Abstract : A family of parsimonious Gaussian process models is presented. They allow to construct a Gaussian mixture model in a kernel feature space by assuming that the data of each class live in a specific subspace. The proposed models are used to build a kernel Markov random field (pGPMRF), which is applied to classify the pixels of a real multivariate remotely sensed image. In terms of classification accuracy, some of the proposed models perform equivalently to a SVM but they perform better than another kernel Gaussian mixture model previously defined in the literature. The pGPMRF provides the best classification accuracy thanks to the spatial regularization.