Homotopic grayscale thinning leads to over-connected skeleton when applied on noisy images. To avoid this phenomenon, the parametric thinning relaxes the thinning constraints by lowering low contrast crests, peaks and ends, according to a manually selected parameter and by using ascendant gray level treatment to guarantee the homotopy of the skeleton. We propose the control of this parameter by considering the lowering decision in the statistical framework of hypothesis testing. This leads to a local adjustment and a standardization of the parametric thinning process, regardless of the gray level image. The statistical adjustment linked the thinning parameter to both noise standard deviation and image contrast. The ascendant gray level treatment is ensured by using hierarchical queues operated in watershed algorithms. Results of the statistical adjustment and implementation are illustrated on synthetic images and real images.