The paper presents a new solution for the face recognition based on two-dimensional hidden Markov models. The traditional HMM uses one-dimensional data vectors, which is a drawback in the case of 2D and 3D image processing, because part of the information is lost during the conversion to one-dimensional features vector. The paper presents a concept of the full ergodic 2DHMM, which can be used in 2D and 3D face recognition. The experimental results demonstrate that the system based on two dimensional hidden Markov models is able to achieve a good recognition rate for 2D, 3D and multimodal (2D+3D) face images recognition, and is faster than ICP method.
 W. Zhao, R. Chellappa, P. Phillips, A. Rosenfeld, “Face recognition: A literature survey”, ACM Computing Surveys 35(4), 99-458 (2003).
 A. Rama, F. Tarres, J. Rurainsky, “Aligned texture map creation for pose invariant face recognition”, Multimedia Tools Applications 49(3), 545-565 (2010).
 K.I. Chang, K.W. Bowyer, “An evaluation of multimodal 2D+3D face biometrics”, IEEE Transaction on Pattern Analysis and Machine Intelligence 27, 619-624 (2005).
 M.H. Mahoor, M. Abdel-Mottaleb, “Face recognition based on 3d ridge images obtained from range data”, Pattern Recognition 42(3), 445-451 (2009).
 A.F. Abate, M. Nappi, D. Riccio, G. Sabatino, “2D and 3D face recognition: A survey”, Pattern Recognition Letters 28(14), 1885-1906 (2007).
 K.W. Bowyer, K. Chang, P.J. Flynn, “A survey of approaches and challenges in 3d and multi-modal 3d+2d face recognition”, Computer Vision Image Understanding, 101, 1-15 (2006).
 P.J. Phillips, P.J. Flynn, T. Scruggs, K.W. Bowyer, J. Chang, K. Hoffman, J. Marques, J. Min, W. Worek, “Overview of the face recognition grand challenge”, IEEE Conference on Computer Vision and Pattern Recognition, 947-954 (2005).
 X. Lu, A.K. Jain, “Deformation analysis for 3d face matching”, 7th IEEE Workshop on Applications of Computer Vision, 99- 104 (2005).
 K.I Chang, K.W. Bowyer, P.J. Flynn, P.J., “Adaptive rigid multi-region selection for handling expression variation in 3D face recognition”, IEEE Workshop on Face Recognition Grand Challenge Experiments, 157-164 (2005).
 G. Passalis, I. Kakadiaris, T. Theoharis, G. Toderici, N. Murtuza, “Evaluation of 3d face recognition in the presence of facial expressions: an annotated deformable model approach”, IEEE Workshop on Face Recognition Grand Challenge Experiments, 3, 171-179 (2005).
 X. Lu, A.K. Jain, D. Colbry, “Matching 2.5D face scans to 3D models”, IEEE Transactions on Pattern Analysis and Machine Intelligence 28(1) 31-43 (2006).
 G. Pan, S. Han, Z. Wu, Y. Wang, “3D face recognition using mapped depth images”, IEEE Workshop on Face Recognition Grand Challenge Experiments, 175-181 (2005).
 B. Achermann, X. Jiang, H. Bunke, “Face recognition using range images”, International Conference on Virtual Systems and MultiMedia, 129-136 (1997).
 A.B. Moreno, A. Sanchez, J.F. Velez, F.J. Diaz, “Face recognition using 3D local geometrical features: PCA vs. SVM”, 4th International Symposium on Image and Signal Processing and Analysis, 185-190 (2005).
 A.B. Moreno, A. Sanchez, J.F. Velez, “Voxel-based 3D face representations for recognition”, 12th International Workshop on Systems, Signals and Image Processing, 285-289 (2005).
 G. Gordon, “Face recognition based on depth and curvature features”, Computer Vision and Pattern Recognition 1, 808-810 (1992).
 H.T. Tanaka, M. Ikeda, H. Chiaki, “Curvature-based face surface recognition using spherical correlation principal directions for curved object recognition”, 3rd International Conference on Automated Face and Gesture Recognition, 372-377 (1998).
 J.A. Cook, V. Chandran, C. Fookes, “3D face recognition using log-Gabor templates”, 17th British Machine Vision Conference, 769-778 (2006).
 Y. Jin, Y. Wang, Q. Ruan and X. Wang, “A new scheme for 3D face recognition based on 2D Gabor wavelet transform plus LBP,” 6th International Conference on Computer Science & Education, Singapore, 860-865 (2011).
 S. Berretti, A. Bimbo, P. Pala, “Automatic facial expression recognition in real-time from dynamic sequences of 3D face scans”, The Visual Computer 29, 1333-1350 (2013).
 S. Eickeler, S. Mller, G. Rigoll, “High performance face recognition using pseudo 2-D hidden Markov models”, European Control Conference, available at: http://citeseer.ist.psu.edu (1999).
 V. Bevilacqua, L. Cariello, G. Carro, D. Daleno, G. Mastronardi, “A face recognition system based on pseudo 2DHMM applied to neural network coefficients”, Soft Computing, 12(7) 615-621 (2008).
 L. Yujian, “An analytic solution for estimating two-dimensional hidden Markov models”, Applied Mathematics and Computation, 185, 810-822 (2007).
 J. Li, A. Najmi, R.M. Gray, “Image classification by a two dimensional hidden Markov model”, IEEE Transactions on Signal Processing, 48, 517-533 (2000).
 R. Kindermann, J.L. Snell, Markov Random Fields and their Applications, American Mathematical Society, Providence, Rhode Island (1980).
 M. Srinivasan and N. Ravichandran, “A new technique for face recognition using 2D-Gabor wavelet transform with 2D hidden Markov model approach”, International Conference on Signal Processing, Image Processing & Pattern Recognition, Coimbatore, 151-156 (2013).
 M. Bicego, U. Castellani and V. Murino, “Using hidden Markov models and wavelets for face recognition”, Proceedings of the 12th International Conference on Image Analysis and Processing, 52-56 (2003).
 P.H. Lee, Y.W. Wang, J. Hsu, M.H. Yang, Y.P. Hung, “Robust facial feature extraction using embedded hidden Markov model for face recognition under large pose variation,” Conference on Machine Vision Applications, Tokyo, 392-395 (2007).
 J. Bobulski, M. Kubanek, “Person identiffication system using an identikit picture of the suspect”, Optica Applicata 42(4) 865- 873 (2012).
 I. Daubechies, “The wavelet transform, time-frequency localization and signal analysis”, IEEE Transaction on Information Theory, 36, 961-1005 (1990).
 A. Prochazka, L. Grafova, O. Vysata, “Three-dimensional wavelet transform in multi-dimensional biomedical volume processing”, Proc. of the IASTED International Conference on Graphics and Virtual Reality, Cambridge, 263-268 (2011).
 J. Bobulski, “Wavelet transform in face recognition”, Proceedings of 12th International Multi Conference on Advanced Computer Systems, Elk, 23-29 (2006).
 J. Bobulski, “2DHMM-based face recognition method”’, Image Processing & Comunication Chalenges 7, 389, 11-18 (2016)
 P.J. Phillips, H. Moon, P.J. Rauss, S. Rizvi, “The FERET evaluation methodology for face recognition algorithms”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 22 (10), 1090-1104, (2000).
 A. Colombo, C. Cusano, R. Schettini, “UMB-DB: A database of partially Occluded 3D faces”, Proc. IEEE International Conference on Computer Vision Workshops, Barcelona, 2113-2119, (2011).