Automatic detection and characterization of impact craters.  Impact craters are among the most studied features on surfaces of planets. They are structures formed by collisions of meteoroids with the planetary surface. Their importance stems from the wealth of information that detailed analysis of their distributions and morphology can bring forth. Thus, surveying impact craters is an important task in planetary research. Presently, all such surveys are done manually from visual inspection of images. As a result only a small percentage of craters contained in the images we already have are actually cataloged; 42,283 craters on Mars, 8497 on the Moon, much less for Mercury and the icy satellites of outer planets. This is because building such data sets is a very laborious process, ill-suited for visual detection but well-suited for an automated technique. Although crater detection algorithms (CDAs) have been developed in the past, none was robust and practical enough to be used in planetary science research. We are pursuing two projects aimed at developing robust and practical CDAs. One focuses on detecting and characterizing craters from digital topography data and another focuses on detecting sub-km craters from high resolution images.

We have developed an original algorithm for detecting and characterizing craters from digital elevation models (DEMs). This algorithm is now in the public domain (http://cratermatic.sourceforge.net/). We have applied it to auto-detect and auto-measure almost 76,000 craters distributed over the entire surface of Mars. This data set reveals, for the first time, a geographical distribution of crater depth/diameter (d/D) ratio on the global scale. We are currently seeking further funding from NASA for applying our methodology for upcoming topographic data from the Moon and the planet Mercury. We are also developing another original algorithm for detecting of small, sub-km craters from high resolution panchromatic images. Such smaller craters are particularly useful for precise and focused dating of planetary surfaces, but, due to the shear number of such craters, their manual surveys are restricted to very small localized areas. Our automated
survey can deliver regional or even global coverage making a “million craters” catalog a reality and facilitating an objective and repeatable analysis, well beyond and above of what can be analyzed using existing catalogs. This technique can be applied to large portions of Mars, as well as to other planets and satellites in the Solar System.  Learn more (3.0MB presentation file).

Automatic mapping of valley networks  on Mars.  Martian valley networks - landscape features on Mars resembling terrestrial river networks - have long been viewed as providing the best evidence of prolonged surface water on ancient Mars. The point of scientific contention is the origin of the valley; did they form through runoff erosion signaling precipitation and a warmer Martian climate or by groundwater sapping that allows for cold and dry climate? Bulk of arguments for and against both hypothesis relied on detailed examination of selected valley segments or individual networks, but it is a global analysis that is required to provide an answer. The only global map of valleys was drawn manually in 1990s. New, higher resolution and quality data have since become available calling for a major update to a global map of the valleys. However, the high cost of mapping valleys manually on a global scale from high resolution images prevented the update from happening. We have realized that it is feasible to acquire the map of valley networks automatically by computer parsing of global topographic data. However, the standard methods for automatic delineation of valleys from digital elevation models could not be used because such methods are not capable of accurate mapping of valleys in areas characterized by nonuniform (spatially variable) dissection that is prevailing on Martian surface. We have developed a new terrain morphology-based, model-free methodology for auto-mapping the valleys. Our method works well on all surfaces including non uniformly dissected surfaces. The valley extraction code is awailable as the web application.   Learn more (1.9MB presentation file)

Automatic geomorphic mappping. Geomorphic mapping of terrestrial and planetary surfaces has been done traditionally via visual interpretation of images. This manual method is slow, labor intensive, and suffers from subjectivity. We submit that machine learning (a branch of artificial intelligence) can play a vital role in automating the process of geomorphic mapping (and other mapping as well). An auto-learning system can be employed to either fully automate the process of discovering meaningful landform classes using clustering techniques (unsupervised learning), or it can be used instead to predict the class of unlabeled landform - after an expert has manually labeled a representative sample of the landform - using classification techniques (supervised learning). We have developed a number of techniques that use unsupervised learning for exploratory mapping of Martian surface, where no prior knowledge about the surface exists and both landform types and their spatial presence need to be derived by an algorithm. Exploratory mapping finds application in expediting creation of geologic maps in planetary science context where surfaces are still being explored and landform classes are not yet defined. We have also developed techniques that use supervised learning for exploitation mapping when only the spatial presence of a priori defi ned landform classes is required. Exploitation mapping finds application in creating final geomorphic maps for terrestrial and planetary sites for which constituting landform classes are known a priori.  Learn more (2.2MB presentation file)

Association analysis-based data exploration in geoscience. We are facing an unprecedented growth of multi-attributed spatial datasets. The complexity of such datasets hides knowledge and insights that may be discovered by exploring their overall structure. Ability to effectively explore such datasets is an important issue with broad range of applications. Present approaches to this problem are based on the notion of regression. Limitation of regression is that it is model dependent and works poorly for multi-attributed datasets. We are engaged in developing a tool for exploring spatial datasets that already possess prior binary classification. In our approach we rely on discriminative patterns – associative itemsets of attributes that are found frequently in one of the two classes present in the dataset, but not in the other. A collection of all discriminative patterns provides an exhaustive set of attribute dependencies existing only in the portion of the dataset that belongs to a given class. These dependencies are interpreted as knowledge about this class that was originally hidden, but has been revealed by the contrast data mining. Our tool finds immediate applications to problems of significant societal importance including environment, biodiversity, and social science. Learn more (4.9MB poster file)

Map classification using mutual information. In order to facilitate fast and objective conversion of data into knowledge about land surface, the auto-mapping system (see above) must be supplemented by another system that analyzes and classifies the resultant maps. Without this additional step, experts would have to analyze large quantity of auto-generated maps manually, thus negating some of the benefits of rapid map generation. We are developing a methodology for comparison of categorical maps using the concept of mutual information. Collection of maps sharing common set of categories is classified on the basis of their patterns using information-theoretic definition of similarity through mutual information. Information contained in the derived similarity matrix is utilized for classification of all maps using agglomerative clustering technique. Although an ultimate application of this method is to auto-generated geomorphic maps of planetary surfaces, the method can also be applied to non-topographic categorical maps such as, for example, land use/land cover (LULC) maps. To validate my method we have applied it to a collection of 18 maps depicting land covers over major metropolitan areas in the United States. The cities are classified into groups each having a distinct land cover pattern. This method can find abroad application in all comparative studies of landscapes. One such application is to map landscape units larger than individual LULC categories - patterns of specific categories. For example, one of the cities in my collection may be divided into tiles or sectors. The collection of sectors can be classified into pattern classes interpreted as downtown, suburbia, industry, etc. Assigning unique labels/colors to these classes results in a meta-map of a city bringing out urban units of higher level than LULC categories.Learn more (1MB presentation file)

Statistical analysis of extrasolar planets' orbits. We have studied statistical similarities between orbital parameters in populations of extrasolar planets and binary stars.

Evolution of solid particles in protoplanetary disks. Solid particles in protoplanetary disks evolve differently from the gas. We have developed a model that calculates the differences between the global evolution of the gaseous and solid components of the protoplanetary disk.  Diversity of possible planetary systems was deduced from the way solids evolve under different conditions.

Modeling the evolution of the solar nebula. The solar nebula was an active and changing environment. This evolutionary aspect of the nebula has shaped the global character of the solar system. Thus, the solar system origin studies require an evolutionary model of the nebula. To address this situation we have built an analytic model of the evolving solar nebula based on the same set of physical principles used in numerical time-dependent models of protoplanetary disks. The analytic model is conceptually transparent, thus, in comparison with its numerical counterparts, it gives much deeper insights into the inner working of the evolving nebula. 

Dynamo generation of magnetic fields in accretion disks. The combined action of non-uniform rotation and helical convection in accretion disks enables an alpha-omega dynamo to generate a large-scale magnetic field. We have studied the properties of such fields and their role in dynamics of the disks.