In the following you can find two papers on the use of image processing in astronomy.
Amelia Carolina Sparavigna, Department of Physics, Politecnico di Torino, Torino, Italy
Published at http://arxiv.org/abs/1005.4323
Homunculus Nebula is surrounding the star system Eta Carinae. The nebula is embedded within a much larger ionized hydrogen region, which is the Carina Nebula. Homunculus is believed to have been ejected in a huge outburst from Eta Carinae in 1841, so brightly to be visible from Earth. This massive explosion produced two polar lobes and an equatorial disc, moving outwards. Though Eta Carinae is quite away, approximately 7,500 light-years, it is possible to distinguish in the nebula, many structures with the size of about the diameter of our solar system. Knots, dust lanes and radial streaks appear quite clearly in many images. In this paper, we compare the imaging of Homunculus Nebula has obtained by HST and Gemini South Telescope research teams. We use some processing methods, to enhance some features of the structure, such as the color gradient, and knots and filaments in the central part of the nebula.
Space telescopes and Earth-based telescopes with adaptive optics provide a huge amount of data, that after a subsequent image processing, are submitted for scientific analysis. Using a combination of many processing techniques, often including deconvolution methods, researchers are creating very high resolution images of extended objects such as nebulae. These images reveals so many details, that the researchers can try to model the history of the nebula expansion. Even faint structures such as the bow shocks created by stellar winds can appear in these images . Let us remember that the images we can see in the scientific literature and published on the world wide web sites, are coming not only from an observation in the visible range of radiation, but are often generated with filters at several specific wavelengths. Resulting images are then composed with a superposition of signals ranging from the infrared to the ultraviolet radiation. This spanning of a large interval of wavelength has many advantages. The infrared astronomy for example, with data coming from devices equipped with infrared sensors, is able to penetrate the dusty regions of space, such as the molecular clouds in nebulae, and detect the planets revolting about our neighboring stars [2,3]. Moreover, the use of filters gives information on the temperature of the observed structures.
Here we discuss
the benefit of a further image processing of astronomical images in enhancing
specific details in the images. The processing will be
applied on images of a specific object, the Homunculus Nebula of Eta Carinae. This nebula is embedded
within a much larger ionized hydrogen region, which is the Carina Nebula. The Homunculus is
believed to have been ejected in an outburst in 1841, so brightly to be visible
from Earth. This massive explosion produced two polar lobes and an equatorial
disk, which are moving outwards from the star [4,5].
We will show processed images, from the originals by the Hubble Space Telescope
(HST) and the Gemini South Telescope in
Eta Carinae’s Homunculus (little man in Latin) is a bipolar nebula, where we see a pair of roughly spherical lobes expanding at 650 km/s, that are connected to each other near the central star ( and references therein). The equatorial plane orthogonal to the axis of the Homunculus contains ejected material expanding from the core at up to 1500 km/s. The bipolar shape of the Homunculus nebulae could be attributed to an equatorial disc composed of gas and dust, as in the case of butterfly nebulae , or due to the fact that Eta Carinae is a binary star system, as recently demonstrated . Wikipedia is also reporting a theory that two small black holes may be at the center of each lobe, one of which is consuming the star.
The Homunculus from Eta Carinae is actually one of the most studied object, as the start itself. Eta Carinae is changing its brightness, and currently is classified as a luminous blue variable binary star. Wikipedia again reports the history of Eta Carinae brightness. In April 1843, the star reached its greatest apparent brightness and it was the second brightest star in the night-time sky after Sirius. About the time of its maximum brightness, it is highly probable that Eta Carinae created the Homunculus. The approximate distance of Eta Carinae is 7,500 light-years, that is quite away: it is nevertheless possible to distinguish in the nebula many structures with the size of about the diameter of the solar system . The images show knots, lanes and radial streaks originated from the star.
Homunculus imaged by the Hubble Space Telescope
Many images of Homunculus can be seen, obtained from the Hubble Space Telescope (HST). In fact one of the early announcement about HST observations was on the resolution of individual clumps in the Homunculus, with a size of about ten times the size of the Solar System, obtained with the Wide Field and Planetary Camera. According to those observations, the nebula was considered as a thin and well defined shell of material, rather than a filled volume. Knots and filaments trace the locations of shock fronts within the nebula .
One of the best images is that
proposed by Jon Morse,
As reported in , using a combination of image processing techniques, the researchers created one among the highest resolution images of an extended object. The resulting picture is so detailed that, even the nebulas is about 7,500 light-years away, structures of about the diameter of our solar system can be distinguished. The Carina Nebula was observed in September 1995 with the Wide Field Planetary Camera 2 (WFPC2). Images were taken through red and ultraviolet filters .
Taking advantage of the spatial resolution of HST measurements, a two-dimensional map of the amount and position angle of the polarization across the Homunculus was proposed [11,12]. The data provide insight into the three-dimensional distribution of dust about the star and in the small-scale dust distribution on the lobes, which gives their cauliflower appearance.
The HST observation clearly confirms that the lobes are essentially hollow. One of the lobes is not a sphere, as it is possible to see from a "flask" edge on its surface . An excess violet light escapes along the equatorial plane between the bipolar lobes. Apparently, there is relatively little dusty debris between the lobes and most of the blue light is able to escape. The lobes, on the other hand, contain large amounts of dust which preferentially absorb blue light, causing their reddish appearance.
Fig.1.a shows the image as it is from . Applying a further image processing, the GIMP curve tool and GIMP brightness-contrast tool, we find 1.b and 1.c respectively. These two images are the best we can do with GIMP, without loosing too many details of the central region. We have a better view of the NW lobe and we see also some rays as whiskers originating from the central star. Fig.1.d has been prepared with another tool, AstroFracTool, to enhance the image edges, based on the use of the fractional gradient [13,14]. The image obtained with AstrFracTool was slightly adjusted with GIMP brightness-contrast tool. The final resolution of this image is better than 1.b and 1.c. Image 1.d shows that the NW lobe has the same cauliflower structure, with a protuberance resembling the flask shape of the SE lobe.
The reader can see that rays are originated from Eta Carinae and also from the two stars at top left corner of the image (see 1.d). Probably, among the observed long Homunculus' whiskers, there are some which are not properly represented or even artificially created, because of the point-spread function of the instrumentation.
AstroFracTool is useful to enhance the
image edges, maintaining the image visibility. Pure edge detections can be
easily obtained with other processing methods, such as the Sobel
algorithm or the recently proposed dipole algorithm [15,16]: image 1.e is
obtained from 1.a with the GIMP Sobel tool whereas
Fig.1 - 1.a shows the image as it is from ref.10. 1.b
and 1.c are obtained after using the GIMP curve and brightness-contrast tools.
These are the best results we can obtain, without loosing details of the
central region. 1.d is obtained enhancing the image edges with AstroFracTool and GIMP brightness-contrast tool. The
resolution of 1.d is better than that of
1.b and 1.c. Rays are originated from Eta Carinae and
from the two stars at the top left corner. Among Homunculus' whiskers, there
are some due to the point-spread function of the instrumentation. In the lower
part of the figure, 1.e and
Homunculus imaged by the Gemini South Telescope
Fig.2.a shows Eta Carinae as imaged by the Gemini South telescope in
The Gemini image is due to the research of John Martin and his team . According to the researchers, the image displays a feature of the nebula never directly imaged before, the Little Homunculus, which is under the visible outer layer of the great outburst, corresponding to the Homunculus. In early 2007, Eta Carinae revealed new surprising features: the ground-based observations indicated that the star was rapidly decreasing in brightness. As reported in , a chaotic variation in brightness is possibly coming from viewing the star directly along the unstable boundary between low and high latitude winds. For the study of Eta Carinae, combined researches with Gemini South and HST were used to compare the spectra in late June 2007 .
As previously done on the HST image, we can try to apply a further image processing to the Gemini image. The use of GIMP curve and brightness-contrast tools were not able to resolve details: in fact, they strongly reduce the image quality. The use of AstroFracTool instead, is able to show many details. Images 2.b and 2.c were obtained with different fractional and visibility parameters (ν=0.8, α=0.4 and ν=1.0,α=0.4, respectively, see Refs.13 and 14 for the meaning of these parameters). Note the pattern formed by the debris of explosion between the lobes in image 2.c. The shape of the NW lobe looks different from the HST image but this is simply due to the fact that the top right corner of the original image is cut.
Fig.2 - 2.a shows the Homunculus imaged by the Gemini
South Telescope in
The shape of the lobes is the same as imaged from HST and from Gemini. The “fan” on the NW lobe is again visible in 2.b after enhancement (note the slight embossment effect of the algorithm). The detail of the laced structures of lobes is actually reduced in the Gemini image: nevertheless, the SE lobe has the "flask" edge on its surface, as clearly shown by image 2.b.
In the lower part of figure, in image 2.c, it is possible to note many rings, concentric with the star, probably due to spread function of the instrumentation. HTS and Gemini instruments have two different point-spread functions and then, after the processing deconvolution methods have been applied to the relative images, the two systems give us an imaging of the central whiskers with different features, long and straight in the HST imaging, as curly hair in the case of the Gemini imaging.
We could ask ourselves whether a quantitative comparison of structures shown in HST and Gemini images is possible or not. In fact, these images are probably obtained from data recorded during quite different periods of time, and the variations in brightness of the star, which are not negligible, as well as the motion of the nebula itself, deeply affect the final result of any comparison. Moreover, each instrument has its specific function affecting the final rendering.
It is not easy then to answer positively or negatively. Here, we show just a possibility based on the use of edge detection algorithms to find reference structures. First of all, we need to enhance knots and filamentary structures in the Gemini original image. The upper part of Fig.3 is obtained using the color dipole method to enhance the edge. In this case, the method is applied on the image corresponding to the green tones. In the lower part, we report an HST image, adapted from a figure in Ref.6. The reader can observe some knots that seem to correspond in both images encircled in red. Assuming these knots as reference points, we observe that several filamentary structures seems to correspond too. Note that in Fig.3 the dipole edges of the Gemini images are compared to the structures shown by the original image from HST, not with its dipole edges.
Fig.1 and Fig.2 separately show that a further image processing can be suitable to enhance specific details in the original images. For comparing the images, we have seen through Fig.3 that the edge detection algorithm is a good starting point to develop a successful method. In spite of the quite different appearance of images obtained with different instrumentation, the use of edge enhancement reveals some specific details that can be seen as reference points. After identifying some of these reference points, it seems more easy to recognize the structures passing from one image to the other.
Fig.3 – Using the dipole algorithm on the green tones of the Gemini image, we can compare it with an image from HST (adapted from Fig.5 in Ref.6). In spite of the quite different appearance of the original images obtained with a different instrumentation, we can see many knots that seem to correspond in both images. These knots are encircled with red.
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Astronomical image processing based on fractional calculus: the AstroFracTool
by Roberto Marazzato and Amelia Carolina Sparavigna (Department of Physics, Politecnico di Torino, Torino, Italy)
published at http://arxiv.org/abs/0910.4637
The implementation of fractional differential calculations can give new possibilities for image processing tools, in particular for those that are devoted to astronomical images analysis. Fractional differentiation is able to enhance the quality of images, with interesting effects in edge detection and image restoration. Here, we propose the AstroFracTool, developed to provide a simple yet powerful enhancement tool-set for astronomical images. This tool works evaluating the fractional gradient of an image map. It can help produce an output image useful for further research and scientific purposes, such as the detection of faint objects and galaxy structures, or, in the case of planetary studies, the enhancement of surface details.
Digital images are arrays of numbers that can be manipulated by computer software. Using for instance the RGB colour model, that is, the additive colour model in which the addition of red, green and blue lights reproduces the colours, we associate to each pixel of the image three numbers ranging form 0 to 255, the colour tones. We can then prepare a code in a programming language to analyse this array of numbers and prepare an output map corresponding to our specific desired evaluations.
There are many image processing resources, most of them freely available and quite friendly to use, which can be useful in manipulating images. In spite of this abundance, the development of new methods and tools is still worthy of efforts. Here, we propose the AstroFracTool, developed to provide an enhancement tool-set for astronomical images. This tool works evaluating the fractional gradient of an image map, that is, it works by means of a fractional differentiation. Let us note that, to the authors’ knowledge, none among the free digital imaging software packages uses routines based on fractional calculus.
Fractional calculus provides derivation and integration of functions to non-integer order [1-3]. The problem is rather old, as shown by a correspondence between Leibniz and L’Hopital . The fact that we are not familiar with fractional calculus is due to its development in the field of pure mathematics . First applications were proposed in 1920. Only recently, it was approached in image processing , where it can be rather interesting for filtering and edge detection [7-9]. As proposed in  and discussed in , fractional differentiation is suitable for edge detection and for enhancing the image quality. In , the fractional differentiation was used for processing astronomical images.
The recording of astronomical images is characterised by very long exposure times, often of many hours, or on the recording a movie. The image is prepared stacking many frames of the sequence. Long time exposure photography suffers from many sources of noise, due to surface lights and flickering of atmosphere. This noise remains recorded in the resulting image. In the case that a stacking procedure is used, the level of noise increases when each image is stacked on . Removing the noise has the consequence to deplete the image of detail and then, in the final image, faint objects are fainter and edges are smoother.
As discussed in [10,11], fractional differentiation can help scan and examine an astronomical image: there, images were processed with a Fortran code running on a Unix machine. Here we propose the package AstroFracTool as the toll, suitable to improve the astronomical images, running on Windows.
AstroFracTool is based on the discrete implementation of the fractional gradient as in Ref.[12,13]. Let be a real number. The fractional gradient is defined as in Ref..
AstroFracToll evaluates the magnitude of gradient of the image map for each colour tone . For each colour, we find the maximum value on the image map. After we define the output map as in the following:
where is a parameter suitable to adjust the image contrast.
The role of parameters in the image processing is illustrated in Fig.1: note that it is possible to see more details near the edges and inside craters. In Fig.2, we see another example with a galaxy image; in this case, parameter was set to a fixed value.
The algorithm enhances image edges turning out to be useful in studying images with faint grey- or colour tone variations. Therefore, the tool reveals faint objects in the image, increasing then possibilities to discover small erratic bodies. Let us remember that fractional differentiation behaves differently from that of integer derivatives and then the results we can obtain by applying the fractional gradient are different from those obtained by means of usual image processing tools, such as GIMP, for instance. These programs in fact have filtering actions based on integer order differentiation. GIMP and other tools are suitable for a further processing of the map obtained from fractional gradient evaluation, to have an enhancement of colours, brightness and contrast
AstroFracTool has been developed to provide a simple enhancement tool-set. As previously told, its first release is based on the fractional gradient concept. The tool is working on any BMP or JPG picture of sky objects. The package runs on Windows NT/2K with a .NET package, which can be downloaded free from the MS site.
The interface is quite simple: it is possible to open a selected image and set the processing parameters (screenshot #1) and choose the image to be displayed (screenshot #2). It is possible to create an HTML report (the use of which is strongly suggested for recording purposes), as the one which is displayed at http://staff.polito.it/roberto.marazzato/pleiades (screenshot #3), editing the most relevant data of the last report.
Here we are discussing and working with the first trial version of AstroFracTool. New features will be added soon. The next one is being theoretically analysed, and will allow the user to control each separate colour channel both in the horizontal and in the vertical direction. Suggestions from astronomers, to improve the software according to the needs of the intended users, will be very useful to prepare the new versions.
AstroFracTool can be freely downloaded at the following URL: http://staff.polito.it/roberto.marazzato/AstroFract.zip .
Examples and discussions
With AstroFracToll we are able to detect the faint stars in the image background. A proposed application for the program could a use for detection of erratic bodies such as comets or asteroids by comparing images of the same region of space. In the upper part of Fig.3, (3.a) is showing the original image, (3.b) and (3.c) the maps obtained with the fractional gradient. The lower part of the figure shows the same images, processed with GIMP, with increased brightness and contrast. Note that image (3.d) is the best result that we can obtain with GIMP.
Being dependent on local tone variations, the application of a fractional gradient to an image is able to enhance galactic structures, which are depending on the density matter variation. Two examples are shown in Fig.4 and 5. AstroFracTool increases both stars and galactic structure visibility. The output image obtained by the software can be improved by increasing brightness and contrast. This further processing does not add or remove information. When brightness and contrast of the input image, which is of the original image, are changed, we often find that some information is lost. For instance, we try to increase the brightness and improve the contrast to have a better stars visibility, but we have, at the same time, that galactic details are removed. Because of processing several astronomical images, we suggest that fractional differentiation could properly enter those image-processing tools devoted to the detection of faint objects in astronomical images.
We have tested the first trial version of AstroFracTool. Future works are needed, improving the algorithm with new possibilities. As previously told, an interesting processing feature could be the separate control of colour channels; another one could be the comparison of images (addition and subtraction of images). As a matter of fact, the use of this tool by astronomers will be very useful to prepare the new versions.
Authors thank Paul Milligan of the British Astronomical Association, Isle of Man Astronomical Society (http://www.eyetotheuniverse.com/), for interesting discussions and suggestions.
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Figure 1. The figure shows the role of parameters in the image processing. The original image (a), taken by Apollo 11, shows Moon craters. Image (b-d) are the maps obtained by means of the AstroFracTool with: (b), (c) and (d) . The original image is obtained again when
Figure 2. Image (a) shows Messier 33 (Triangulum galaxy, author: Paul Milligan, http://www.eyetotheuniverse.com/). (b), (c) and (d) are the maps obtained with , and respectively. For the three images, we have set . See  for more details.
Figure 3. In the upper part of Fig.2, (a) is showing the original image, (b) and (c) the maps obtained with the fractional gradient. (b) has and (c) . The lower part of the figure shows the same images, processed with GIMP, to increase brightness and contrast. Note that image (d) is the best result that we can obtain with GIMP. The original image is published by the Nordic Optical Telescope Scientific Association, authors L.Ø. Andersen, L.Malmgren, F.R. Larsen.
Figure 4. AstroFracTool image, with a subsequente GIMP adjustment, obtained from an image of NGC1961 galaxy (Nordic Optical Telescope Scientific Association, Jyri Näränen and Kalle Torstensson).
Figure 5. AstroFracTool image, with a subsequente GIMP adjustment, obtained from an image of M94 galaxy, by Hillary Mathis, N.A.Sharp/NOAO/AURA/NSF.
You can also see a movie the Halley comet. It is obtained by means of several images developed with AstroFracTool and different values of parameters.