Fractal-Based Fuzzy Technique For Detection Of Active Regions From Solar Images

Fractal concepts are used to describe the irregular structures and regions of interest of solar images. The most common and easiest way to extract regions of interest from an image is through segmentation. Segmentation techniques vary from conventional edge-detection mechanism to fuzzy c-means clustering. In this study, the pixelwise local fractal dimension of solar images is computed by different techniques. This is followed by different segmentation procedures including the fuzzy-based approach, for extracting the active regions from chromospheric images and assessing their performance. These techniques have also been applied on solar images to extract active regions from Solar Heliospheric Observatory (SOHO) Extreme Ultraviolet Telescope (EIT) images.     

Fractal properties of solar magnetic fields

We study the spatial properties of solar magnetic fields using data from the Solar Vector Magnetograph of the Marshall Space Flight Center (MSFC) (FeI 5250.2 Å) and SOHO/MDI longitudinal magnetic field measurements (Ni 6767.8 Å) (96-min full-disk maps). Our study is focused on two objects: the fractal properties of sunspots and the fractal properties of the spatial magnetic field distribution of active and quiet regions considered as global structures. To study the spatial structure of sunspots, we use a well-known method of determining the fractal dimension based on an analysis of the perimeter—area relation. To analyze the fractal properties of the spatial magnetic field distribution over the solar surface, we use a technique developed by Higuchi. We have revealed the existence of three families of self-similar contours corresponding to the sunspot umbra, penumbra, and adjacent photosphere. The fractal coefficient has maxima near the umbra—penumbra and penumbra—photosphere boundaries. The fractal dependences of the longitudinal and transverse magnetic field distributions are similar, but the fractal numbers themselves for the transverse fields are larger than those for the longitudinal fields approximately by a factor of 1.5. The fractal numbers decrease with increasing mean magnetic field strength, implying that the magnetic field distribution is more regular in active regions.     

Approaching a homogeneous galaxy distribution: results from the Stromlo–APM redshift survey

Recent results from a number of redshift surveys suggest that the Universe is well described by an inhomogeneous, fractal distribution on the largest scales probed. This distribution has been found to have fractal dimension, D , approximately equal to 2.1, in contrast to a homogeneous distribution in which the dimension should approach the value 3 as the scale is increased. In this paper we demonstrate that estimates of D , based on the conditional density of galaxies, are prone to bias from several sources. These biases generally result in a smaller measured fractal dimension than the true dimension of the sample. We illustrate this behaviour in application to the Stromlo–APM redshift survey, showing that this data set in fact provides evidence for fractal dimension increasing with survey depth. On the largest scale probed, r ≈60  h ⁻¹ Mpc, we find evidence for a distribution with dimension D =2.76±0.10. A comparison between this sample and mock Stromlo–APM catalogues taken from N -body simulations (which assume a CDM cosmology) reveals a striking similarity in the behaviour of the fractal dimension. Thus we find no evidence for inhomogeneity in excess of that expected from conventional cosmological theory. We consider biases affecting future large surveys and demonstrate, using mock SDSS catalogues, that this survey will be able to measure the fractal dimension on scales at which we expect to see full turn-over to homogeneity, in an accurate and unbiased way.     

Diffusion of magnetic flux elements on a fractal geometry

Recent observations have indicated that magnetic field elements are distributed on the Sun in fractal patterns with dimension D < 2. We suggest that the transport of magnetic field elements across the solar surface should be treated as diffusion on a fractal geometry. We review a semi-analytical, theoretical treatment of fractal diffusion. Comparison with observations of small-scale motions of solar magnetic flux concentrations indicates that fractal diffusion may be taking place with dimension in the range 1.3 to 1.8. It is shown that, compared to the predictions that would be made for two-dimensional diffusion, fractal diffusion in this range would lead to an increased level of in situ flux cancellation in decaying active regions by 7% to 35%. Other work in specialities outside of solar physics may be useful in explaining solar magnetic phenomena.     

Fractal dimensions of the time variation of solar radio emission

The fractal dimensions of solar radio fluxes at 245, 410, 610, 1415, 2695, 2800, 4995, 8800, and 15400 MHz are calculated for the data period 1976–1990. The fractal dimension used here is an index to quantify the time variability of radio emission. The fractal dimensions were found to have values in the range of 1.2–2.0 for time scales of 10 days, 1–10 months, and 10 months. The lowest values were found around 3 GHz. The annual variations of fractal dimensions are small and are not in concert with the solar cycle for most of the fractal dimension at the analyzed frequencies except those for 4995 and 8800 MHz. The annual variations of the fractal dimensions are similar for the sunspot number and radio emission around 3 GHz; this implies a close relation between them. According to a simulation, larger fractal dimensions correspond to shorter e-folding time constants in the distribution of radio-source lifetimes.     

A STUDY OF MAGNETIC COMPLEXITY USING HURST'S RESCALED RANGE ANALYSIS

A fractal analysis using the classical Hurst method has been applied to artificial data, simulated sunspot magnetic field data, and to data acquired with NASA/Marshall Space Flight Center's vector magnetograph. The main goals of this study are to quantify the complexity of an active region and to determine if significant changes in complexity are associated with flare activity. We tested the analysis using three basic types of two-dimensional synthetic data: (1) data composed of gaussians with various types of superimposed features, (2) random data, and (3) synthetic sunspots created from a basic, simple configuration on which are placed increasingly smaller structures. Our results confirm that the Hurst method of analysis is sensitive to the presence of large-scale structures within a two-dimensional image. When the large-scale structure has been removed, the value of the Hurst exponent is inversely proportional to increasing complexity in the image. The Hurst exponent of magnetograph data with the large-scale structure of the sunspot removed, shows a tantalizing variation in the shear parameter five minutes prior to a flare.     

A New Algorithm for Pattern Recognition and its Application to Granulation and Limb Faculae

We have developed a new pattern-recognition algorithm based on multiple intensity clips which assures an optimal adaptation to the solar structure under study. The shapes found at higher clip levels are repeatedly extended to lower levels, thus filling more and more of the observed intensity contours. Additionally, at each intensity threshold new shapes, exceeding the level, are integrated. The number and height of the levels can be optimized making this `multiple level tracking' algorithm (MLT) superior to commonly used Fourier-based recognition techniques (FBR). The capability of MLT is demonstrated by application to the intensity structure of solar granulation near the disk center, both speckle reconstructed and not. Comparisons with Doppler maps prove its reliability. The granular pattern recognized by MLT differs essentially from that obtained with FBR. Elongated `snake-like' granules do not occur with MLT and, consequently, the perimeter-area distribution exhibits only a marginal `second branch' of higher fractal dimension, which dramatically diminishes the better the MLT pattern matches the granular structure. The final distribution obtained with optimized parameters has a single fractal dimension near 1.1, making the question of a `critical size', a `second branch', and the often discussed dimension of 4/3; highly questionable. This result is equally obtained from application of MLT to the corresponding Doppler velocity map of granular up-flows. In contrast, the pattern of down-flows contains some elongated `snake-like' structures with higher fractal dimension. We also use the new algorithm to recognize speckle-reconstructed limb faculae, which MLT separates from their granular surroundings, and compare both, granules and faculae, using large statistical samples. The facular grains near cos=57° exhibit a slightly different ellipticity than the (geometrically foreshortened) adjacent granules. However, small facular grains are more round than small granules and larger grains are more similar to granules.     

基于盲退卷积的AIA图像增强方法

太阳图像中存在各种不同尺度、亮度和结构的物理活动现象,由于太阳日冕高动态活动和传感器设备等因素的影响,太阳图像成像质量不佳。根据太阳动力学天文台(Solar Dynamic Observatory,SDO)的大气成像仪(Atmospheric Imaging Assenbly,AIA)拍摄不同波段数据结构的动态范围大、噪声大、结构相对模糊等特点,提出一种基于盲退卷积的图像增强方法。首先对图像进行去噪和降低动态范围的处理,基于图像功率谱的分布假设,从原图中估计点扩散函数(Point Spread Function,PSF)的功率谱;然后使用相位提取算法恢复点扩散函数的相位,再退卷积得出较高质量的目标图像;最后通过轮廓切片分析、功率谱分析以及点扩散函数分析对增强结果进行定量和定性评价。实验结果表明,相比现有的图像增强方法,该方法在有效增强太阳日冕图像细节结构的同时,能够复原原图中因模糊无法识别的结构。     

Are Solar Active Regions with Major Flares More Fractal, Multifractal, or Turbulent Than Others?

Multiple recent investigations of solar magnetic-field measurements have raised claims that the scale-free (fractal) or multiscale (multifractal) parameters inferred from the studied magnetograms may help assess the eruptive potential of solar active regions, or may even help predict major flaring activity stemming from these regions. We investigate these claims here, by testing three widely used scale-free and multiscale parameters, namely, the fractal dimension, the multifractal structure function and its inertial-range exponent, and the turbulent power spectrum and its power-law index, on a comprehensive data set of 370 timeseries of active-region magnetograms (17?733 magnetograms in total) observed by SOHO’s Michelson Doppler Imager (MDI) over the entire Solar Cycle 23. We find that both flaring and non-flaring active regions exhibit significant fractality, multifractality, and non-Kolmogorov turbulence but none of the three tested parameters manages to distinguish active regions with major flares from flare-quiet ones. We also find that the multiscale parameters, but not the scale-free fractal dimension, depend sensitively on the spatial resolution and perhaps the observational characteristics of the studied magnetograms. Extending previous works, we attribute the flare-forecasting inability of fractal and multifractal parameters to i)?a?widespread multiscale complexity caused by a possible underlying self-organization in turbulent solar magnetic structures, flaring and non-flaring alike, and ii)?a?lack of correlation between the fractal properties of the photosphere and overlying layers, where solar eruptions occur. However useful for understanding solar magnetism, therefore, scale-free and multiscale measures may not be optimal tools for active-region characterization in terms of eruptive ability or, ultimately, for major solar-flare prediction.     

A High-Resolution Solar Telescope Using Dark-Lens Diffractive Optics

A telescope based upon dark-lens diffractive optics would be a uniquely new instrument for solar astronomy. The image formation process in such a telescope gives an intrinsically higher resolving power and a greatly reduced image intensity compared to that of refracting or reflecting optical systems of similar lens dimension. This low image intensity would be an advantage for solar observations made using a very large imaging element. After a brief overview of the history of solar instrument development, a quantitative evaluation of the dark-lens diffracting solar telescope concept is presented, showing the potential of this imaging method to meet or even to exceed the most demanding resolution goals currently being considered for future space-borne solar telescopes.     

Steps Toward a Large-Scale Solar Image Data Analysis to Differentiate Solar Phenomena

We detail the investigation of the first application of several dissimilarity measures for large-scale solar image data analysis. Using a solar-domain-specific benchmark dataset that contains multiple types of phenomena, we analyzed combinations of image parameters with different dissimilarity measures to determine the combinations that will allow us to differentiate between the multiple solar phenomena from both intra-class and inter-class perspectives, where by class we refer to the same types of solar phenomena. We also investigate the problem of reducing data dimensionality by applying multi-dimensional scaling to the dissimilarity matrices that we produced using the previously mentioned combinations. As an early investigation into dimensionality reduction, we investigate by applying multidimensional scaling (MDS) how many MDS components are needed to maintain a good representation of our data (in a new artificial data space) and how many can be discarded to enhance our querying performance. Finally, we present a comparative analysis of several classifiers to determine the quality of the dimensionality reduction achieved with this combination of image parameters, similarity measures, and MDS.     

Analysis of TTE/BATSE time profiles for short gamma-ray bursts

The TTE/BATSE time profiles for short gamma-ray bursts (GRBs) are analyzed. A sample of 287 short GRBs and a sample of 143 background regions are studied. Bursts similar to BRBs with precursors and bursts with time profiles that are not encountered among the bursts whose time profiles were investigated by using a combination of DISCSC and PREB data. In addition, there are fewer events with single-peak time profiles among short GRBs than among long GRBs (many double and triple bursts). A fractal analysis of the TTE time profiles for short GRBs is performed. According to the TTE data, the range of fractal dimensions for short bursts is 0.80≤D≤2.25. The derived fractal-dimension distribution exhibits two peaks that correspond to a similar distribution obtained previously by reducing the DISCSC data for short GRBs (D=1.44±0.02 and D=1.90±0.03) and a third peak (D=1.05±0.03). The bursts with 〈D〉=1.90±0.03 correspond to events in whose sources the processes with long-term variations and (or) quasi-periodicity take place, while the event time profiles with a fractal dimension 〈D〉=1.05±0.03 correspond to events in whose sources many extremely short random processes take place. A more detailed analysis of a subgroup of bursts with D=1.44±0.02 shows that its fractal dimension distribution is broader than that for a group with the same (within the limits of the measurement errors) D. At least two more GRB subgroups can be distinguished in this subgroup: (1) bursts with 〈D〉=1.51±0.04; according to the TTE data, their fractal dimensions correspond to those of the background; i.e., these are events with smooth time profiles without any variability in the sources on the time scales on which the fractal dimension is analyzed; and (2) bursts with 〈D〉=1.31±0.05, whose time profiles can correspond to those of the events obtained from the fireball model with internal shock waves. We present time profiles for the events obtained by using this model. The range of fractal dimensions for the modeled time profiles is 1.213≤D≤1.400, with the fractal dimensions for such an event and for the real GRB 990208 being equal, within the error limits, for some model parameters. A study of the TTE and DISCSC fractal-dimension distributions for the background indicates that the fractal dimension distributions obtained by analyzing these two types of data can be processed simultaneously.     

Statistical properties of the spatial distribution of galaxies

The methods of determining the fractal dimension and irregularity scale in simulated galaxy catalogs and the application of these methods to the data of the 2dF and 6dF catalogs are analyzed. Correlation methods are shown to be correctly applicable to fractal structures only at the scale lengths from several average distances between the galaxies, and up to (10 ? 20)% of the radius of the largest sphere that fits completely inside the sample domain. Earlier the correlation methods were believed to be applicable up to the entire radius of the sphere and the researchers did not take the above restriction into account while finding the scale length corresponding to the transition to a uniform distribution. When an empirical formula is applied for approximating the radial distributions in the samples confined by the limiting apparent magnitude, the deviation of the true radial distribution from the approximating formula (but not the parameters of the best approximation) correlate with fractal dimension. An analysis of the 2dF catalog yields a fractal dimension of 2.20 ± 0.25 on scale lengths from 2 to 20 Mpc, whereas no conclusive estimates can be derived by applying the conditional density method for larger scales due to the inherent biases of the method. An analysis of the radial distributions of galaxies in the 2dF and 6dF catalogs revealed significant irregularities on scale lengths of up to 70 Mpc. The magnitudes and sizes of these irregularities are consistent with the fractal dimension estimate of D =2.1–2.4.     

Radiocarbon evidence of the global stochasticity of solar activity

An estimate of the dimension of the attractor of the dynamic system responsible for solar activity is obtained from the time series of carbon 14 experimental data (4300 BC to 1950 AD). According to this estimate the attractor is a fractal, in shape close to a 3-torus. The attractor's trajectories characterizing the evolution of the magnetic field exhibit irregular long-term behaviour.     

Chaotic behavior of the north-south asymmetry of sunspots?

North-south asymmetry in the distribution of sunspots was examined. Weak correlations between north-south asymmetry and sunspot number were found in several time lags. Higuchi's fractal dimension (1988) was calculated to evaluate irregularity in north-south asymmetry. The fractal dimension obtained is 1.90 ± 0.01 and this implies that the north-south asymmetry is highly irregular. The method of Sugihara and May (1990), based on the nonlinear prediction method, was used to distinguish between deterministic chaos and noise. The results do not confirm the idea that north-south asymmetry is an example of deterministic chaos.     

Multifractal Analysis Of Solar Magnetograms

As solar observational techniques improve, fine small-scale structures observed on the solar surface become more pronounced. Complex filigree structures of solar granulation, sunspots, photospheric magnetic and velocity fields cannot be described adequately by a single parameter (e.g., filling factor, fractal dimension, or power-law index). Methods which incorporate parameters that are a function of scale (multiscale methods) to describe the complexity of a field under study, should be involved. The multifractal approach offers such a possibility. In this paper the scaling of structure functions is proposed in order to analyze multifractality. Application of the approach to SOHO/MDI high-resolution magnetograms of active regions show that the structure functions differ for all active regions studied. For a given active region, the functions may maintain their shape during several hours; however, they can significantly change during a day. Flare-quiet active regions tend to possess a lower degree of multifractality than flaring active regions do. The increase in multifractality is a signal that a magnetic structure is driven to a critical state, thus gaining tangential discontinuities of various length scales.     

Turbulence In The Solar Atmosphere: Manifestations And Diagnostics Via Solar Image Processing

Intermittent magnetohydrodynamical turbulence is most likely at work in the magnetized solar atmosphere. As a result, an array of scaling and multi-scaling image-processing techniques can be used to measure the expected self-organization of solar magnetic fields. While these techniques advance our understanding of the physical system at work, it is unclear whether they can be used to predict solar eruptions, thus obtaining a practical significance for space weather. We address part of this problem by focusing on solar active regions and by investigating the usefulness of scaling and multi-scaling image-processing techniques in solar flare prediction. Since solar flares exhibit spatial and temporal intermittency, we suggest that they are the products of instabilities subject to a critical threshold in a turbulent magnetic configuration. The identification of this threshold in scaling and multi-scaling spectra would then contribute meaningfully to the prediction of solar flares. We find that the fractal dimension of solar magnetic fields and their multi-fractal spectrum of generalized correlation dimensions do not have significant predictive ability. The respective multi-fractal structure functions and their inertial-range scaling exponents, however, probably provide some statistical distinguishing features between flaring and non-flaring active regions. More importantly, the temporal evolution of the above scaling exponents in flaring active regions probably shows a distinct behavior starting a few hours prior to a flare and therefore this temporal behavior may be practically useful in flare prediction. The results of this study need to be validated by more comprehensive works over a large number of solar active regions. Sufficient statistics may also establish critical thresholds in the values of the multi-fractal structure functions and/or their scaling exponents above which a flare may be predicted with a high level of confidence. Based on the author's contributed talk “Manifestations and Diagnostics of Turbulence in the Solar Atmosphere”, presented at the Solar Image Processing Workshop II, Annapolis, Maryland, USA, 3–5 November 2004.     

Structure of the solar granulation

The structure of the solar granulation has been analysed using computer-processed images of two very high resolution (0.25) white-light pictures obtained at the Pic-du-Midi Observatory.The narrow dispersion in the distribution of granule sizes is not confirmed. On the contrary, it is found that the number of granules increases continuously toward smaller scales; this means that the solar granulation has no characteristic or mean scale. Nevertheless, the granules appear to have a critical scale of 1.37, at which drastic changes in the properties of granules occur; in particular the fractal dimension changes at the critical scale. The granules smaller than this scale could be of turbulent origin.     

Automatic Detection of Sunspots and Extractionof Their Feature Parameters

Sunspots are solar features located in active regions of the Sun, whose number is an indicator of the Sun's magnetic activity. With a substantial increase in the quantity of solar image data, the automated detection and verification of various solar features have become increasingly important for the accurate and timely forecasts of solar activity and space weather. In order to use the high time-cadence SDO/HMI data to extract the main sunspot features for forecasting solar activities, we have established an automatic detection method of sunspots based on mathematical morphology, and calculated the sunspot group area and sunspot number. By comparing our results with those obtained from the Solar Region Summary compiled by NOAA/SWPC, it is found that the sunspot group areas and sunspot numbers computed with our algorithm are in good agreement with the active region values released by SWPC, and the corresponding correlation coefficients for the sunspot group area and sunspot number are 0.77 and 0.79, respectively. By using the method of this paper, the high time-cadence feature parameters can be obtained from the HMI data to provide the timely and accurate inputs for the solar activity forecast.     

The method of a two-point conditional column density for estimating the fractal dimension of the distribution of galaxies

We suggest a new method for estimating the fractal dimension of the spatial distribution of galaxies: the method of selected cylinders. We show the capabilities of this method by constructing a two-point conditional column density for galaxies with known redshifts from the LEDA database. The fractal dimension of a sample of LEDA and EDR SDSS galaxies has been estimated to be 2.1±0.1 for cylinder lengths of 200 Mpc. A major advantage of the suggested method is that it allows scales comparable to the catalog depth to be analyzed for galaxy surveys in the form of conical sectors and small fields in the sky.