Homotopic grayscale thinning leads to " over-connected skeleton " when applied on noisy images. One way to avoid this phenomenon is the parametric thinning. It consists in relaxing the initial constraint by lowering low contrast crests, peaks and ends, according to a manually selected parameter and under the constraint of ascendant gray level processing. We propose to control this parameter by considering the lowering decision in a statistical framework of hypothesis test under the assumption of an additive Gaussian noise. A unitary hypothesis test based on the minimum test statistic is used for the elimination of peaks and noise related extremities, while a fusion of multiple tests is required for the insignificant crest lowering decision. This leads to a local adjustment and a standardization of the parametric thinning process that depends only on the chosen significance level of the test.