Application of Support Vector Regression to Derive Crater Depth/Diameter From Satellite Images

Through the study of impact crater shapes, one can draw important conclusions about the nature and evolution of planetary surfaces [e.g., 1-4].In particular, studying the depth (d) to diameter (D)ratio (d/D) of a population of impact craters, in combination with crater count statistics, can yield valuable insights regarding rates of erosion and burial[5]. Motivated by the great abundance of available planetary surface image data, the goal of this project is to develop an efficient way to estimate d/D from satellite images of impact craters for which stereo information is not available [6]. We set out to develop and train a machine learning algorithm to extract d/D from a dataset of synthetic impact crater images for which model d/D is known. The applications of machine learning to planetary science are numerous and diverse [7], including automatic planetary surface mapping [8] and the detection of impact craters [9]. Our algorithm makes use of Support Vector Regression (SVR), which is a type of Support Vector Machine (SVM) [10, 11].SVMs are a branch of supervised machine learning valued for their straightforward implementation and versatility in solving both classification and regression problems. In regression analysis, an SVR algorithm produces a hyperplane function to fit the training data points, as well as an ε-tube that surrounds the hyperplane. Tunable hyperparameters include the width of the ε-tube (ε) and the amount an algorithm is penalized for points which fall outside the ε-tube.