We develop a data structure, the spatialized normal cone hierarchy, and apply it to interactive solutions for model silhouette extraction, local minimum distance computations, and area light source shadow umbra and penumbra boundary determination. The latter applications extend the domain of surface normal encapsulation from problems described by a point and a model to problems involving two mo...

Spectropolarimetric time series data of the primary spot of active region NOAA 9448 were obtained in the Si i 10827 Å line and the He i 10830 Å multiplet with the Tenerife Infrared Polarimeter. Throughout the time series the spectrograph slit was fixed over a region covering umbra, a light bridge, penumbra, and quiet sun. We present speeds of running penumbral waves in the chromosphere, their r...

The umbral regions of sunspots and pores in the solar photosphere are generally dominated by $3$~mHz oscillations, which due to $p$-modes penetrating magnetic region. In these locations, wave power is also significantly reduced with respect quiet Sun. However, here we study a pore where oscillations umbra not only comparable, or even larger than that Sun, but main dominant frequency as expected...

| EEcient implementation of morphological operations requires the decomposition of structuring elements into the dilation of smaller structuring elements. Zhuang and Haralick presented a search algorithm to nd optimal decompositions of structuring elements in binary morphology. In this paper we use the concepts of Top of a set and Umbra of a surface to extend this algorithm to nd an optimal dec...