GRAPHICAL MODELS AND IMAGE PROCESSING Vol. 60, No. 2, March, pp. 166–172, 1998 ARTICLE NO. IP970463 NOTE Digital Elevation Model Data Analysis Using the Contact Surface Area Ernesto Bribiesca Department of Computer Science, Institute of Research in Applied Mathematics and Systems, Universidad Nacional Aut´ onoma de M´ exico, Apdo. 20-726, M´ exico, D.F., 01000 E-mail: ernesto@uxcomp2.iimas.unam.mx Received May 29, 1997; accepted December 5, 1997 We present an approach for analyzing digital elevation model (DEM) data using the concept contact surface area and mathema- tical morphology. DEMs are digital representations of the Earth’s surface. Generally speaking a DEM is generated as a uniform rect- angular grid organized in profiles. In order to analyze DEM data by means of binary morphology, the models are represented as binary solids composed of regular polyhedrons (voxels). In the content of this work, we use morphological operators to erode DEMs, simplify binary solid data, preserve essential shape characteristics, under- stand shape in terms of a decomposition, and identify object fea- tures. This is shown by means of some simple examples. We define the contact surface area for DEMs composed of voxels. The contact surface area corresponds to the sum of the contact surface areas of the neighboring voxels of DEMs. A relation between the area of the surface enclosing the volume and the contact surface area is pre- sented. The definition of contact surface area permits us to obtain a fast and efficient method for plotting models composed of a large number of voxels. c  1998 Academic Press 1. INTRODUCTION Mathematical morphology plays an important role in com- puter vision [1–5]. This work deals with binary morphology and digital elevation model (DEM) data. DEMs have a large num- ber of applications [6]. Some of these applications include pro- duction of slope, aspect, hill-shaded maps, engineering calcu- lations, line-of-sight calculations, urban and regional planning, navigation, geomorphology, components in complex models, and geographic information systems. When we use morpholog- ical operations on DEM data the number of applications may be increased; this is due to morphological operators permit to erode DEMs, simplify DEM data, preserve essential shape char- acteristics, understand shape in terms of a decomposition, and identify model features. Thus, the importance of mathematical morphology on DEM data is evident. In order to use morphological operators on DEMs it is nece- ssary to select an appropriate representation. In this work the DEMs are represented as three-dimensional (3D) arrays of cells (voxels) which are marked as filled with matter [7]. Recently, a method for measuring 3D shape similarity using this represen- tation was presented in Ref. [8]. Several authors have been using different kinds of representations for solids: rigid solids repre- sented by their boundaries or enclosing surfaces are shown in Refs. [9] and [10]; constructive solid geometry schemes are pre- sented in Refs. [11] and [12]; generalized cylinders as 3D volu- metric primitives are shown in Refs. [13–15]; and superquadrics are shown in Ref. [16]. In order to plot our results efficiently, we present the defini- tion of contact surface area for DEMs as composed of a larger number of voxels. Furthermore, we present the relation between the area of the surface enclosing the volume and the contact sur- face area. This definition of area is the extension in 3D domain of the concept termed contact perimeter [17]. The organization of the paper is as follows: Section 2 contains a set of definitions which describe the contact surface area and the method used for plotting, Section 3 presents DEM data char- acteristics, Section 4 describes binary morphology applied to DEMs and some simple examples, and finally, Section 5 presents conclusions. 2. CONCEPTS AND DEFINITIONS First, we present the definition of contact surface area and subsequently the morphological operations used on DEMs. We use volumetric representation for DEMs by means of spatial occupancy arrays. Thus, the DEMs are represented as 3D arrays of voxels which are marked as filled with matter. Furthermore, shape is referred to as shape-of-object and object is considered as a geometric solid composed of voxels. In the content of this work, area is a numerical value expressing 2D extent in a plane, or sometimes it is used to mean the interior region itself [18]. Another consideration is the assumption that an entity has been isolated from the real world. This is called the DEM and is defined as a result of previous processing. Also, the length of all edges of voxels is considered equal to 1. 166 1077-3169/98 $25.00 Copyright c  1998 by Academic Press All rights of reproduction in any form reserved.