Image estimators based on marked bins

The problem of approximating an ‘image’ S?? ^d from a random sample of points is considered. If S is included in a grid of square bins, a plausible estimator of S is defined as the union of the ‘marked’ bins (those containing a sample point). We obtain convergence rates for this estimator and study its performance in the approximation of the border of S. The practical aspects of implementation are discussed, including some technical improvements on the estimator, whose performance is checked through a real data example.