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Recovering convex boundaries from blurred and noisy observations. (English) Zbl 1113.62116

Summary: We consider the problem of estimating convex boundaries from blurred and noisy observations. In our model, the convolution of an intensity function \(f\) is observed with additive Gaussian white noise. The function \(f\) is assumed to have convex support \(G\) whose boundary is to be recovered. Rather than directly estimating the intensity function, we develop a procedure which is based on estimating the support function of the set \(G\). This approach is closely related to the method of geometric hyperplane probing, a well-known technique in computer vision applications. We establish bounds that reveal how the estimation accuracy depends on the ill-posedness of the convolution operator and the behavior of the intensity function near the boundary.

MSC:

62M40 Random fields; image analysis
62G05 Nonparametric estimation
62H35 Image analysis in multivariate analysis
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