The geometry of fractal sets
Consistent estimation of the intensity function of a cyclic Poisson process
Journal of Multivariate Analysis
Computer Vision: Algorithms and Applications
Computer Vision: Algorithms and Applications
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Many real phenomena may be modeled as random closed sets in R^d, of different Hausdorff dimensions. Of particular interest are cases in which their Hausdorff dimension, say n, is strictly less than d, such as fiber processes, boundaries of germ-grain models, and n-facets of random tessellations. A crucial problem is the estimation of pointwise mean densities of absolutely continuous, and spatially inhomogeneous random sets, as defined by the authors in a series of recent papers. While the case n=0 (random vectors, point processes, etc.) has been, and still is, the subject of extensive literature, in this paper we face the general case of any n