## 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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### References:

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