prompt.txt

A vital component of analyzing brain coral terrain is precisely quantifying the spatial distribution and density of rocks, which can provide insights into potential rock sorting processes involved in its formation. To achieve this, we implement  an automated rock detection algorithm that identifies boulders in HiRISE images based on their shadows. By leveraging machine learning to identify and segment the rock shadows, the algorithm derives rock sizes and abundances. It generates spatial density maps revealing variations in boulder populations across brain coral regions. The technique can resolve rocks down to ~0.7 m diameter using HiRISE's 30 cm/pixel scale. The rock distribution maps enable testing hypotheses related to cryoturbation and freeze-thaw, as processes like terrestrial stone circles should concentrate rocks on ridges. Integrating the boulder density data with morphology, thermal inertia, crater statistics, and other measurements will allow robust assessment of competing brain coral formation hypotheses. The rock detection results will be a vital dataset for interpreting these enigmatic landforms.
- State of the art machine learning algorithms which enable estimating the rock size and abundance.
- We built a tool to create training data so the algorithm can quickly improve over time

Here are some improvements made over existing similar software by using machine learning:
-Most previous rock detection algorithms rely on manual feature engineering and thresholding rather than machine 
learning. Our approach uses modern deep convolutional neural networks which automatically learn optimal rock 
features from the data.
-Machine learning allows our model to improve over time as more labelled data becomes available, while traditional 
algorithms remain static. The neural network can continue to enhance rock detection accuracy.
-Deep learning techniques like transfer learning allow us to fine-tune powerful pre-trained models rather than training a 
model from scratch, improving results.
-Our system can detect smaller rocks than prior methods by leveraging HiRISE's 30 cm/pixel resolution, while traditional
algorithms are limited to larger boulders.
-The neural network model intrinsically handles variations in illumination, contrast, and surface materials better than 
thresholding techniques.
-Our end-to-end pipeline from detection to density mapping enables new holistic rock distribution analysis rather than just count rocks.

The rock detection algorithm helps solve the problem of quantifying rock distributions across brain coral terrain in order 
to test hypotheses about how these landforms formed. Specifically:
- Brain coral has similarities to sorted stone circles formed by freeze-thaw on Earth, which concentrate rocks on the 
surface. 
- Determining if brain coral has higher rock densities on ridges and knobs could indicate freeze-thaw origins.
- But manually counting rocks in images is impractical over large areas.
- The algorithm automates rock detection using shadow measurements.
- It produces spatial density maps of rock populations. 
- This enables analyzing variations across brain coral regions.
- Higher densities on ridges would support freeze-thaw processes.
- Lower and uniform densities may point to other formation mechanisms.
- Integrated with other datasets, the rock maps can test formation hypotheses.
- Saving significant human effort, the algorithm facilitates new analyses to decipher the genesis of brain coral terrain.
So in summary, the rock detection algorithm provides an efficient way to map and quantify boulder distributions so we can evaluate if brain coral terrain formed via freeze-thaw cycles that concentrated surface rocks like stone circles on Earth. This crucial information will help resolve the origin of these rare and geologically young Martian landforms.

Quantifying rock distributions in rare brain coral terrain on Mars can provide insights into its formation, but manually mapping boulders is impractical over large areas. We present a methodology to automatically detect surface rocks and generate spatial density maps using random forest classification of HiRISE images. The algorithm identifies pixel-scale rock shadows based on shadow darkness, proximity values, and color channels. Shadow shape fitting then derives rock sizes for abundance mapping. This enables resolving ~1.5 m diameter boulders across brain coral regions. We assess detection accuracy using manually labeled validation data. The rock density maps reveal variations indicative of potential sorting processes during formation. Increased concentrations on ridges would support freeze-thaw origins akin to stone circles on Earth. Integrating morphology, thermal inertia and other data, the rock distribution measurements will help test hypotheses for the genesis of brain coral. By rapidly quantifying rock populations, the technique facilitates new constraints on formation mechanisms for these rare, astrobiologically relevant Martian landforms.

Yes, this work relates to current and future NASA planetary exploration goals and technologies in several ways that bring value to space activities:
- Demonstrates advanced computer vision techniques to rapidly analyze massive planetary image datasets, which can 
maximize scientific return from current and future missions.
- Automated mapping of landforms like brain coral helps identify regions of interest for understanding planetary 
habitability and climate, aligning with high-level NASA objectives.
- The pipeline architecture could be adapted to map other geologic features relevant to NASA science campaigns, like 
recurring slope lineae, deltas, gullies, etc.
- Showcases AI/ML techniques to accelerate analysis tasks unfeasible manually, consistent with NASA's increasing 
focus in this area.
- Operationally, the approach helps prioritize data downlink and targeting for orbital and landed assets based on 
science value.
- Could potentially aid future commercial/reimbursable applications like base siting, ISRU prospecting, and infrastructure planning for planetary settlement. 
In summary, by demonstrating an innovative application of AI to enhance planetary mapping and surface characterization, this work strongly aligns with and brings value to NASA's strategic goals for solar system exploration and utilization. The technique supports both scientific and future human-exploration objectives on Mars and other bodies.

Brain coral terrain – so named for its resemblance to the human brain or aquatic brain coral – is a distinctive surface texture found across concentric crater fill (CCF), lobate debris apron (LDA), and lineated valley fill (LVF) terrains.

Impact craters on brain coral terrain are rare, and many impact craters observed on brain coral terrain are heavily modified, indicating that these surfaces are young. Previous efforts [e.g., Levy (2009), Malin M. C. & Edgett K. S., (2001), Mangold N. (2003)] to date these surfaces have provided an important groundwork in understanding brain coral terrain but have been hindered by several limitations. Individual brain coral terrain areas are small, and ages derived from crater statistics on small areas are subject to high uncertainties. Furthermore, small count areas require the use of small craters in order to have enough data points for a statistically significant sample. The identification of these smaller fresh craters is challenging due to obscuration by similar-scale brain coral terrain cells, particularly when using data such as MOC, where a 50 m crater can be only several pixels across. The wide availability of high-resolution images from the HiRISE camera and automated methods of landform identification serves as a compelling motivation for further investigation.

Methods: We combine geomorphic mapping and analyses of impact crater size frequency distributions (CSFDs) to interpret the surface ages and resurfacing history of martian brain coral terrains. We began with 456 HiRISE images that a deep learning model identified as containing brain coral terrain [Pearson et al. (2024)]. We visually inspected each of these HiRISE images with potential detections in addition to any adjacent HiRISE images which the detector did not identify but were thought to have brain coral terrain based on their proximity with the detected images.

Although HiRISE resolution permits the identification of meter-scale craters, we only included those > 50 m diameter because smaller craters are difficult to identify against the similar scale brain coral terrain cells. We omitted obvious secondary craters based on clustering and orientation patterns. We classified craters as being either fresh, moderately degraded, or heavily degraded. This scale is inherently qualitative, so to limit the amount of subjectivity we exported images of each crater to view and classify the degradation scale outside of the GIS environment. Each crater was classified three separate times.

Crater data were imported into CraterStats 2 [Michael G. G. & Neukum G. (2010)] for analysis. We used the assigned degradation state to group the craters into three crater populations: (1) fresh craters only, (2) fresh and moderately degraded craters, and (3) fresh, moderately degraded, and heavily degraded craters (Fig. 1). Interpreted ages for each region were derived from the segments of the plots that best matched the [Michael, G.G. (2013) Icarus 226, 885–890] production function using pseudo-log binned reverse differential histograms. Absolute model ages were derived using [Hartmann W. K. & Daubar I. J. (2016). Meteoritics & Planet. Sci. 52, 493–510] iteration of the [Hartmann W. K. (2005) Icarus 174, 294–320] chronology function. We use the Poisson probability analysis approach of [Michael, G. G. et al. (2016) Icarus 277, 279–285], which yields an exact mathematical solution to the model crater chronology function according to the observed CSFD regardless of the bin size, which is useful when deriving statistics for surfaces with a small number of impact craters.

The total mapped brain coral terrain covers a total area of 6,602 km2 across parts of the northern lowlands and hemispheric dichotomy (Fig. 2). We focus our attention on the Ismenius Lacus (including Protonilus and Deuteronilus Mensae) as this region contains the largest area of mapped brain coral terrain (5,683 km2). 

Fresh impact craters on brain coral terrains on all three terrain types in Ismenius Lacus exhibit fits to the production function at ~3 Ma and ~25 Ma (Fig. 3). The multiple fits are indicative of partial resurfacing, whereby some process has removed craters smaller than ~100 m diameter until ~3 Ma, when craters began to reaccumulate in accordance with the production function. The ~3 Ma fit is not at a shallower slope than the production function, which indicates that this resurfacing process is not ongoing on modern Mars.

Of particular interest is the same ~25 Ma age for fresh craters >~ 100 m diameter and both fresh and moderately degraded craters less than ~100 m diameter on LDA and CCF (Fig. 3a,b). This similarity suggests that some process during the past 25 Ma preferentially moderately degraded craters smaller than ~100 m diameter. The ~3 Ma age is that this value closely corresponds with a shift in Mars' mean obliquity as modeled by [Laskar J. et al., (2004) Icarus 170, 343–364]. Modeling results from Laskar et al. (2004) suggest that Mars' mean obliquity shifted from 35° to 25° at around 3 to 5 Ma. Ice-related landforms would undergo higher rates of resurfacing during these higher obliquity periods.

One possible degradation process that could explain the observed data is deflation of the underlying surface, which is believed to have occurred over the past tens to hundreds of Myr [Levy (2010), Morgan G. A. et al. (2009) Icarus 202, 22–38]. Although the ~25 Ma fit of fresh and moderately degraded craters on LDA in Ismenius Lacus closely matches the slope of the production function, there is a slight decrease in slope for craters <70 m, suggesting that the surface may have deflated enough to erase craters up to about this size from the surface. Assuming a 1:5 depth to diameter ratio, this suggests that the surface has undergone ~10 meters of deflation since ~25 Ma.

Brain coral terrains may form during landform deflation, possibly from aeolian infill of polygon edges [Levy (2009), Malin & Edgett (2001)] or sorting of surficial boulders [Noe Dobrea et al.]. 

The accumulation of small craters along the ~3 Ma isochron indicates that brain terrain has been largely dormant over the past several million years. Alternatively, brain coral terrain may have been active over the past ~3 Ma but does not modify the surface sufficiently rapidly to modify craters >50 m over ~3 Myr timescales. Future work into the thermophysical properties at the location of brain terrain under different obliquity regimes may provide more insight into whether brain coral terrain could actively form from stone circles over the past 3 Myr, perhaps modulated by Mars ~100 kyr ±5° obliquity cycles.

Here's the table digitized into markdown format:

| Observable | H1. Sublimation lag | H2. Topographic inversion | H3. Stone sorting mechanisms |
|------------|---------------------|---------------------------|------------------------------|
| Correlation to regions of transient melting* | () None expected | () None expected | () Yes |
| Correlation to local topography | (-) Asymmetry in pole vs. equator-facing slopes | (-) None expected | (+) At base of local topography |
| Mean cell-size vs. latitude* | () Potentially | () Yes | () Yes |
| Decameter Slopes | (-) Unconstrained | (-) Unconstrained | (+) ≤ 3° |
| Slopes of ridges | (+) ≤ angle of repose | (+) ≤ angle of repose | (+) ≤ angle of repose |
| Thermal inertia | Low – dust must protect ice from sublimation | Low – dust must protect ice from sublimation | Intermediate – rocky ridges, soil-rich cell-interiors |
| Rock distribution | (-) Heterogeneous, potentially higher in troughs due to rolling of undermined stones downhill | (+) Rocks and boulders concentrate on ridges. | (+) 1) Rock Concentration: closed-cell > open-cell 2) Rocks and boulders concentrate on ridges and mesas. |

*The narrow latitudinal band in which these terrains are found prevents testing, but suggests a strong climatological control.

Note: Colors represent confirmation (+) or refutation (-) of hypothesis. Empty boxes () indicate ambiguous results. White boxes indicate hypotheses have not yet been tested or are untestable.
The slides discuss the potential for the formation of sorted stone circles on Mars, particularly in the mid-latitude regions. These regions exhibit evidence of glacial and periglacial processes in recent geological history, with many young geomorphic features resembling terrestrial periglacial landforms, such as fractured mounds, boulder rings, and "brain coral terrain" (Mangold 2005; Burr et al., 2009; Dundas and McEwen, 2010; Soare et al., 2013; Noe Dobrea et al., 2007; Balme et al., 2009; Gallagher et al., 2011).

The "brain coral terrain" consists of circular and elongate knobs and mesas that transition into closed-form ridges, bearing photogeological similarities to terrestrial sorted stone circles. These features are found in flat terrains (< 3º), typically in topographic lows, and are associated with lineated valley fill (LVF) and concentric crater fill (CCF) (Squyres 1978; Malin and Edgett 2000; Carr 2001). The terrains are relatively young (10-100 Myr) and geologically active (Levy et al., 2009).

Several formation hypotheses are discussed, including sublimation lag (Malin and Edgett 2000; Mangold, 2003), sublimation/sand wedging (Levy et al., 2009), and sorted stone circles (Noe Dobrea et al., 2007). The sorted stone circle hypothesis suggests that soil plugs form and intrude upper layers due to differential frost heave, mobilizing stones to the edges of plugs to form stone circles.

The discovery of vast concentrations of "open-cell" circles in the Arcadia region, not associated with lineated valley fill, concentric crater fill, or lobate debris aprons, is presented. The morphology and morphometry of these features appear to be similar on different sides of Mars. Preliminary results indicate that the geological conditions for the formation of sorted stone circles are met, with the terrains being young (around 10 Ma based on "fresh" craters and several 10 of Ma based on all craters) and constrained to slopes < 3º in the vicinity of higher relief-forms.

The implications of identifying such broad regions of freeze-thaw on Mars are significant from an astrobiological perspective, as locations that experience periodic thawing of near-surface ice are attractive targets to search for extant life.

One of the key drivers of the Mars Exploration Program is the search for evidence of past or present life, and locations that experience periodic thawing of near-surface ice are attractive targets to search for extant life.  Although liquid water is not stable on present day Mars at or near the martian surface, modeling studies of the atmosphere and climate system suggest recent and periodic occurrence of conditions conducive to transient thawing [Costard et al. (2002), Science 295; Mischna and Richardson (2005), Geophys res let, 32(3); Kreslavsky et al. (2008), Planet Space Sci, 56(2)].
Multiple intriguing classes of young geomorphic features that resemble terrestrial periglacial landforms have been identified on Mars [e.g., Mangold (2005), Icarus 174; Burr et al. (2009), Planetary and Space Science, 57(5); Dundas and McEwen (2010), Icarus 205; Soare et al. (2013), Icarus, 225(2); Mellon et al. (2008), J. Geophys. Res, 113; Noe Dobrea et al. (2007), 7th Int Conf Mars, p.3358; Balme et al. (2009), Icarus 200; Gallagher et al. (2011), Icarus 211].  Of these, a terrain type known as Brain Terrain is particularly interesting because it bears morphological similarity to terrestrial sorted stone circles on Earth (Figure 1) [Noe Dobrea et al. (2007), 7th Int Conf Mars, p.3358].  On Earth, sorted stone circles develop via freeze-thaw processes [e.g., Kessler and Werner (2003), Science, 299].  However, while their morphologies are similar, similarity in form does not necessarily imply the same underlying process.  It is therefore important to compare available hypotheses by performing a careful and detailed study of this terrain.
The goal of this study is to assess whether "brain coral" is the martian equivalent of terrestrial sorted stone circles.

We consider the multiple hypotheses presented in the literature and identify a set of characteristics that can be tested for using available data (Table 1):
Hypothesis 1. Sublimation lag [Mangold, N. (2003) J. Geophys. Res., VOL. 108, NO. E4]: complex patterns of small pits and buttes result from the sublimation of ice from a dust matrix cemented by interstitial ice, where the sublimation of the ice is especially initiated and accelerated by subsurface heterogeneities like fractures.
Hypothesis 2. Topographic inversion of thermal contraction polygons [Levy et al. (2009) Icarus 202]: polygonally fractured terrain forms from thermal contraction and expansion cycles of the ground.  Ice/Sand/rock wedges form at the fractures, and subsequent sublimation of the polygons' interiors and protection of the wedge by a lag deposit results in the formation of closed-cell brain coral.  Further sublimation of the ice from the wedge creates narrow ridges, which constitute the ridges of open-cell brain coral.
Hypothesis 3. Rock sorting processes akin to sorted stone circles [Noe Dobrea et al. (2007), 7th Int Conf Mars, p.3358]: Cryoturbation caused by cyclic ground heave separates rocks from soil and causes the soil to convect in well-defined cells.  At low stone-to-soil ratios, the sorting process will generate individual rock piles.  As the stone concentration increases, these stone piles merge to form labyrinthine and closed-form ridges, and at higher rock concentrations these form mesas. (e.g., Kessler et al., 2003).

On Earth, the formation of sorted stone circles is constrained to areas known to exhibit freeze thaw cycles, independent of geology or surface composition although topographically higher terrains nearby provide hydraulic head to maintain groundwater at the sites of the stone circle formation.  Their formation is limited to terrains with slopes <3º [Mangold (2005), Icarus 174], above which they devolve into stone lines.  The sorted stone circles of western Spitsbergen, Norway, exhibit the greatest morphological similarity to the open-form cells identified on Mars.

Global distribution: We applied convolutional neural networks to the MRO/HiRISE dataset in order to detect images containing "Brain Coral" [Pearson et al. 2024].  Figure 2 shows the extent of our survey highlighting the positive detections in green (187), possible detections in orange (243), and negative detections in red (55886).  We found that brain coral terrain is dominantly found in a narrow range of latitudes and elevations, with the largest fraction occurring around 40°N  at the dichotomy boundary in the northern hemisphere (Fig. 2).  Comparison to local slopes (based on HiRISE-derived DEMs) show that these form dominantly on slopes <a few degrees.
Age: Using the large number of HiRISE images with positive detections, we derived crater size-frequency distributions and found them to exhibit fits to the production function at ~3 Ma for craters smaller than ~100m and ~25 Ma for larger ones  (Morgan et al. in prep.). The multiple fits indicate partial resurfacing until ~3 Ma, when craters < 100m began to reaccumulate in accordance with the production function.
Rock distribution: We developed an automated algorithm for measuring the frequency and size distribution of boulders on Mars using data from the HiRISE camera on the MRO spacecraft [Pearson et al. 2024]. The algorithm uses a random forest ensemble trained on around 4,000 hand-labeled training samples to detect and segment rocks in HiRISE images. Building on this work, we have integrated the rock detection algorithm with segmentation masks, such as those delineating the "brain coral" terrain [Gallagher et al. (2011), Icarus 211]. This allows for comparative studies of rock distributions inside and outside these geologically interesting regions.  Our ongoing analyses suggest that rocks are preferentially concentrated on the ridges and their escarpments.

The relatively narrow band of latitudes and elevations in which brain coral terrain is found suggests that  climate may be a driving mechanism  Climate models suggest that above-freezing temperatures can occur at the mid to high latitudes in the near surface during periods of high obliquity [Costard et al. (2002), Science 295; Kreslavsky et al. (2008), Planet Space Sci, 56(2)] or during periods in which periapsis coincides with northern summer [Mischna and Richardson (2005), Geophys res let, 32(3)].  Crater counting ages show in turn show that this terrain preferentially evolved during higher obliquity periods.  This latitudinal/elevation band could represent sweet spot between the lower-lying higher latitudes that may never see sufficient thawing and the higher elevation and lower latitude terrains where the ice sublimates instead.  The topographic setting and range of slopes on which this terrain occur lends further credence to the rock sorting hypothesis.

One of the main objectives of the Mars Exploration Program is to search for evidence of past or current life on the planet. To achieve this, Mars exploration has been focusing on regions that may have liquid water. Certain areas may have seen cycles of ice thawing in the relatively recent past in response to periodic changes in the obliquity of Mars. In our study, we employ the use of convolutional neural networks to identify specific areas of the Martian surface that have a feature referred to as "Brain Terrain". This terrain type is similar in morphology to "sorted stone circles" found on Earth, which may indicate that it formed due to cycles of freezing and thawing. Determining the spatial distribution of 
rocks is important for understanding the geological processes involved in the formation of brain terrain. Therefore, we also designed a machine-learning algorithm to help map boulders automatically.

Brain coral is a term used to describe the texture of a specific type of Martian terrain, which is characterized by stippled, labyrinthine ridges and are found primarily in mid-latitudes. They are often associated with lineated valley fill (LVF) and concentric crater fill (CCF) (e.g., 
Squyres, 1978; Malin and Edgett, 2001; Carr, 2001). In arctic regions on Earth, "sorted stone circles" form because of rock-bearing and water-rich soil layers undergoing cycles of expansion and contraction in response to periodic freezing and thawing of the soil (Taber, 1929; Taber, 1930; Williams et al., 1989). These cycles result in rock and soil separation which in turn leads to pattern formation (e.g. Konrad and Morgenstern, 1980; Werner, 1999; Kessler and Werner, 2003). However, even though brain coral on Mars and sorted stone circles on Earth have similar appearances, it does not necessarily mean that the same processes formed them. There are multiple young geomorphic features on Mars that suggest thawing occurred in the recent past and may still be ongoing, but there is ongoing controversy about it (Mangold, 2003; Milliken et al., 2003; Costard et al., 2002; Kreslavsky et al., 2008; McEwen et al., 2011). As such, it is crucial to compare existing hypotheses and conduct a thorough examination of this terrain to better understand its formation.

Determining the spatial distribution of rocks is important for understanding the geological processes involved in the formation of brain terrain. A key characteristic of stone circle formation on Earth is the concentration of rocks 
at the surface, separated from soil (Kessler and Werner, 2003). We are interested in spatial patterns since rock sorting should concentrate rocks on ridges and knobs. Freeze-thaw may not move very large rocks although, meter-scale clasts do form stone circles on Earth (Gallagher et al., 2011). If brain terrain formed similarly, we would expect increased rock abundance on ridges and in the transition from open to closed terrain. Where HiRISE DEMs exist, we can compare rock locations to ridges. Quantifying rock distribution will help test hypotheses related to possible cryoturbation and freeze-thaw processes in brain terrain formation. A future study by Pearson et al. will focus on boulder counting in brain terrain regions using machine learning techniques applied to HiRISE images.

Our methodology employs an automated algorithm trained on approximately 4,000 hand-labeled boulders using a random forest ensemble to detect and segment rocks in HiRISE images. The algorithm was integrated with segmentation masks to enable comparative studies of rock distributions inside and outside geologically interesting regions, such as "Brain Terrain". We derived cumulative distribution functions (CDFs) of size vs. frequency from the detected rocks to investigate underlying geological processes shaping the rock populations and estimated relative elevation by combining rock masks with digital elevation 
models (DEMs) derived from HiRISE stereo imagery. The algorithm also allowed for subtraction of a local plane fit to better isolate elevation variations associated with individual rocks and calculated gradient distributions from DEM data to further explore relationships between rock distributions and topography.

Results and Discussion: Our recent work focused on developing an automated algorithm for measuring the frequency and size distribution of boulders on Mars using data from the HiRISE camera on the MRO spacecraft. The algorithm uses a 
random forest ensemble trained on around 4,000 hand-labeled training samples to detect and segment rocks in HiRISE images. Building on this work, we have integrated the rock detection algorithm with segmentation masks, such as those delineating the "brain coral" terrain on Mars (Pearson et al., 2024). This allows for comparative studies of rock distributions inside and outside these geologically interesting regions. If the rock distributions and sizes are consistent with processes like freeze/thaw cycles and cryoturbation, as observed for patterned ground features on Earth, it would provide important evidence for the role of such geomorphic processes in shaping the Martian surface.

Our future work will focus on mapping rock distributions in HiRISE images using shadow measurements to derive size and abundance. This will help test hypotheses related to possible cryoturbation and freeze/thaw processes in brain terrain formation. Integrating multiple remote sensing datasets, such as high-resolution imagery, crater counts, thermal data, and rock counting can provide robust tests of the competing brain terrain formation hypotheses. This, in turn, can reveal valuable insights into Mars' recent climate, geology, and potential habitability, which have important implications for future landing site selection and the study of these rare Martian landforms.