Abstract A crucial challenge of statistical shape modeling is to find corresponding points. The task is much more difficult especially in cases of objects with greater shape diversities (such as liver). In this paper, we propose a new fast algorithm to find corresponding points based on modified Coherent Point Drift technique which is comparable to the state-of-the-art “Minimum Description Length” (MDL) algorithm. Combining fuzzy correspondence and deterministic annealing method together with non-rigid registration of shapes helps to find corresponding points of different liver shapes. We optimized the algorithm parameters to prevent it from producing unacceptable results. Evaluation of the results was performed using Compactness, Generality, Specificity, and run-time measures. We compared our method using both conventional and state-of-the-art techniques including “Iterative Closest Point” (ICP), “Thin Plate Spline-Robust Point Matching” (TPS-RPM) and MDL. The performance of our method is superior to ICP and TPS-RPM algorithms and our results are close to the MDL results. The Generality of ICP, TPS-RPM, MDL and our method are 7.1 ± 1.80, 3.78 ± 0.96, 2.64 ± 0.65 and 3.64 ± 0.85 respectively. The Specificity of MDL and TPS-RPM is the same as ours (0.21 ± 0.06) and the ICP stands in the fourth rank (0.30 ± 0.18). The Compactness of ICP, TPS-RPM, MDL and our method are 23, 19, 16 and 18 respectively. The run-time of ICP, TPS-RPM, MDL and our method are 30, 390, 3600 and 68 s. Contrary to the MDL, our algorithm does not trap into degenerate cases.