Through-the-sensor performance estimation of the Mondrian detection algorithm in sonar imagery

The Mondrian detection algorithm (MDA) is a powerful method for automatic object detection of targets on the sea floor using synthetic aperture sonar (SAS) images. If a target is present, this will be reflected in a highlight with an accompanying acoustic shadow downrange. In this work we focus on the core detection stage of the MDA which consists of threshold checks of mean sonar intensity of sub-patches of different sizes within the SAS image (e.g. the shadow is generally larger than the highlight). We use statistical analysis to evaluate the probability of passing and failing these tests, given the statistics of the target we want to detect (e.g. a naval mine) and the SAS image statistics (e.g. signal-to-noise levels). The highlight, shadow and background signals are modelled using gamma distributions, leading to closed-form expressions for the multiple detector tests. From these estimated probabilities for passing the corresponding detector tests, the False Positive (FP) and False Negative (FN) rates can be calculated. The utility of these estimates is two-fold: 1) They can be used to optimize the MDA's performance as a function of the threshold parameters used in the detector tests. Given a preferred balance between FPs and FNs, the best parameter values can be found to be used in future ATR scenarios; 2) Once the parameters for MDA are set, we can use the false negative estimate to quantify the remaining risk of an undetected mine being present in a given SAS image. This can be used in a performance evaluation framework to determine whether further investigation is required (i.e. more SAS images of the same area of sea bed should be captured). We illustrate the effectiveness of our proposed methodology by applying it to previously gathered SAS data.