We propose a novel local appearance modeling method for object detection and recognition in cluttered scenes. The approach is based on the joint distribution of local feature vectors at multiple salient points and factorization with Independent Component Analysis (ICA). The resulting densities are simple multiplicative distributions modeled through adaptive Gaussian mixture models. This leads to computationally tractable joint probability densities which can model high-order dependencies. Furthermore, different models are compared based on appearance, color and geometry information. Also, the combination of all of them results in a hybrid model which obtains the best results using the COIL-100 object database. Our technique has been tested under different natural and cluttered scenes with different degrees of occlusions with promising results. Finally, a large statistical test with the MNIST digit database is used to demonstrate the improved performance obtained by explicit modeling of high-order dependencies.