The Annals of Statistics

Recovering convex boundaries from blurred and noisy observations

Alexander Goldenshluger and Assaf Zeevi

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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.

Article information

Ann. Statist., Volume 34, Number 3 (2006), 1375-1394.

First available in Project Euclid: 10 July 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G05: Estimation 62H35: Image analysis

Image analysis convex sets boundary estimation deconvolution support function geometric probing rates of convergence


Goldenshluger, Alexander; Zeevi, Assaf. Recovering convex boundaries from blurred and noisy observations. Ann. Statist. 34 (2006), no. 3, 1375--1394. doi:10.1214/009053606000000326.

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