In this paper, an adaptive approach has been developed for automatic initialization of the thickening curve using machine vision technology, which makes it possible to determine with high accuracy the material parameters necessary for the design of thickening and clarification apparatuses. Software has been developed that made it possible to search for the coordinates of the condensation critical point in automatic mode. Studies on two samples of materials (tailings of apatite-containing ores and gold-bearing concentrate) were carried out and made it possible to statistically prove the reproducibility of the results obtained using the parametric criteria of Fisher and Bartlett. It has been established that the deposition curves are approximated with high accuracy by the Weibull model, which, together with the piecewise linear approximation, makes it possible to formalize the method for determining the critical point coordinates. The empirical coefficients of the Weibull model for two samples are found, and the final liquefaction and settling rates of the studied materials are determined.