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Extraction of Mountains from Digital Elevation Models Using Mathematical Morphology


Dinesh Sathyamoorthy
Science and Technology Research Institute for Defence (STRIDE),
Ministry of Defence, Malaysia.
dinsat@yahoo.com




Abstract
In this paper, a mathematical morphological based algorithm to extract mountains from digital elevation models (DEMs) is proposed. First, ultimate erosion is used to extract the peaks of the DEM. Conditional dilation is performed on the extracted peaks to obtain the mountain regions. The effectiveness of the proposed algorithm is tested by implementing it on the Global Digital Elevation Model (GTOPO30) of Great Basin, Nevada, USA. Connected component labelling is used to identify the individual mountains objects. Each mountain object is described based on their size, perimeter length, maximum elevation, mean gradient, local relief and relative massiveness

1 Introduction

Mountains are the portions a terrain that are sufficiently elevated above the surrounding land (greater than 300 to 600m) and have comparatively steep sides. In a mountain, two parts are distinctive:

1. The summit, the highest point (the peak) or the highest ridges
2. The mountainside, the part of a mountain between the summit and the foot (Bates and Jackson, 1987).

The mapping of mountains is generally performed manually through fieldwork and visual interpretation of topographic maps, which is a time consuming and labor intensive activity. In recent times, extraction techniques have evolved from manual through computer assisted to automated methods; with digital elevation models (DEMs) as the input data. In seeking the efficient extraction of mountains from DEMs, various algorithms have been proposed (Graff and Usery, 1993; Miliaresis and Argialas, 1999; Miliaresis, 2000)

In this paper, a mathematical morphological based algorithm to perform the extraction of mountains from digital elevation models (DEMs) is developed. Mathematical morphology is a branch of image processing that deals with the extraction of image components that are useful for representational and descriptional purposes (Gonzalex and Wood, 1993). In mathematical morphology, the grey level of a greyscale image is taken to represent height above a base plane, so that the greyscale image represents a topographic surface in 3D Eucledian space. Hence, a DEM can be easily represented as a greyscale image since it is enough to associate each elevation with a grey level proportional to the considered elevation. A DEM is therefore thought of as a greyscale function defined over a subset of 2D digital space, with the grey level at any point being the altitude at this point (Soille and Ansoult, 1990). The fundamental morphological operators are discussed in Matheron (1975), Serra (1982) and Soille (2003). Morphological operators generally require two inputs; the input image A, which can be in binary or grayscale form, and the kernel B, which is used to determine the precise effect of the operator (Serra, 1982).

In the Section 2, the proposed mathematical morphological based mountain extraction algorithm is discussed. In Section 3, the effectiveness of the proposed algorithm is tested by implementing on the Global Digital Elevation Model (GTOPO30) of Great Basin, Nevada, USA. Concluding remarks regarding the scope of the study is provided in the final section.

Table 1: Numerical description of the extracted mountain objects

Object ID	Area(pixels)	Perimeter(pixels)	Maximum elevation(grey level)	Mean gradient(°)
1	1227	219	178	11.94
2	10422	2277	191	10.61
3	1353	161	149	8.28
4	298	88	123	10.08
5	14232	3391	240	10.22
6	432	113	143	10.87
7	6444	999	255	9.56
8	311	162	112	10.66
9	1119	353	167	8.03
10	219	124	130	6.48
11	3574	754	237	9.18
12	3058	651	231	13.20
13	494	172	170	9.55
14	261	112	170	8.01

2 The Proposed Mountain Extraction Algorithm
Mountains have a gradient range of 6º and above. The gradient values of a terrain are usually minimized in the pits and peaks, in contrast to the usually steep valley sides or cliff sides. Hence, physiographic segmentation cannot be performed through gradient thresholding of the DEM. The proposed mountain extraction algorithm is as follows:


An example of the ultimate erosion operation. Ultimate erosion is implemented through the iterative erosion of the image until all objects vanish (images Xi), and the reconstruction of each eroded image using the eroded image E(Xi) as the mask and the erosion of smaller size as the marker. The reconstructed images (images Yi) are subtracted from the corresponding eroded images to form the eroded sets (images Ui). The final resultant image, known as the ultimate eroded set, contains only the objects’ pseudo-centres. (Source: Duchane and Lewis, 1996).