Cartographic Method Of Surface Characteristics Analysis1.docx

Cartographic Method of Surface Characteristics Analysis1,2 R. I. Iziumov and A. L. Svistkov Institute of continuous media mechanics UB RAS, acad. Koroleva st. 1, Perm, 614013 Russia email: [email protected] Abstract—A wide range of investigations is based on analysis of experimental data, which are represented as a function of two variables (height of the relief h(x, y), microhardness, color, etc.). In the studying of process or phenomenon change of these functions after the experiment is of great interest. On numerous occasions the main problem in comparative analysis of the data sets is the absence of a natural reference level (such as sea level), respect to which changes of the surface characteristics can be determined. We suggest the possible algorithm of determining of the reference level. Also there is its comparison with the standard methods in this paper. This method was used for AFM data processing in the study of effects of natural and artificial factors on the surface of human tooth enamel. The paper presents the main results of this research and shows the necessity of additional data processing using the developed method. Keywords: data processing, reference level, topography, atomic force microscopy. DOI: 10.1134/S1054661816010090 Received May 20, 2015 APPLIED PROBLEMS 126 PATTERN RECOGNITION AND IMAGE ANALYSIS Vol. 26 No. 1 2016 IZIUMOV, SVISTKOV surface before and after treatment, while preserving previous information about the reference level of relief elevations, in order to adequately determine the occurring changes. This can be illustrated by Fig. 1, which depicts a surface formed by a horizontal plane with loosely disposed columns of equal height and square section. A part of the horizontal plane is shown as rectangle ABCD. The plane passes through the axes x and y. The vertical axis is indicates the height h at each point of the surface. It has two values: either this is h = 0 (if the points are on the plane), or h = H (if the points are on the columns). The height of the columns is denoted by H. In this example, it seems reasonable to use the level of the plane as the reference level, and the height of columns should be counted off from this reference plane. Further we will discuss how we can create the algorithm for calculating the reference level. The first thing which we should take note of is that the arithmetic mean of the maximum and minimum heights cannot be used as a reference level. On the one hand, the result will not depend on the kind of rectan gular areas selected for the analysis—S1, S2 or S3. However, the reference level will cross the columns in the middle, provided that the examined region con tains at least part of the column and part of the surface, on which it stands. But such a result has no physical meaning (Fig. 2). Alternatively, we can find a reference level as an average height of a set of points on the surface. But in this case, the result will depend on the choice of area S1, S2 or S3, on which the average height is determined (Fig. 1). It means that the result depends on the choice of a researcher. This result is not objective, and cannot be used for a quantitative analysis of the sample sur face. REQUIREMENTS TO THE METHOD OF PROCESSING Thus, we can establish the following requirements that must be satisfied by the method used to study sur face properties: (1) The adequacy of the result of applying the method to real expectation. It means that the choice of the reference level should be physically valid and, to some extent, should not contradict the common sense. For example, when we analyze the surface with sparsely distributed peaks and valleys, we must determine the reference level embracing most of the surface points. (2) The ability of visual representation. This requirement is essential for comparative anal ysis when it is necessary to select only such regions of the surface, which experience changes. In other words, a small change in the investigated area (an increase in the size or a shift of the area boundaries) should not significantly affect the value of the refer ence level. (3) Efficiency. The operating speed of the algorithm can be essen tial when it is necessary to process a large volume of data. THE CONCEPT OF THE CARTOGRAPHIC METHOD In this study we propose one of the possible variants of determining the reference level. Since the method of obtaining numerical information is based on the ideas used in cartography, then the

proposed method of obtaining quantitative information can be named “cartographic”. The paper extends the idea of using the contour lines to visual representation of the exam ined surface topography [19]. The novelty of the pro posed approach is the method used to evaluate the ref erence level, which, in our opinion, defines more ade quately the boundary of the material. Maps have been used since ancient times. The most important step in the cartography was made in the XVIII century when the concept of height above sea level was first elaborated and practically applied and the technique for imaging heights with the use of con tour lines was developed. In modern science, the iso lines are used to visualize a scalar function of two vari ables. They are the lines of equal value of any quantity. There are a large number of computer programs, which allows us to create isolines and fill the areas between the lines with a specified color. Moreover, the reference level plays an important role in geography