Making measurements is the cornerstone of the empirical sciences and making measurements automatically from planetary images is what we’ve been trying to do for the past few years. In particular we’d like to measure the areas of different types of terrain on Mars and make measurements of how many features, such as dunes and craters, there are in regions of interest. Moreover, we want our measurements to be useful for science, which means we need to understand not just how to make measurements, but also how to assess the trustworthiness of those measurements.
Theories for how things work can be great, but without the evidence to corroborate them they are just ideas waiting to be tested. The best way to test a theory, in my opinion and the opinion of many others, is to test it quantitatively, i.e. to make a prediction that can be measured and then make that measurement and see how well the real world agrees. For example, there are predictions for how many impact craters should appear in particular sizes on planetary surfaces, given a particular age. This is an intuitive theory based on the observation that things fall out of the sky at some rate and the older a surface is the more things would have fallen upon it. So, if a lava flow covered over some part of a surface millions of years ago there should be fewer craters on that relatively fresh surface than the surfaces adjacent to it. This gives planetary researchers a great method for identifying the different phases over which a terrain has been modified. Sounds simple enough right? Well, it isn’t that simple, as the real world (or planet) is a noisy place.
The solar system is nowhere near as clockwork as was once thought by those ancient astronomers with romantic ideas of perfect geometric shapes etc. In truth there is a lot of randomness out there and things don’t fall out of the sky at exactly n rocks per m units of time. Instead we might ‘expect’ to see a certain number of rocks fall from outer-space over, say, a year, but we would not be surprised if a slightly fewer or greater number of rocks actually fell. So, a vital question for planetary scientists looking to identify overlapping surfaces of different ages is “how many more craters do we have to find over there to say with confidence that it is definitely older than over here?”.
The naturally occurring perturbations in cratering over time can be approximately described using a well-known statistical distribution called the Poisson distribution. The Poisson distribution describes an expected number of events likely to occur within a unit of time and has the property that the greater the expected number of events the more accurately, proportionally, predictions of those events can be made. So the first barrier to overcome in claiming that one part of a surface is older than another based upon automated crater counting is seeing differences larger than would be expected naturally through Poisson random noise.
An automated measurement from a computerised analysis of planetary images contains additional noise, above and beyond the natural randomness of the things being measured. The camera used to take the picture has a certain amount of error due to the electronics and sensors; the lighting conditions and illumination angles make craters more or less distinctive at different times of day; there are crater-like features which can be confused with craters if viewed under less than ideal conditions; there are levels of degradation and erosion of craters that makes many hard to see; and there are other problems too. The second barrier to overcome before claiming that one part of a surface is older than another is being able to observe differences larger than would be expected due to errors in the automated method’s ability to make measurements. These errors can not be described using the well understood Poisson distribution. In fact, most of our time over the past few years have been spent trying to figure out what these errors are. We have pages of mathematics describing how subtle changes due to noise in images affect our ability to measure the things we would like to measure within them.
Without a good understanding of these sources of uncertainty it would be impossible for a scientist to say with confidence that one measurement was larger than another, because an observed difference could be just due to noise. It is a good understanding of how noise effects measurements that makes the difference between a measurement tool which can be used for science and one which can not.
We are closer than ever to having an automated system for making quantitative scientific measurements from planetary images. We’re not completely there yet, but our methods have been corroborated using simulated data, including some simulated Martian terrain images. We have been able to make area measurements of different terrain types within accuracies predicted by our error theories on several types of surfaces. In the New Year we hope to be applying our methods to crater counting with the help of data kindly provided by Moon Zoo and undergraduates at Manchester’s School of Earth, Atmospheric and Environmental Sciences.