edges and straight lines. Therefore, methods have been proposed to select linear pixel group or detect  
lines including possible edge pixels from image edges. The typical methods used by most studies on lineament  
detection are Hough transform (HT) and its variations (11). They convert a pixel group laid in a straight line into  
a point in another parameter space of polar coordinates to detect the lineament including the pixel group. As  
many points included in a straight line in image domain are expressed as a point in the parameter space called  
Hough space, HT can easily detect the line by detecting only one point in Hough space instead of many points  
in image space. Although it is recognized to be a useful tool for pattern recognition including lineament detection,  
its lineament detection ability is low in noisy images including lineaments that are roughly rectilinear (12). Edges  
detected using image gradients contain information on their directions which can be helpful in lineament  
detection. The HT and its variations can hardly use this information.  
Some lineaments are not related with image edges, but with anomalies or extrema in image intensity. Most  
morpholineaments such as valleys and ridges in a digital elevation model (DEM) are anomaly-type. Such  
lineaments are usually extracted from derived images, e.g. shaded relief (hillshade) or from second derivatives  
of images (5). As anomaly-type lineaments in an image can be converted with edge-type one in its hillshade,  
they can be extracted using lineament detection based on image edges from the hillshade. However, the hillshade  
is not unique for an image, but a little changed relying on the illumination altitude and azimuth. It can lead to  
different responses for a lineament. Šilhavý et al. tried to extract unique lineament by clustering of different  
lineaments detected from multiple hillshades. Other studies have applied second derivative operators such as  
Laplacian filter to detect anomaly-type lineaments. Mallast et al. introduced omni-directional image from four  
directional images convolved with directional Laplacian filters. Extrema in a DEM can preserve as extrema in  
the omni-directional image of the DEM. Both methods using first derivative and second derivative masks detect  
lineaments based on extrema detection. The former detects exact lineaments easily through comparing gradient  
magnitude along gradient direction, whereas the latter cannot do so and should use some thresholds and thinning.  
This work aims to propose the method to detect lineaments associated with edges and anomalies based on  
directional CWT. Omni-directional CWT coefficient which can reflect gradient magnitude and be used as  
derived image for detecting anomaly-type lineaments is determined from multiple directional CWT coefficients  
based on the Gaus1 wavelet which is the first derivative of the 2D Gaussian function. Image edges are detected  
using the omni-directional CWT coefficient and omni-direction image. Edges are also segmented into several  
parts and the parts with similar direction are linked each other using them. Finally, every edge segment object is  
transformed into a lineament based on regression analysis.  
METHOD  
Omni-directional CWT and image gradient  
2D wavelet function  
s (x), where x= (x, y) is the spatial variable vector, can be obtained from mother  
u
wavelet (x) by dilation, translation and rotation as follows.  
1
x u  
s
u,,s (x) R-  
,
(1)  
s
where u= (ux, uy) is the translation parameter vector, s is the scale parameter,  
is the rotation angle and R  
Page 3946  
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)  
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025  
is the rotation matrix.  
The 2D directional CWT of a 2D signal f(x) with respected to the wavelet  
at scale s is defined as  
1
x u  
s
WT (u,  
f (x)  
R-  
dx  
.
(2)  
)   
s
s
2
R
The space parameter vector x is eliminated after CWT and the translation parameter vector u is the same as x in  
essence. For convenience, we replace u with x to express the CWT as a function of the space parameter vector  
and rotation angle.  
The omni-directional CWT, WTOD (x), is given from multi-directional CWTs and defined as  
s
WTOD (x) WT (x,(x))  
,
(3)  
OD  
s
s
WT (x,OD (x)) max WT (x,)  
where  
,
OD(x) is omni-direction function. That is, the omni-directional  
s
s
CWT means the modulus maximum of directional CWT at x with respect to and the omni-direction function  
is the direction of the omni-directional CWT at x. The directional CWT of f(x) with Gaus1 wavelet is the same  
as the first derivative of the function smoothed with 2D Gaussian function. Therefore, the omni-directional CWT  
is proportional to image gradient magnitude and the omni-direction function reflects gradient direction. This  
means we can detect lineaments using the omni-directional CWT and omni-direction function instead of image  
gradient.  
Convert of extremum points into edge points using omni-directional CWT  
In the view of mathematics, anomaly-type lineaments such as ridges and valleys are associated with lines  
consisting of extremum points, which seem to be detected more hardly than edges. Derived image where edges  
correspond to extremum points in source image is necessary to detect anomaly-type lineaments using edge-based  
lineament detection method. Here, the omni-directional CWT of the source image is supposed to be used as the  
derived image. In general, if a 2D function has an extremum along the direction at the point x, the directional  
derivative of the function along the direction at the point is to be zero. This is certainly possible along the gradient  
direction. For convenience, let’s consider 1D function along the gradient direction (Fig. 1).  
Fig.1 Principle of conversion of extreme points such as peaks and valleys into edges using the omni-directional  
CWT  
Page 3947  
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)  
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025  
As shown in Fig. 1a, the peak and valley are expressed as extrema in the section along the gradient direction.  
They exist at extremum points where the dip tendency is changed from increase to decrease or from decrease to  
increase, which leads to sudden change in gradient magnitude (Fig. 1b). The extremum points in primary image  
are changed into edges in its omni-directional CWT. Therefore, edge-type lineaments detected from the omni-  
directional CWT are the same as anomaly-type lineaments of the primary image.  
Edge detection using the omni-directional CWT and omni-direction  
Omni-directional CWT is proportional to the gradient magnitude and omni-direction reflects the gradient  
direction. Therefore, edges can be detected using them.  
An edge point at scale s is a point xf satisfying the condition given as  
OD  
OD  
,
(4)  
WT (xf ) max WT (x)  
s
s
x
where  
for  
small enough to keep the omni-direction OD(x) unchanged to be the same  
x xf   
n OD  
( x  
)
f
as OD(xf), n is an unit vector along the direction  
.
The edge function E(x) is determined based on this condition. Its value is one for points where Eq. 4 is satisfied  
and zero for other points. In order to detect the positive and negative lineaments respectively, the positive and  
negative edge functions E+(x) and E-(x) can be determined as follows.  
E(x) E(x)(WTOD (x) 0)  
,
E(x) E(x)(WTOD (x) 0)  
.
(5)  
s
s
Edge segmentation and linkage  
An edge can be partly rectilinear or curvilinear and lineaments correspond to rectilinear edge parts. Most  
lineaments reflecting geological structures are not strictly rectilinear, but roughly rectilinear and the criterion to  
evaluate whether an edge part is rectilinear or not is relative. HT uses too strict criterion for straight lines to  
detect such roughly rectilinear lineaments.  
As an edge is perpendicular to gradient direction, omni-direction can reflect edge direction. In this paper a  
lineament is supposed to be a group of linked edge points with similar direction. Edges are segmented into nearly  
rectilinear parts with similar direction using omni-direction. Edge part image EP(x) consisting of nearly  
rectilinear edge part objects can be defined as follows.  
n
   
OD  
1,  
if E(x) 1 and(x)( i , i   
)
,
(6)  
EP(x)   
,i 0,1,...,n 1  
2n n 2n  
0,  
otherwise  
where n is a number of divisions of omni-direction which defines how rectilinear each edge part is. Each object  
direction can be determined using mean of omni-direction values of edge points of the object or regression  
coefficient with respect to their positions. If neighboring objects have similar direction, they are linked to be an  
object. This is achieved by changing the value of edge part image from zero to one for the boundary points of  
object to be linked.  
Linearization of edge part objects  
Each edge part object has to be transformed into a straight line. This can be realized using regression analysis  
Page 3948  
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)  
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025  
with respect to positions of edge points belonging to an object. The regression model is supposed as  
you=l(x)=axo+b for the edge points of the object, xo= (xo, yo). The regression coefficients a and b are determined  
by regression analysis. The starting point xls and end point xle of the lineament corresponding to the object are  
set from the regression coefficient of the object, xo and xo as  
s
e,  
xsl (xs0 (ys0 l(xs0 ))sin,l(xs0 (ys0 l(xs0 ))sin))  
,
,
(7)  
(8)  
xel (xe0 (ye0 l(xe0 ))sin,l(xe0 (ye0 l(xe0 ))sin))  
where = arctan(a). Finally, the lineament is determined as  
L {xl (xl ,l(xl )), x[xl , xl ]}  
.
(9)  
s
e
Examples  
Here, the proposed method is tested and compared with the HT method using a simple example image to prove  
its accuracy and efficiency. The image includes an edge-type lineament which is a fault expressed as a  
lithological boundary and three anomaly-type lineaments which are faults expressed as valleys (Fig. 2a). The  
lineaments are not strictly rectilinear, but have linear tendency.  
Fig.2 Example image including roughly rectilinear features (a), its omni-directional CWT (b) and omni-direction  
(c), detected edge image (d)  
Firstly, the omni-directional CWT and omni-direction image are determined from eight directional CWT with  
the scale four (Fig. 2b, 2c). Edges are detected using the omni-directional CWT and omni-direction (Fig. 2d).  
The edges are segmented into nearly rectilinear parts using edges and omni-direction (Fig. 3a). The four edges  
are respectively segmented into four, four, seven and four edge parts. The segmented edge parts with similar  
direction are linked to form an object (Fig. 3b).  
Page 3949  
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)  
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025  
Fig.3 Edge segmentation using omni-direction (a), linkage of edge parts with similar direction (b), lineaments  
detected by the proposed method (c) and those by the HT (d)  
Every parts of each edge are evaluated to be similar in their direction and four edges correspond to four objects.  
Finally, they are linearized to form four lineaments (Fig. 3c, red line). Note that the edge-type lineament  
corresponding to the lithological boundary reflects it exactly, whereas other lineaments are a little deviated from  
the valleys corresponding to them. The anomaly-type lineaments are detected using the omni-directional CWT  
instead of the source image (Fig. 3c, blue line). In contrary to the edge-type lineaments, the anomaly-type  
lineaments exactly correspond to valleys, but not to rock facies boundary. Therefore, exact one among both types  
of lineaments should be selected relying on characters of geological features. The proposed method is compared  
with the HT. The lineaments detected by the HT (Fig. 3d) are more, but reflect the features less exactly and  
sufficiently than those by the proposed method. Lineaments detected by the HT are overlapped and grouped each  
other to reflect geological features, whereas those by the proposed method agree well with geological features  
and each lineament corresponds differently to each feature. This shows the proposed method can detect  
geological lineaments such as faults, lithological boundary and so on, which are roughly rectilinear, more easily  
and effectively than the HT method.  
Applications  
Here, the proposed method is applied to extraction of geological faults using RS and DEM data images. The first  
principal component image of the Landsat ETM+ data and the corresponding DEM data with spatial resolution  
of 30 m are used (Fig 4). Their size are all 1500×1500 pixels.  
Fig.4 The primary component image of Landsat ETM+ data (a) and DEM image (b) of the study area.  
Faults are generally expressed as lithological boundaries which can correspond to sudden changes in image  
intensity of RS data or valleys which are the morphometric features involved in DEM data. Therefore, edge-type  
lineaments corresponding to lithological boundaries are tried to be extracted from the RS data and negative  
anomaly-type lineaments corresponding to valleys are extracted from the DEM data. The first derivative of 2D  
Gaussian function is used as a mother wavelet and the scale is set as 24 which is similar to the width of the faults.  
The edges and edge-type lineaments extracted from the first principal component image of the Landsat ETM+  
data are shown in Fig. 5a and 5b.  
Fig.5 Edges (a) and edge-type lineaments (b) detected from the RS data (Fig. 4a) using the proposed method  
Page 3950  
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)  
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025  
Edges including lithological boundaries are exactly extracted, which provides the condition for detecting  
lineaments. Edges are segmented into several parts which are roughly rectilinear and the parts with similar  
direction are linked to form objects. The objects are linearized to be transformed into lineaments. These edge-  
type lineaments agree well with lithological boundaries which can be faults. The omni-directional CWT of the  
DEM data is determined (Fig. 6a) and its edges (extreme lines of the DEM data) are detected (Fig. 6b).  
Fig. 6 The omni-directional CWT of the DEM data (Fig. 4b) (a), edges detected from the CWT (b) and anomaly-  
type lineaments detected from the DEM data by the proposed method  
The negative anomaly-type lineaments corresponding to valleys are detected from the DEM data (Fig. 6c). The  
valleys in the DEM image are expressed as edges reflecting sudden changes in the omni-directional CWT image  
(Fig. 6a). This shows the omni-directional CWT can be used as a derived image for detecting anomaly-type  
lineaments instead of hillshades. Therefore, valleys can be detected by detecting edges from the omni-directional  
CWT (Fig. 6b). The lineaments lead from the edges are shown with the DEM data (Fig. 6c). The lineaments  
agree well with valleys. The NW-SE oriented valleys are specially rectilinear which are expressed as long  
lineaments.  
Finally, the edge-type and anomaly-type lineaments are displayed together and compared with faults of the  
geological map of the study zone (Fig. 7a).  
Fig. 7 Comparison of detected lineaments to faults (a) and rose diagram of lineaments azimuth (b)  
As shown in the Fig. 7a, the NW-SE oriented strike-slip faults are mainly developed and NNW-SSE oriented  
and NNE-SSW oriented faults are additionally developed. Comparing detected lineaments with the faults (Fig.  
7a), the lineaments correspond well with the NW-SE oriented strike-slip faults. These faults are nearly explained  
by detected long anomaly-type lineaments as they form roughly rectilinear anomaly-type lineaments such as  
valleys and narrow rectilinear bands. Other oriented faults are hardly detected as they do not form clear  
lineaments in the RS and DEM image. The result shows the anomaly-type and edge-type lineaments detected by  
the proposed method can express the faults and lithological boundaries well. The rose diagram made using the  
direction and length of detected lineaments reflects well the distribution of faults in study area.  
Page 3951  
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)  
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025  
DISCUSSION AND CONCLUSION  
This paper proposes the method to extract lineaments using directional 2D CWT. The omni-directional CWT  
and omni-direction determined from eight directional CWTs can be used as a tool to detect edges from RS and  
DEM data instead of image gradient. Moreover, the anomalies in the source image are converted into sudden  
changes in image intensity by the omni-directional CWT. Therefore, it can be used as drive image for detecting  
anomaly-type lineaments instead of hillshades which produce a little different lineament relying on the  
illumination altitude and azimuth. And edge detection of the omni-directional CWT seems to be superior to other  
methods using only the magnitude of the second derivative of the image, as the method uses the omni-direction.  
The omni-direction is used to segmentation of edges into roughly rectilinear parts. The neighbor edge parts with  
similar direction are linked to form an object. Roughly rectilinear objects are linearized to construct lineaments  
using regression analysis. Such segmentation, linkage and linearization are effectively used instead of the HT.  
The examples show the method is more effective in detecting roughly rectilinear lineaments, which is the  
character of geological features, than the HT and the method using hillshades which lead several overlapped and  
colinear lineaments or false additional lineaments for a geological feature. The method has been applied to  
extraction of lineaments from the RS and DEM data for studying geological features including faults and  
lithological boundaries. The anomaly-type and edge-type lineaments extracted by the method agree well with  
most faults. However, both lineaments correspond to a geological feature. Therefore, lineament selection is  
necessary in order to express a geological feature using a proper lineament.  
REFERNECES  
1. Arellano-Baeza AA, Zverev AT, Malinnikov VA, Study of changes in the lineament structure, caused  
by earthquakes in South America by applying the lineament analysis to the Aster (Terra) satellite data,  
Advances in Space Research 37 (2006) 690–697.  
2. Bagheri HS, Crustal lineament control on mineralization in the Anarak area of Central Iran, Ore Geology  
Reviews 66 (2015) 293–308  
3. Das DP, Chakraborty DK, Sarkar K, Significance of the regional lineament tectonics in the evolution of  
the Pranhita–Godavari sedimentary basin interpreted from the satellite data, Journal of Asian Earth  
Sciences 21 (2003) 553–556  
4. Mallast U, Gloaguen R, Geyer S, R¨odiger T, Siebert C, Derivation of groundwater flow-paths based on  
semi-automatic extraction of lineaments from remote sensing data, Hydrol. Earth Syst. Sci. 15(2011)  
2665–2678  
5. Soto-Pinto C, Arellano-Baeza A, Sánchez G, A new code for automatic detection and analysis of the  
lineament Patterns for geophysical and geological purposes (ADALGEO), Computers &Geosciences 57  
(2013)9 3–103.  
6. Ramli MF, Tripathi NK, Yusof N, Shafri HZM, Ali Rahman Z, Lineament mapping in a tropical  
environment using Landsat imagery, International Journal of Remote Sensing 30(23) (2009) 6277-6300  
7. Marghany M, Hashim M, Lineament mapping using multispectral remote sensing satellite data,  
International Journal of the Physical Sciences 5(10) (2010) 1501-1507.  
8. Shirazi SKG, Safabakhsh R, Omnidirectional edge detection. Computer Vision and Image  
Understanding 113 (2009) 556–564  
9. Heric D, Zazula D, Combined edge detection using wavelet transform and signal registration. Image and  
Vision Computing 25 (2007) 652–662  
10. Heric D, Zazula D, Combined edge detection using wavelet transform and signal registration. Image and  
Vision Computing 25 (2007) 652–662  
Page 3952  
INTERNATIONAL JOURNAL OF RESEARCH AND SCIENTIFIC INNOVATION (IJRSI)  
ISSN No. 2321-2705 | DOI: 10.51244/IJRSI |Volume XII Issue X October 2025  
11. Šilhavý J, Minár J, Mentlík P, Sládek J, A new artefacts resistant method for automatic lineament  
extraction using Multi-Hillshade Hierarchic Clustering (MHHC), Computers & Geosciences 92 (2016)  
9–20  
12. Budak, Ü, Guo YH, Sengür, A, Smarandache, F, Neutrosophic Hough Transform, Axioms 6(35) (2017)  
1-11.  
Page 3953