We present a method for recognizing polyhedral objects from range images. An object is said to be recognized as one of the models of a library of object models when many features of the model can be made to match the features of the observed object by the same rotation-translation transformation (the object pose). In the proposed approach, the number of considered pairs of image and model features is reduced by selecting at random only a few of all the possible image features and matching them to appropriate model features. The rotation and translation required for each match are computed, and a robust LMS (Least Median of Squares) method is applied to determine clusters in translation and rotation spaces. The validity of the object pose suggested by the clusters is verified by a similarity measure which evaluates how well a model in the suggested pose would fit the original range image. The pose estimation and verification are performed for all models in the model library. The recognized model is the model which yields the smallest value of the similarity measure, and the pose of the object is found in the process.