Thematic Maps of Martian Topography Generated by a Clustering

We have developed a method for autonomous construction of thematic maps of Martian terrain from digital topography. These maps show spatial distribution of topographical features and are generated by a computer algorithm that classifies pixels on the basis of topographical information they carry. We apply our technique to generate a thematic map of Tisia Valles region on Mars. Introduction. The morphology of Martian terrain is of great interest because it helps to identify physical processes responsible for the observable topography. Traditionally, the descriptive method, applied to imagery data, has been used to study and categorize Martian terrain (1). We are developing a complementary approach, wherein a thematic map of topographical features is automatically constructed by clustering computer algorithm applied to perform an unsupervised classification of pixels in a digital elevation model (DEM) of a given Martian terrain. The input data is a DEM constructed from the Mars Orbiter Laser Altimeter (MOLA) data, and the output is the thematic map, wherein each pixel is assigned a label associated with a particular topographical feature. To illustrate our technique we have constructed a thematic map of topographical features for Tisia Valles region (see Fig. 1). We use DEM with resolution of 1/128 degree in both latitude and longitude. The terrain shown in Fig. 1 is covered by a DEM with 385 rows (south to north) and 424 columns (west to east). Methods. Digital topography, as represented by a DEM, is a digitized elevation field, where space is discretized into a 2D grid and each cell (which we call a pixel) carries an elevation value. We modify a DEM, so, in addition to elevation, each pixel carries five other "bands" of information derived from the elevation field. Thus, we construct a "multiband DEM" in which each pixel carries topographical information in a form of a list of six numbers. Our approach is analogous to a concept of multispectral image where each pixel also carries a list of numbers describing intensity at number of wavelengths. The analogy to multispectral images extends to our method of analysis, we classify all pixels in a multiband DEM into a number of classes using clustering algorithm to produce thematic map of topography, whereas similar classification of pixels in multispectral image produces thematic map of composition. The six bands of topographical information are: 1) elevation, 2) elevation difference between flooded and original terrain, 3) slope in an original terrain, 4) slope in a flooded terrain, 5) contributing area in original terrain, 6) contributing area in flooded terrain. The original elevation field is "flooded" in order to make it fully drainable (2). On Mars the presence of craters and other natural pits makes flooded and original terrain different. The difference between the two terrains is the second band in multiband DEM. Pixels with high values in the second band are likely to be located inside craters. The Figure 1: Viking image of Tisia Valles. The center of this image is located at 46.13E, 11.83S. The terrain shown is approximately 215 km west to east and 192 km south to north. This is a typical Noachian Martian surface, heavily cratered and showing presence of channels. third and fourth information bands are slopes in original and flooded terrain, respectively. The slope of a given pixel is the slope between its center and the center of neighboring pixel in the direction of steepest descent. Pixels that are flooded have zero slope. Pixels at the boundary, where slope cannot be determined have values of -1. The fifth and sixth information bands are contributing areas in original and flooded terrain, respectively. Contributing area is the number of pixels (including itself) that drains through a given pixel. Pixels with high values of contributing areas are likely locations of streams and rivers. Pixels with contributing area = 1 are ridges, nothing drains through them, except themselves. Note that information in bands 2, 5, and 6 is not local, but instead depends on geographical context of a pixel. Clustering a large number of pixels is computationally expensive. Our approach sampled the data first to generate a smaller dataset as follows. The multiband DEM was divided into 10X10=100 equal sized cells. From each cell we sampled with replacement 400 pixels. The result is a dataset of 40,000 pixels. We cluster this dataset using probabilistic clustering algorithm that follows the Expectation Maximization (EM) technique (3). It groups vectors into classes by modeling each class through a probability density function. Each vector in the dataset has a probability of class membership and is assigned to the class with highest posterior probability. Euclidean metric in space of topography descriptors is used to measure the Thematic Maps of Martian Topography: R. Vilalta & T. F. Stepinski CLASS COLOR PIXELS TOPOGRAPHICAL INTERPRETATION GROUPS