Face images are an important source of information for biometric recognition and intelligence gathering. While face recognition research has made significant progress over the past few decades, recognition of faces at extended ranges is still highly problematic. Recognition of a low-resolution probe face image from a gallery database, typically containing high resolution facial imagery, leads to lowered performance than traditional face recognition techniques. Learning and super-resolution based approaches have been proposed to improve face recognition at extended ranges; however, the resolution threshold for face recognition has not been examined extensively. Establishing a threshold resolution corresponding to the theoretical and empirical limitations of low resolution face recognition will allow algorithm developers to avoid focusing on improving performance where no distinguishable information for identification exists in the acquired signal. This work examines the intrinsic dimensionality of facial signatures and seeks to estimate a lower bound for the size of a face image required for recognition. We estimate a lower bound for face signatures in the visible and thermal spectra by conducting eigenanalysis using principal component analysis (PCA) (i.e., eigenfaces approach). We seek to estimate the intrinsic dimensionality of facial signatures, in terms of reconstruction error, by maximizing the amount of variance retained in the reconstructed dataset while minimizing the number of reconstruction components. Extending on this approach, we also examine the identification error to estimate the dimensionality lower bound for lowresolution to high-resolution (LR-to-HR) face recognition performance. Two multimodal face datasets are used for this study to evaluate the effects of dataset size and diversity on the underlying intrinsic dimensionality: 1) 50-subject NVESD face dataset (containing visible, MWIR, LWIR face imagery) and 2) 119-subject WSRI face dataset (containing visible and MWIR face imagery).