Fast and exact computation of moments using discrete Green's theorem

Green's theorem evaluates a double integral over the region of an object by a simple integration along the boundary of the object. It has been used in moment computation since the shape of a binary object is totally determined by its boundary. By using a discrete analogue of Green's theorem, we present a new algorithm for fast computation of geometric moments. The algorithm is faster than previous methods, and gives exact results. The importance of exact computation is discussed by examining the invariance of Hu's moments. A fast method for computing moments of regions in grey level image, using discrete Green's theorem, is also presented

Properties of sunspots in cycle 23: I. Dependence of brightness on sunspot size and cycle phase

In this paper we investigate the dependence of umbral core brightness, as well as the mean umbral and penumbral brightness on the phase of the solar cycle and on the size of the sunspot. Albregtsen & Maltby (1978) reported an increase in umbral core brightness from the early to the late phase of solar cycle from the analysis of 13 sunspots which cover solar cycles 20 and 21. Here we revisit this topic by analysing continuum images of more than 160 sunspots observed by the MDI instrument on board the SOHO spacecraft for the period between 1998 March to 2004 March, i.e. a sizable part of solar cycle 23. The advantage of this data set is its homogeneity, with no seeing fluctuations. A careful stray light correction, which is validated using the Mercury transit of 7th May, 2003, is carried out before the umbral and penumbral intensities are determined. The influence of the Zeeman splitting of the nearby NiI spectral line on the measured 'continuum' intensity is also taken into account. We did not observe any significant variation in umbral core, mean umbral and mean penumbral intensities with solar cycle, which is in contrast to earlier findings for the umbral core intensity. We do find a strong and clear dependence of the umbral brightness on sunspot size, however. The penumbral brightness also displays a weak dependence. The brightness-radius relationship has numerous implications, some of which, such as those for the energy transport in umbrae, are pointed out.Comment: 16 pages, 21 postscript figures, accepted for publication in A&

Structural Invariance of Sunspot Umbrae Over the Solar Cycle: 1993-2004

Measurements of maximum magnetic flux, minimum intensity, and size are presented for 12 967 sunspot umbrae detected on the NASA/NSO spectromagnetograms between 1993 and 2004 to study umbral structure and strength during the solar cycle. The umbrae are selected using an automated thresholding technique. Measured umbral intensities are first corrected for a confirming observation of umbral limb-darkening. Log-normal fits to the observed size distribution confirm that the size spectrum shape does not vary with time. The intensity-magnetic flux relationship is found to be steady over the solar cycle. The dependence of umbral size on the magnetic flux and minimum intensity are also independent of cycle phase and give linear and quadratic relations, respectively. While the large sample size does show a low amplitude oscillation in the mean minimum intensity and maximum magnetic flux correlated with the solar cycle, this can be explained in terms of variations in the mean umbral size. These size variations, however, are small and do not substantiate a meaningful change in the size spectrum of the umbrae generated by the Sun. Thus, in contrast to previous reports, the observations suggest the equilibrium structure, as testified by the invariant size-magnetic field relationship, as well as the mean size (i.e. strength) of sunspot umbrae do not significantly depend on solar cycle phase.Comment: 17 pages, 6 figures. Published in Solar Physic

Stray-light restoration of full-disk CaII K solar observations: a case study

AIMS: We investigate whether restoration techniques, such as those developed for application to current observations, can be used to remove stray-light degradation effects on archive CaII K full-disk observations. We analyze to what extent these techniques can recover homogeneous time series of data. METHODS:We develop a restoration algorithm based on a method presented by Walton & Preminger (1999). We apply this algorithm to data for both present-day and archive CaII K full-disk observations, which were acquired using the PSPT mounted at the Rome Observatory, or obtained by digitization of Mt Wilson photographic-archive spectroheliograms. RESULTS:We show that the restoring algorithm improves both spatial resolution and photometric contrast of the analyzed solar observations. We find that the improvement in spatial resolution is similar for analyzed recent and archive data. On the other hand, the improvement of photometric contrast is quite poor for the archive data, with respect to the one obtained for the present-day images. We show that the quality of restored archive data depends on the photographic calibration applied to the original observations. In particular, photometry can be recovered with a restoring algorithm if the photographic-calibration preserves the intensity information stored in the original data, principally outside the solar-disk observations.Comment: 10 pages; 9 figure

Properties of sunspot umbrae observed in Cycle 24

We analyzed the size, intensity, and magnetic field strength of sunspot umbrae to compare the present cycle 24 with the previous one. We used data of the Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory and selected all sunspots between May 2010 and October 2012, using one image per day. We created two subsets of this data with a manual tracking algorithm, both without duplication. One is containing each sunspot (910 umbrae within 488 spots) and was used to analyze the distribution of umbral areas, selected with an automated thresholding method. The other one contains 205 fully evolved sunspots. We find nonlinear relations between umbral minimum intensity and size and between maximum magnetic field strength and size. The field strength scales linear with the intensity and the umbral size scales roughly linear with the total magnetic flux, while the size and field strength level off with stronger flux. When separated in hemisphere and averaged temporally, the southern umbrae show a temporal increase in size and the northern umbrae stay constant. There is no temporal variation in the umbral mean intensity detectable. The probability density function of the umbral area in the ascending phase of the current solar cycle is similar to that of the last solar cycle. From our investigation of umbral area, magnetic field, magnetic flux and umbral intensity of the sunspots of the rising phase of cycle 24, we do not find a significant difference to the previous cycle, and hence no indication for a long-term decline of solar activity.Comment: 11 pages, 9 figures, to be published in Astronomy & Astrophysic

Center-limb dependence of photospheric velocities in regions of emerging magnetic fields on the Sun

We investigate the ratio of the vertical and horizontal velocities of the photospheric plasma flows in the region of emerging magnetic fields on the Sun. We carried out a study of photospheric velocities during the first hours of the appearance of 83 active regions with magnetic flux more than 10^21 Mx with data acquired by the Michelson Doppler Imager (MDI) on board the Solar and Heliospheric Observatory (SOHO). The emerging magnetic fluxes under investigation were isolated from extended concentrations of existing magnetic fields; they have different spatial scales and are located at different distances from the solar disk center. We found that the values of maximum negative Doppler velocities that accompany the emergence of active region magnetic fields during the first 12 hours increase nonlinearly with the heliocentric angle. This result shows that the horizontal photospheric velocities of plasma outflows are higher than the vertical ones of the plasma upflows during the first hours of the emergence of active regions. The horizontal velocity component at the site of emerging active regions exceeds that of convective flows in the quiet Sun. A comparison between the velocities and the maximum value of the total magnetic flux has not revealed any relation.Comment: 5 pages, 4 figures, accepted in A&

Association Between Proportion of Nuclei With High Chromatin Entropy and Prognosis in Gynecological Cancers

Background: Nuclear texture analysis measuring differences in chromatin structure has provided prognostic biomarkers in several cancers. There is a need for improved cell-by-cell chromatin analysis to detect nuclei with highly disorganized chromatin. The purpose of this study was to develop a method for detecting nuclei with high chromatin entropy and to evaluate the association between the presence of such deviating nuclei and prognosis. Methods: A new texture-based biomarker that characterizes each cancer based on the proportion of high–chromatin entropy nuclei (<25% vs ≥25%) was developed on a discovery set of 175 uterine sarcomas. The prognostic impact of this biomarker was evaluated on a validation set of 179 uterine sarcomas, as well as on independent validation sets of 246 early-stage ovarian carcinomas and 791 endometrial carcinomas. More than 1 million images of nuclei stained for DNA were included in the study. All statistical tests were two-sided. Results: An increased proportion of high–chromatin entropy nuclei was associated with poor clinical outcome. The biomarker predicted five-year overall survival for uterine sarcoma patients with a hazard ratio (HR) of 2.02 (95% confidence interval [CI] = 1.43 to 2.84), time to recurrence for ovarian cancer patients (HR = 2.91, 95% CI = 1.74 to 4.88), and cancer-specific survival for endometrial cancer patients (HR = 3.74, 95% CI = 2.24 to 6.24). Chromatin entropy was an independent prognostic marker in multivariable analyses with clinicopathological parameters (HR = 1.81, 95% CI = 1.21 to 2.70, for sarcoma; HR = 1.71, 95% CI = 1.01 to 2.90, for ovarian cancer; and HR = 2.03, 95% CI = 1.19 to 3.45, for endometrial cancer). Conclusions: A novel method detected high–chromatin entropy nuclei, and an increased proportion of such nuclei was associated with poor prognosis. Chromatin entropy supplemented existing prognostic markers in multivariable analyses of three gynecological cancer cohorts.publishedVersio

The intensity contrast of solar photospheric faculae and network elements II. Evolution over the rising phase of solar cycle 23

We studied the radiative properties of small magnetic elements (active region faculae and the network) during the rising phase of solar cycle 23 from 1996 to 2001, determining their contrasts as a function of heliocentric angle, magnetogram signal, and the solar cycle phase. We combined near-simultaneous full disk images of the line-of-sight magnetic field and photospheric continuum intensity provided by the MDI instrument on board the SOHO spacecraft. Sorting the magnetogram signal into different ranges allowed us to distinguish between the contrast of different magnetic structures. We find that the contrast center-to-limb variation (CLV) of these small magnetic elements is independent of time with a 10% precision, when measured during the rising phase of solar cycle 23. A 2-dimensional empirical expression for the contrast of photospheric features as a function of both the position on the disk and the averaged magnetic field strength was determined, showing its validity through the studied time period. A study of the relationship between magnetogram signal and the peak contrasts shows that the intrinsic contrast (maximum contrast per unit of magnetic flux) of network flux tubes is higher than that of active region faculae during the solar cycle.Comment: 11 pages, 6 figures, A&A in pres