Automated Principal Curve Detection in Images of Solar Coronal Loops Conclusions There are many difficult problems that arise in finding only the most prominent loop shapes in an image. Many times the shapes present themselves as many segments and the algorithm must fill in the gaps between them, while correctly not filling in the gaps going to segments that are part of other shapes. Determining which shape a segment belongs to of course requires identifying key characteristics of each segment, such as their location, orientation, and curvature direction and degree. The algorithm used here seems promising in its ability to identify only the most interesting loop shapes. It will hopefully be useful in solving this problem for astrophysicists who analyze solar images, and others who could benefit from detection of loop-shaped curves. -Input Image (after ridge detection) -Ideal Output Image (manually traced) (Gaps, noise, non-loop segments) (Gaps closed, noise cleaned, principal segments only) Problematic Cases -Multiple choices when closing gaps All the choices must be checked, but only if the resulting curve is long enough and smooth enough do you actually join together a group of segments in the final image. - Curves with both first order and second order transitions The distinct segments must be split and considered separately. Only the best ones will be kept. -Attempting and checking all the possible joins in an image is computationally complex – instead you must narrow the search space by checking to see that the resulting curve will still be smooth and continuous before trying to join yet more segments to the current shape. Specifically, check that the following three tests are passed: 1. That the closest pair of endpoints between the two segments, which would be used to join them, are not too far apart in the image. 2. That the second segment is somewhat oriented in the path of the first one (if you were to extrapolate). 3. That the resulting curve is consistent; namely, no first- order or second-order transitions are found when testing the point of junction (using the same transition tests described earlier). Motivation We aim to automate the principal loop finding process by automatically tracing curves in an image, determining which segments represent separate curve shapes, closing gaps within curves, and lastly keeping only the longest, most interesting, smoothest curve segments. Garett Ridge, Nurcan Durak, Dr. Olfa Nasraoui Knowledge Discovery and Web Mining Lab Department of Computer Engineering and Computer Science, University of Louisville {g0ridg01, nurcan.durak, Introduction Coronal loops are immense arches of hot gas on the surface of the Sun, thought to be jets of hot plasma flowing along in the alleys between the strong coronal magnetic fields. [2] These loops are essential in studies of the Coronal Heating Problem which is one of the longest standing unsolved mysteries in astrophysics. The exact properties of temperature distribution along coronal loops help in understanding and modeling the Coronal Heating Problem. Method 1. Preprocessing Perform ridgelet detection [1] followed by a curve tracing algorithm. 2. Smooth the lines in the image to reduce subtle pixel noise and jaggedness. 1. Thicken the lines in the image using a Gaussian blur, followed by binarization of the blurred areas. 2. Re-thin the lines using a morphological skeleton. 3.Retrace the segments Obtain a list of segments in the image that consist of contiguous points. 4. Split each segment based on any first-order (linear) transitions that are identified. For each point, check the angle between sections on the left and right. 5.Split each of those segments further based on any second-order (curvature) transitions. Since our focus is on loop shapes, we ultimately are only looking for curves that are smooth on the second-order (no inflection points). For each point: 1. Consider a segment that straddles it 2. Check that the angle difference between the first two quartiles of that segment matches the angle difference between the final two. 6. Find the optimal way to join segments together to produce the longest, smoothest second- order curves. Do this by performing a depth-first-search through all possible combinations of segments, checking each combination along the way to verify that the segments chosen can combine to form a smooth curve. Throw out the short noisy segments if they didn’t join up with other segments as part of a better curve. 7. Close the gaps within each curve by drawing a Bresenham line [4] across the gaps and then using the aforementioned smoothing function on each curve shape to make the transition subtle. References [1] B. Inhester, L. Feng and T. Wiegelmann: "Segementation of Loops from Coronal EUV Images", Solar Physics, Volume 248, Number 2/April, 2008 [2] Nurcan Durak, Olfa Nasraoui: "Feature Exploration for Mining Coronal Loops from Solar Images". ICTAI (1) 2008: [3] NASA EIT Catalog : [4] Jack E. Bresenham, "Algorithm for computer control of a digital plotter", IBM Systems Journal, Vol. 4, No.1, January 1965, pp SOFTWARE USED - Matlab 2003 Problem NASA has thousands of solar images in a database [3] that has been growing since Astrophysicists currently waste a lot of time manually doing the following: Downloading images from NASA solar image databases Looking at every solar image to detect which ones have loops Determining the exact position of coronal loops. This problem is made complex by missing parts (gaps) in the curve segments, by erroneous junctions between unrelated segments, by jaggedness in segments, and by other forms of noise and clutter. Only the principal coronal loops are desired from this cluttered image.