This work proposes a new formulation of the objects modeling combining geometry and appearance. The object local appearance location is referenced with respect to an invariant which is a geometric landmark. The appearance (shape and texture) is a combination of Harris-Laplace descriptor and local binary pattern (LBP), all is described by the invariant local appearance model (ILAM). We applied the model to describe and learn facial appearances and to recognize them. Given the extracted visual traits from a test image, ILAM model is performed to predict the most similar features to the facial appearance, first, by estimating the highest facial probability, then in terms of LBP Histogram-based measure. Finally, by a geometric computing the invariant allows to locate appearance in the image. We evaluate the model by testing it on different images databases. The experiments show that the model results in high accuracy of detection and provides an acceptable tolerance to the appearance variability.