AbstructEfficient 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 find 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 find a...

Shadow detection is useful in many applications like image segmentation, scene interpretation and object recognition/tracking. Shadow in images is formed when direct light from a light source cannot reach due to obstruction by an object. Shadow removal is a critical step for improving object detection and tracking. Many algorithms for shadow detection have been proposed in the literature. This ...

Extending the rigorous presentation of the “classical umbral calculus” [28], the so-called partition polynomials are interpreted with the aim to point out the umbral nature of the Poisson random variables. Among the new umbrae introduced, the main tool is the partition umbra that leads also to a simple expression of the functional composition of the exponential power series. Moreover a new shor...

In the present work a statistical investigation of the spatial distribution of longitudinal coordinates of sunspot data has been carried out. For the analysis the maximal area of umbra plus penumbra of sunspot groups has been taken into account. Spatial distributions of longitudinal coordinates of sunspot data are obtained in diierent coordinate systems (e.g. Carrington, equatorial and diierent...

This is the third part of the five-part saga on the umbral transfermatrix method, based on Gian-Carlo Rota’s seminal notion of the umbra. In this article we describe the Maple package ZOO that for any specific k, automatically constructs an umbral scheme for enumerating “k-board” lattice animals (polyominoes) on the two-dimensional square lattice. Such umbral schemes enable counting these impor...

Efficient implementation of morphological operations requires the decomposition of structuring elements into the dilation of smaller structuring elements. Zhuang and Haralick (1986) presented a search algorithm to find optimal decompositions of structuring elements in binary morphology. We use the concepts of Top of a set and Umbra of a surface to extend this algorithm to find an optimal decomp...

We report spectropolarimetric observations of a supersonic downflow impacting the lower atmosphere within large sunspot umbra. This work is an extension Schad et al. using acquired in He i 10830 Å triplet by Facility Infrared Spectropolarimeter. Downflowing material accelerating along cooled coronal loop reaches peak speeds near 200 km s−1 and exhibits both high speed emission absorption umbra,...