BME researchers' mathematical model could help find water on extraterrestrial bodies

If you have ever wondered how scientists are able to find out so much about distant celestial bodies from photographs alone, we have exciting news for you: researchers at BME have shown that from a single image of a surface—be it rock, ice, or mud—featuring a fracture pattern, it is possible to determine, with a high probability, whether water played a significant role in the formation of the pattern.

Here, the emphasis is on “single image”: if we could follow the evolution of the pattern over time, such conclusions would be relatively straightforward. However, a complex mathematical model recently published in the Proceedings of the National Academy of Sciences (PNAS) allows us 

to infer the future and past states of a structure from a single snapshot.

Perhaps it goes without saying how significant such an innovation could be in space exploration: The discovery of Gábor Domokos, Krisztina Regős, and Douglas Jerolmack and Sophie Silver from the University of Pennsylvania could even have important applications in geology.

Gábor Domokos and Krisztina Regős 

"The vast majority of the information we have about celestial bodies in our Solar System is taken by satellites, sometimes in surprisingly high quality. Even when a robotic lander, such as the Curiosity rover on Mars, is available, imaging remains a primary source of information. Image analysis is therefore a key tool in space exploration, receiving substantial investment—and this is unlikely to change anytime soon. In a sense, our method also falls under image analysis, 

but rather than focusing on pixel enhancement, it is a geological-mathematical model aimed at providing a deeper understanding of the image

—specifically, using our algorithm to infer the presence of water,” Gábor Domokos explained to bme.hu.

It is clearly not feasible to deploy stationary satellites to film the same locations on planetary surfaces for years or even millennia. On the other hand, the Hungarian-American research group has developed a fictive time-lapse from a single still image, reconstructing both the past and future of a fracture pattern. Interestingly, in the case of a sufficiently mature pattern, the future can be inferred first, followed by the past—though this process requires a thorough understanding of geology.

In case anyone didn't realise, this is the surface of Venus

"Just as an artistic photograph can tell an entire story, we infer the past and future of a pattern from combinatorial averages measurable in its present state. These patterns evolve according to universal rules, and our model can be parameterised according to the material and the environment," said Gábor Domokos, university professor at the Department of Morphology and Geometric Modelling at the Faculty of Architecture and head of the HUN-REN-BME Morphodynamics Research Group.

The mathematical foundations of the model were largely established in an earlier paper by Gábor Domokos, Krisztina Regős, and Péter Bálint, Director of the Institute of Mathematics at the BME. “That research laid down the rigorous mathematical groundwork—this new paper would not have been possible without it", Gábor Domokos noted.

And this is Jupiter's moon Europa

He added that beyond its potential practical applications, the recent findings are outstanding because “mathematical models of this complexity rarely find such immediate confirmation in real-world phenomena—but this one is easily verifiable and demonstrably works.”

All that remains is image analysis and the development of a professional software tool capable of running the algorithm, which could significantly advance search for water on other celestial bodies. Fortunately, the team already has ties with NASA, or as Gábor Domokos put it, 

"we've sent instructions to the Curiosity rover from my desk".

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