The triplet Markov field (TMF) can obtain more promising classification results of nonstationary images than the Markov random field (MRF). However, TMF has limitedly specialized applications to polarimetric synthetic aperture radar (PolSAR) images with nonstationarity properties. In addition, it is difficult to interpret the meaning of the auxiliary field derived by TMF. This implies that the auxiliary field may not have the physical meaning. We propose Wishart TMF with a specific auxiliary field for PolSAR image classification. We define a smoothness characteristic, which describes the extent of pixel smoothness in its neighborhood. This characteristic acts on the energy of the proposed TMF to supervise the classification of the auxiliary field. The auxiliary field can distinguish the smoothness stationarity and nonsmoothness stationarity of PolSAR images, which indicates that the auxiliary field has the specific physical meaning. The effectiveness of the proposed TMF is demonstrated by real PolSAR image classification experiments.