AUTONOMOUS REAL-TIME DETECTION OF PLUMES AND JETS FROM MOONS AND COMETS

Some moons, comets, and other bodies are known to emit plumes or jets of material that can provide information about the body's internal composition and the forces it is experiencing. Volcanic plumes on Io result from tidal forces exerted by Jupiter (Strom et al. 1979). Saturn's moon Enceladus also responds to tidal heating by generating plumes, but its plumes are composed of icy volatiles rather than basaltic magma (Hansen et al. 2006; Hedman et al. 2009). Hansen et al. posited that these plumes originate from a deep, salty ocean inside Enceladus (Hansen et al. 2011). The possible implications for planetary science and astrobiology render these observations highly valuable, and there has been great interest throughout the scientific community (McKay et al. 2012; Quick et al. 2013). Comet 103P/Hartley (Hartley 2) emits H₂O vapor, H₂O ice particles, CO₂, CH₃OH, and HCN from different locations on its nucleus, yielding insights into its composition (A'Hearn et al. 2011; Dello Russo et al. 2011; Drahus et al. 2012; Lin et al. 2013). Knowledge of comet composition is essential for theories of the early evolution of the solar system and the path by which volatiles arrived at our planets.

However, the timing and location of plumes can be difficult to predict on the first encounter, especially for small distant targets with few prior observations. To maximize our coverage of such informative, transient phenomena, a real-time method for their detection and characterization is needed. This capability enables an agile approach to autonomous spacecraft exploration: spacecraft can independently prioritize data for downlink to Earth and plan fast follow-up observations with other instruments. Similar capabilities have been demonstrated for the EO-1 Earth orbiter (Chien et al. 2005) and for surface operations for Mars rovers (Castaño et al. 2008; Estlin et al. 2012).

This paper contributes a new method for the automatic detection of plumes and jets that does not assume that the host body is spherical. It therefore applies to irregularly shaped bodies such as asteroids and comets. We report on a study of this method applied to raw data as it is available on board the spacecraft, yielding results that are likely to be more representative of onboard performance than previous studies that used ground-processed images. We evaluated plume detection on a total of 756 Cassini images from nine flybys of Enceladus, a spherical body, and 45 EPOXI images of comet Hartley 2, which is decidedly not spherical. We found that performance on both targets was higher when using the proposed convex hull method, compared to a brightest-pixel baseline and the state of the art in ellipse-fit methods. The new convex hull method is also orders of magnitude more computationally efficient than the ellipse-fit method.

Real-time data processing algorithms running onboard spacecraft have demonstrated the potential to substantially increase science return in several planetary and terrestrial applications. In the planetary context, computer vision techniques have been successfully applied to autonomously detect dust devils, clouds, and salient surface features from imagery gathered by the Mars Exploration Rovers (Castaño et al. 2008; Estlin et al. 2012). For terrestrial applications, software running on the EO-1 spacecraft has been used to autonomously detect volcanic activity from thermal imagery (Davies et al. 2006) and to identify signatures representing distinct material species from hyperspectral imagery (Thompson et al. 2013). Similar autonomous, onboard techniques lend themselves well to detecting plumes on comets, particularly because "it is likely that comet activity changes on timescales faster than ground control's traditional command cycle and uplink interval" (Thompson et al. 2012b). Consequently, the spacecraft must respond quickly to ensure accurate targeting and hazard avoidance during proximity operations.

The earliest image-based plume detection algorithm was proposed by Wagstaff et al. (2006). That approach computes an initial circle fit to the planetary body using the Hough transform, which is subsequently refined by filtering out background pixels and pixels distant from the initial circle fit. Bright pixels adjacent to the exterior of the refined circle fit are flagged as plumes. This approach successfully detected several plumes from imagery of the Jovian moon Io captured during the Galileo and Voyager 2 missions, and Cassini imagery of Saturn's moon Enceladus.

Bue et al. (2007) extended this method to incorporate an adaptive histogram-based filter to select candidate surface pixels as well as a spherical-harmonics-based technique (Udomkesmalee et al. 1997) to locate the horizon of the planetary body. As before, bright pixels on the exterior of the horizon are flagged as plume candidates. These modifications improved both the efficiency and accuracy of the algorithm over the original circle-fit approach (Wagstaff et al. 2006) and enabled plume detection for elliptical, not just spherical, planetary bodies.

Thompson et al. (2012a) further improved these methods by using a Random Sample Consensus (RANSAC; Fischler & Bolles 1981) approach. The algorithm first applies an edge detector and then repeatedly selects five random pixels from the detected edges and computes an ellipse fit from only those pixels. Each such ellipse fit is scored according to how well it models the entire set of edge pixels. After 10,000 random trials, the best-scoring ellipse fit is used to mask out the body and the search proceeds for bright exterior (plume) pixels. This method showed strong performance on a test set of images from Enceladus and Io. It successfully detected 11 out of 17 distinct plumes in several Cassini and Voyager 2 images. Moreover, this high detection rate was accomplished without any false positives, which is a substantial improvement over the best false positive rate (≈23%) achieved by the spherical harmonics approach (Bue et al. 2007).

All of the preceding methods are unable to accommodate targets with irregular shapes, such as asteroids and comets, since they assume that the body of interest is spherical or elliptical. The earliest published plume detection technique applicable to non-elliptical bodies was proposed by Thompson et al. (2012b). This technique applies edge detection and convex hull algorithms to flag bright pixels outside of the boundary of the object of interest as plume candidates. This method successfully identified 9 of 12 images containing plumes from a data set of 27 EPOXI images of the (distinctly non-spherical) bodies of comets Tempel 1, Hartley 2, Wild 2, Ida, Dactyl, Borrelly, and Gaspra. However, these evaluations were restricted to radiometrically calibrated and post-processed JPL Photojournal images. Consequently, such results may be somewhat optimistic, as the uncalibrated imagery available in onboard settings typically has a lower signal-to-noise ratio before performing post-downlink calibration and image enhancements.

Another plume detection method that can be applied to non-spherical bodies was proposed by Lin et al. (2012). Their method takes a substantially different, non-geometric approach that computes a set of 128-dimensional descriptors via the Scale Invariant Feature Transform (SIFT; Lowe 1999) algorithm, which identifies image pixels that are most invariant to illumination, scale, rotation, noise, and small changes in viewpoint. A supervised classifier is then trained to classify the SIFT descriptors as plumes or background pixels. Their methodology yields a high detection rate (≈88%–95%) on uncalibrated Cassini and Voyager 2 imagery, with false positive counts ranging from 18 to 150, depending on the data set. Such high false positive counts suggest their method is overly permissive with respect to plume detections. However, since the authors do not provide the total number of SIFT descriptors they extracted for classification, we cannot compute the false positive rate of their algorithm.

We seek to enable the onboard detection of plume and jets in a variety of target shapes. This capability is applicable for both one-time flyby encounters and extended campaigns in orbit around a body of interest. Specifically, for each image analyzed, we aim to provide

• 1.  
  a decision about whether a plume is present or not that is sufficiently reliable for use in making selective downlink decisions; and
• 2.  
  plume localization that is sufficiently precise to enable follow-up imaging or study by another instrument.

Accuracy requirements for both detection and localization depend on the nature of the mission and the specific follow-up activities that the detection can trigger. One use of plume detection would be to monitor a dark or quiescent limb for outbursts of plume activity during an extended encounter. This could be used to prioritize data for best use of limited bandwidth, or to trigger additional image acquisitions if new anomalous events are detected. This might not require precise localization of the bright material, since the spacecraft pointing is never changed.

For greater responsiveness, plume detection could be used to inform the pointing of narrow field of view (FOV) instruments during a flyby. If all of the instruments are bore-sighted, then the follow-up imaging might require only a slight attitude adjustment. A wide range of sensors could be targeted in this way. One example is an IR slit spectrometer such as the one carried on board Deep Impact (Hampton et al. 2006). This instrument has a FOV typically coaligned with the navigation cameras, with a sensitive region approximately one pixel tall and 256 pixels wide. Pushbroom spectrometers for mapping, such as the Dawn Visible and Infrared Spectrometer (VIR), typically use a wider FOV (for the Dawn VIR, it was 366 along-slit and 0014 cross-slit). In such cases, the instrument FOV would be a horizontal rectangle that is 24 pixels tall and 6384 pixels wide, with each map pixel's instantaneous FOV subtending approximately 24 × 24 pixels in navigation camera images. Narrow angle cameras are a third possibility. The Deep Impact instrument suite included a multifilter high-resolution camera with 2-microradian pixels, so that the instrument FOV spanned 0118. This provided a spatial resolution of 1.4 m pixel⁻¹ at the closest approach of 700 km, suitable for resolving fine particles and structure in the plumes (Hampton et al. 2006). The narrow-angle camera FOV is a square window 205 pixels wide in the navigation camera images, so it would not require precise localization. Finally, UV spectrometers could be used to analyze plume composition. Such instruments also have a large FOV, projecting to tens of pixels in navigation camera images.

We propose a plume detection method inspired by an observation made in the final section of the paper by Thompson et al. (2012a). Instead of modeling the body with an ellipse, we compute the convex hull of its visible portions and then look for plume or jet activity outside of that model. This allows for planetary bodies of complex shape and enables plume detection for otherwise challenging targets such as asteroids and comets.

The convex hull is computed over the pixels identified in the edge detection step. For this to successfully enable plume detection, the plume pixels themselves must not be contained within the convex hull. Success of this approach relies on the validity of an assumption that the body has crisply defined edges while plumes or jets, if present, have diffuse edges that will not trigger the edge detector.

The plume detection algorithm takes as input a parameter, τ, that specifies the brightness detection threshold for candidate plumes. The algorithm proceeds as follows:

• 1.  
  Remove cosmic ray artifacts: Fill in any isolated bright pixels with a per-image empirically computed background value b that is the average of background pixels p_low, where

  $$\begin{equation*} p_{{\rm low}} < \bar{p} + 3 \sigma, \end{equation*}$$

  and $\bar{p}$ is the mean and σ is the standard deviation of pixel values p in the image.
• 2.  
  Segment surface from exterior: Find edges using the Canny edge detector (Canny 1986) with an edge threshold range of 0.1 to 0.25. Compute the convex hull of all detected edges. Compute the limb of the body by dilating (growing) the convex hull edges by 8 pixels, then mask this region out of the convex hull interior to yield a model of the target surface. Define the exterior as pixels outside of the convex hull, also excluding the limb.
• 3.  
  Posit a candidate plume at the brightest pixel in the exterior (non-surface, non-limb) region of the image.
• 4.  
  Define the annulus as the region within 0.5r of the limb, where r is the effective radius of the target's surface. For all targets, regardless of shape, the effective radius is defined as the square root of the area of the surface (number of pixels) divided by π. The annulus is treated the area of interest for filtering to avoid spurious detections far from the target.
• 5.  
  Filter detections: Keep the candidate plume detection unless

Detailed Matlab code for this algorithm is provided in Appendix A.

We evaluated the convex hull plume detection method on images from Enceladus, for comparison with the existing results from the RANSAC-based elliptic model approach (Thompson et al. 2012a), and on images of comet Hartley 2, which is irregularly shaped.

5.1. Enceladus Data

The Cassini mission to Saturn has made an extensive study of its moon Enceladus since the first discovery of its active water vapor plumes in 2005 (Hansen et al. 2006). The Cassini Imaging Science Subsystem (Porco et al. 2004) narrow-angle camera (ISS-NAC) provides a square FOV that is 035 across. Images are recorded by a CCD with 1024 by 1024 pixels. Each observation is obtained by looking through two selectable spectral filters. ISS-NAC images have been used extensively to study the plumes over several years of observations.

We obtained ISS-NAC observations from NASA's Planetary Data System in 12-bit raw IMG format. We restricted our analysis to narrow-angle images obtained with the two clear filters (CL1 and CL2). We collected 756 images from nine flybys of Enceladus spanning six years (2005 to 2011) and applied the cosmic-ray artifact removal method described in Section 4. We hand-labeled 28 of those images, 8 of which contain plumes (see Table 3 in Appendix B). An example image is shown in Figure 1(a). Enceladus is illuminated from the right, and the plume is clearly visible near the center of the image. The bottom portion of the image is missing (black). In Figure 1(b), our manually created labels are shown as an overlay. We labeled the target body in red and plume pixels, if present, in blue. Because it can be difficult or impossible to precisely label individual pixels, we included a thin border around the body in gray to indicate potentially ambiguous pixels that are not used for evaluation. The plume has a diffuse appearance and an ambiguous border, so we also surrounded it by a larger gray region. Black pixels are those that can be confidently said not to contain plume or target pixels. Missing data is labeled in white.

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Figure 2 shows example output from our proposed convex-hull plume detection method with the detection threshold τ set to 6.0. The detected convex hull is shown in cyan, which outlines the visible portion of the body. The brightest pixels exterior to this shape are used to compute the detection (cyan ×) which is almost exactly on top of the blue circle which indicates the centroid of the labeled plume pixels. For comparison, the proposed plume location using a simple baseline of computing the centroid of the brightest pixels in the entire image (i.e., no modeling of the target body) is shown with a magenta +. The proposed plume falls inside the body, an error that is mitigated by the convex hull approach.

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5.2. Enceladus Results

Using the 28 hand-labeled images described above, we compared the performance of the proposed convex hull method to that of a simple baseline method that identifies the brightest pixel in the image as a candidate plume. This baseline reliably detects plumes, when present, but it also has a very high false positive rate, since it always detects some pixel as the brightest one in the image. We also compared performance to that of a state-of-the-art ellipse-fit method (Thompson et al. 2012a), which is the RANSAC-based technique previously described.

Figure 3 shows the results obtained as we varied τ, the detection threshold. The left plot shows that, for τ ⩽ 4, all three methods successfully detected all of the plumes present. For higher values of τ, the convex hull method suffered a slight drop in detection rate.

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The right plot shows the false positive rate for each method. For low values of τ, the false positive rates are very high (71.4% of the detections are spurious). As τ increases, the convex hull and ellipse-fit methods progressively filter out poor detections. The bright pixel method does not use τ, so its behavior remains constant. Overall, if 100% detection is desired, and a 50% false positive rate can be tolerated, then the ellipse-fit method is best; however, in most cases we wish to keep the false positive rate low. For that objective, the convex hull method is superior, achieving a 0% false positive rate while only missing one true plume (e.g., at τ = 6.0, the true positive rate is 88%). At this detection threshold, the ellipse-fit method returns spurious detections for seven images, yielding a false positive rate of 46.7%. All of the false detections occurred in images in which Enceladus was only partially illuminated, so it appeared as a quarter crescent rather than a full disk. The elliptic model performs best when the target is approximately ellipse-shaped, which only happens when the target is ellipsoidal and its entire surface is illuminated, as viewed by the camera.

For context, Thompson et al. (2012a) reported that the ellipse-fit method, applied to a (different) data set consisting of 26 images of Enceladus, achieved one true positive and zero false positives. However, it missed 12 plumes entirely, yielding a true positive rate of 8% on that data set. Further, those images were fully post-processed versions and therefore not representative of the images that are available on board the spacecraft.

We also computed the average error of the true positive detections, measured as the Euclidean distance (in pixels) between the detection and the nearest plume pixel as specified in the manual labels (see Table 1). We found that the brightest-pixel baseline had the largest error, which is not surprising since it performs no modeling of the target and simply selects the brightest pixel(s) in the image. The ellipse-fit and convex hull methods had much lower errors across all τ values. The best error rate was achieved by the proposed convex hull method at τ = 4, but this had a false positive rate of 42.9%. At τ = 6, the convex hull method missed one detection but achieved a false positive rate of 0.0% along with a very low positional error of 2.29 pixels.

Table 1. Plume Detection Performance on the Hand-labeled Enceladus Images

Method	Number of	False Positive	Mean Positional Error
	True Positives	Rate	of Detections (in pixels)
Brightest pixel	8	71.4%	15.76
Ellipse-fit (τ = 4)	8	50.0%	2.85
Ellipse-fit (τ = 6)	8	46.7%	2.85
Convex hull (τ = 4)	8	42.9%	2.00
Convex hull (τ = 6)	7	0.0%	2.29

Download table as:  ASCIITypeset image

We also ran the convex hull and ellipse-fit plume detection methods on a larger set of ISS-NAC Enceladus observations that consists of 756 images. We simulated an operational environment in which we wish to report only the most confident detections for hypothetical follow-up (either by retargeting a spacecraft instrument for additional observations or by requesting manual review of the detection). With τ = 6, the convex hull method reported 316 detections, far more than we would want to manually review. We increased τ to 40, which yielded only 71 highly confident detections. We obtained approximately the same number of detections (60) with the ellipse-fit method by setting τ to 25. We then manually assessed each of the reported detections from each method and categorized them as shown in Table 2.

Table 2. Assessment of All Candidate Plume Detections for the Ellipse-fit and Convex Hull Methods on the Enceladus Data Set

	Ellipse-fit		Convex Hull
Total plume detections	60		71
Valid plume detections	30	(50%)	49	(69%)
False detections in poor quality images	17	(28%)	15	(21%)
False detections in full-surface images	3	(5%)	2	(3%)
False detections (other reason)	10	(17%)	5	(7%)

Note. The best values are bolded (highest for "valid plume detections," lowest for "false detections").

Download table as:  ASCIITypeset image

The ellipse fit method was correct in 50% of its detections, while the convex hull method was more reliable (69% correct). The convex hull method's new positive detections came from flybys 10, 13, and 15. This demonstrates that the method generalizes well beyond the initial study of hand-labeled images from flybys 1, 3, 7, 8, and 10.

Most of the false detections, for both methods, came from images with extremely poor quality, which suggests that a pre-analysis image filter to omit such images would be important for onboard use. A small number of detections occurred in images that were entirely spanned by the Enceladus surface; another simple filter could easily exclude these images from consideration. Another small group of images generated false detections for other reasons; these constituted 17% of the ellipse-fit detections but only 7% of the convex hull detections. One of these images is shown in Figure 4, in which the ellipse-fit and bright pixel methods both generated false detections, but the convex hull method did not. In this image, the viewing geometry is such that Enceladus is only partially illuminated by the sun, and therefore it appears as a slim crescent, which cannot be well modeled by an ellipse, as discussed earlier.

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Overall, the convex hull detections were more reliable than the ellipse-fit detections. In general we find that the target model generated by the convex hull more accurately fits the body visible in the image. The ellipse-fit method's requirement that the model be elliptic is too stringent for all cases, especially when the target is only partially illuminated. While the body may be elliptic, its appearance in the image is not.

In the next section, we evaluate these methods for harder cases in which the body itself is distinctly non-elliptic.

5.3. Comet Hartley 2 Data

The EPOXI mission flyby of comet Hartley 2 (A'Hearn et al. 2011; Klaasen et al. 2013) provides a stark contrast with Enceladus with respect to both imaging conditions and the object itself. Hartley 2 is an excellent example of a small, irregularly shaped body; it is a bilobate object 4 km along its long axis, with diverse rough and smooth terrain types on both lobes and a narrow, smooth "waist" in the center (A'Hearn et al. 2011). Such irregular, convex bodies may be common, since they have also been observed for comet Halley (Keller et al. 1986) and Borrelly (Soderblom et al. 2002). In 2010 November, the EPOXI spacecraft flew by Hartley 2, reaching a closest approach of 694 km. Our data set consists of 304 frames from the Medium Resolution Imager collected at the closest proximity to the comet (Klaasen et al. 2013). Multiple outgassing jets are visible in isolated areas along the limb and terminator (Li et al. 2013). Raw, uncalibrated images were used to simulate the data available on board.

We hand-labeled 45 of the 304 images (see Table 4 in Appendix B). We selected these 45 images from the full flyby sequence to concentrate on the central segment in which the body and plumes subtend a usefully large portion of the image. Unlike our Enceladus data set, these images were all collected from the same flyby, and plumes or jets are visible in all of the images. Localizing the plume is complicated by the fact that there are multiple sources of material.

An example Hartley 2 image is shown in Figure 5, in which the plume is labeled in blue, the comet body is labeled in red, space is labeled in black, and ambiguous areas are in gray. Bright surface features, which have been incorrectly detected as plumes by some methods, are indicated in green. Note that plumes appear from multiple locations on the comet body. An intensity stretch reveals that plume particles surround the body entirely, giving rise to the blue labeled region.

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5.4. Comet Hartley 2 Results

Figure 6(a) shows the detection performance of all three methods on this distinctly non-elliptic target. In this case, there were no false positives because all of the labeled images contained plumes. For low values of τ, all three methods detected plumes in all of the images. As τ increases, we found that the ellipse-fit and convex hull methods performed nearly the same, with a slightly higher recall (number of true positives) for the ellipse-fit method with 2 ⩽ τ < 4.

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The methods were more clearly differentiated when we examined their positional errors (Figure 6(b)). The brightest-pixel baseline had an average error of 4.16 pixels, and most of its detections were incorrectly positioned inside the comet body (bright surface features). This underscores the importance of constructing a model of the target surface so that such features can be excluded from consideration. Model-free approaches that instead rely on image features such as those generated by SIFT can more easily provide off-limb detections, but with higher false positive rates (Lin et al. 2012).

The ellipse-fit method also frequently placed the plume detection inside the comet body because it could not accurately model the shape with an ellipse (e.g., see Figure 7). In contrast, the convex hull method performed perfectly on these 45 images: every detection corresponded exactly with a plume pixel, yielding a positional error of 0. Note that Hartley 2 does not have a convex appearance in these images, so modeling it with a convex hull is also only an approximation. This is evident in the right panel of Figure 7, in which the cyan outline of the convex hull does not tightly fit the "waist" of the comet. Plumes in this area could go undetected by the convex hull algorithm. In general, more sophisticated models may be needed to more precisely capture non-convex irregularly shaped bodies.

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We found the best success with low values of τ because the plume region is so large and diffuse. Individual plume pixels do not stand out sharply from the background as they do with isolated plumes such as those on Enceladus. This is an important guideline for future investigations; different τ values will be appropriate depending on the type and extent of plumes encountered.

For these images, the assumption of an elliptic body leads to reasonable coarse detection (determining which images contain a plume), but they yield inferior localization of the plume feature itself. The convex hull method, which adapts to the shape of the body visible, provides more reliable results.

5.5. Runtime Evaluation

In this study, we proposed and evaluated a new method for plume detection for use in onboard data analysis. Methods of low computational complexity and high reliability are essential in an operating environment that is constrained in terms of computation and time (e.g., during a flyby). Successful detections of interesting phenomena enable an agile response to new scientific discoveries. Our proposed method goes beyond existing techniques that assume an elliptical host body. We calculate the convex hull of the body, then look for bright pixels indicative of ejecta near the hull. This hull accommodates bodies of arbitrary shape, an important capability for irregular bodies such as asteroids and comets.

In an evaluation on 795 images of Enceladus and 45 images of comet Hartley 2, we found that the convex hull method provides better performance than an ellipse-fit approach, in terms of plume detection and localization. A particular strength of the convex hull approach is that it provides a reliable model of the target body, enabling a custom analysis of the region very close to the edge of the body, which is an area of particular scientific interest beyond just plume detection and analysis. Further, the convex hull method is computationally efficient and well suited to operation in an onboard environment.

Prior to integration into a specific spacecraft or mission, the particular instrument resource requirements should be considered against the expected performance of the system. These resource requirements include the cost of image acquisition, storage, and later transmission of any data collected in a follow-up observing mode.

One limitation of our approach is its reliance on the construction of a model of the target body which enables the search for plume pixels near the limb of the body. If this model is inaccurate, detection reliability suffers. The approach also assumes that there is only a single target in the image. If multiple bodies are present, the convex hull will encompass both of them and all pixels between them. Further, the restriction to detections near the limb excludes detections in other regions of the image, which might be more successfully detected by a SIFT-based approach such as that of Lin et al. (2012), if false positives are acceptable.

The ability to detect and characterize plumes observed on distant moons, asteroids, and comets can add greatly to the scientific reach of remote spacecraft operations. The Rosetta mission, which will reach comet 67P/Churyumov-Gerasimenko in 2014 August, will conduct shadow mission operations in which the plume detection method described in this paper will operate in a simulated onboard environment, analyzing new data as it becomes available. Future mission concepts such as Comet Hopper, Comet Nucleus Sample Return, and Coma Rendezvous and Sample Return, all stand to benefit from the onboard plume detection capability.

We gratefully acknowledge the Planetary Data System (PDS) for providing the Cassini and Deep Impact data used in this study. We thank Kenneth Klaasen for his assistance with the Deep Impact images of comet Hartley 2. This work was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. Government sponsorship acknowledged. Copyright 2014, California Institute of Technology.

function detect_plumes_convex_hull(I, tau)

% Requires the Image Processing Toolbox

% Step 1. Remove cosmic rays and other small artifacts

% by replacing small, bright areas with the mean background value

% Find background, compute intensity mean and threshold for filling

bg_pixels  = I < (mean(I(:)) + 3 * std(I(:)));

threshold  = mean(I(bg_pixels)) + 3 * std(I(bg_pixels));

fill_value = mean(I(bg_pixels));

% Make a copy of the image and find regions that exceed the intensity threshold

M = I;

stats = regionprops(I>threshold, I, 'MeanIntensity', 'Area', 'PixelIdxList');

for i=1:numel(stats)

    if stats(i).Area < 1000  % only regions smaller than 1000 pixels

        % replace these pixels with the fill value

        M(stats(i).PixelIdxList) = fill_value;

    end

end

% Update the original image

I = M;

% Step 2. Segment the surface from the exterior

% Detect edges, compute the convex hull

E = edge(I, 'canny', [0.1, 0.25]);

${\tt [}$er,ec]  = find(E);

${\tt [}$K,A]    = convhull(er,ec);

% Identify the limb, surface, and exterior pixels

inside   = poly2mask(ec(K), er(K), size(I,1), size(I,2));

limb     = imdilate(edge(inside), strel('disk', 8), 'same');

surface  = inside &  limb;

exterior =  inside &  limb;

% Step 3. Posit a plume target (brightest exterior pixel);

${\tt [}$maxval, maxind] = max(I(:) .* exterior(:));

${\tt [}$cvxhul_plumey, cvxhul_plumex] = ind2sub(size(M),maxind);

% Step 4. Identify the annulus: region within a half-radius of the limb

radius   = sqrt(sum(sum(surface)) / pi);

maxdist  = floor(.5 * radius);

annulus  = imdilate(limb, strel('disk', maxdist), 'same');

% Step 5. Filter out detections that are too faint or too small

limbpix   = M(find(annulus));

lightlimb = limbpix(find(limbpix>0));

bg        = mean(lightlimb);

sigma     = std(lightlimb);

thresh    = bg + tau * sigma;

plumepix  = find(limbpix > thresh);

if (isempty(plumepix))

  fprintf('No detection (too faint).\n');

elseif (length(plumepix) < 5)

  fprintf('No detection (too small).\n');

else

  fprintf('Detected plume at (%.2f, %.2f)\n', cvxhul_plumex, cvxhul_plumey);

end

We hand-labeled 28 Cassini ISS-NAC images of Enceladus and 45 EPOXI MRI images of comet Hartley 2.