13.4.1.1 Active Appearance Models - AAM

Lanitis, A.[Andreas], Taylor, C.J.[Chris J.], Cootes, T.F.,
Automatic Interpretation and Coding of Face Images Using Flexible Models,
PAMI(19), No. 7, July 1997, pp. 743-756.
IEEE Abstract.
WWW Version. 9708
BibRef
Earlier:
A Unified Approach for Coding and Interpreting Face Images,
ICCV95(368-373).
IEEE DOI Link
WWW Version. Tracking to get pose and expression. BibRef

Lanitis, A.[Andreas], Taylor, C.J.[Chris J.], Cootes, T.F.,
Automatic Face Identification System Using Flexible Appearance Models,
IVC(13), No. 5, June 1995, pp. 393-401.
WWW Version. BibRef 9506
Earlier: BMVC94(xx-yy).
PDF Version. 9409
BibRef
Earlier:
A Generic System for Classifying Variable Objects using Flexible Template Matching,
BMVC93(329-338).
PDF Version. Parameterized model for apearance, 3D pose, facial expression and lighting, thus both the shape and gray level appearance. 100 parameters for reconstruction use these for identification. 630 face database. See also Model-Based Image Interpretation Using Genetic Algorithms. See also Automatically building appearance models from image sequences using salient features. See also Toward Automatic Simulation of Aging Effects on Face Images. BibRef

Lanitis, A.[Andreas], Taylor, C.J.[Chris J.], Cootes, T.F.,
Automatic Tracking, Coding and Reconstruction of Human Faces using Flexible Appearance Models,
IEE Electronic Letters(30), 1994, pp. 1578-1579 BibRef 9400

Edwards, G.J., Lanitis, A.[Andreas], Taylor, C.J.[Chris J.], Cootes, T.F.,
Statistical Models of Face Images: Improving Specificity,
IVC(16), No. 3, March 16 1998, pp. 203-211.
WWW Version. 9804
BibRef
Earlier:
Modelling the variability in face images,
AFGR96(328-333).
IEEE DOI Link 9610
BibRef
And:
Statistical Models of Face Images: Recent Advances,
BMVC96(Faces). 9608
University of Manchester BibRef

Edwards, G.J.[Gareth J.], Taylor, C.J.[Chris J.], Cootes, T.F.[Timothy F.],
Improving Identification Performance by Integrating Evidence from Sequences,
CVPR99(I: 486-491).
IEEE Abstract.
WWW Version. Evaluation, Face Recognition. Learn how the face changes through a sequence, use the video to identify the face. BibRef 9900

Cootes, T.F., Wheeler, G.V., Walker, K.N., Taylor, C.J.,
Coupled-View Active Appearance Models,
BMVC00(xx-yy).
PDF Version. 0009
BibRef

Edwards, G.J., Taylor, C.J., and Cootes, T.F.,
Learning to Identify and Track Faces in Image Sequences,
AFGR98(260-265).
IEEE DOI Link BibRef 9800
Earlier: ICCV98(317-322).
IEEE DOI Link BibRef BMVC97(xx-yy).
HTML Version. 0209
BibRef

Edwards, G.J., Taylor, C.J.[Christopher J.], Cootes, T.F.,
Interpreting Face Images Using Active Appearance Models,
AFGR98(300-305).
IEEE DOI Link See also Active Appearance Models. BibRef 9800

Edwards, G.J., Cootes, T.F., Taylor, C.J.[Christopher J.],
Face recognition using active appearance models,
ECCV98(II: 581).
WWW Version. BibRef 9800

Matthews, I.[Iain], Baker, S.[Simon],
Active Appearance Models Revisited,
IJCV(60), No. 2, November 2004, pp. 135-164.
WWW Version. 0406
BibRef
Earlier: CMU-RI-TR-03-02, April, 2003.
HTML Version. 0306
BibRef

Dedeoglu, G.[Göksel], Baker, S.[Simon], Kanade, T.[Takeo],
Resolution-Aware Fitting of Active Appearance Models to Low Resolution Images,
ECCV06(II: 83-97).
Springer DOI Link 0608
See also Asymmetry of Image Registration and Its Application to Face Tracking, The. BibRef

Baker, S., Matthews, I., Schneider, J.,
Automatic Construction of Active Appearance Models as an Image Coding Problem,
PAMI(26), No. 10, October 2004, pp. 1380-1384.
IEEE Abstract.
HTML Version. 0409
BibRef
Earlier:
Image Coding with Active Appearance Models,
CMU-RI-TR-03-13, April, 2003.
HTML Version. 0306
BibRef

Gross, R.[Ralph], Matthews, I.[Iain], Baker, S.[Simon],
Generic vs. Person Specific Active Appearance Models,
IVC(23), No. 12, 1 November 2005, pp. 1080-1093.
WWW Version. 0510
BibRef
Earlier: BMVC04(xx-yy).
HTML Version. 0508
BibRef

Gross, R.[Ralph], Matthews, I.[Iain], Baker, S.[Simon],
Active appearance models with occlusion,
IVC(24), No. 6, 1 June 2006, pp. 593-604.
WWW Version.
HTML Version. 0606
BibRef
Earlier:
Constructing and Fitting Active Appearance Models with Occlusion,
FaceVideo04(72).
HTML Version.
HTML Version. 0502
Model-based face analysis; Robust model fitting; Fitting with occlusion. Generative model to track faces in video. BibRef

Theobald, B.J., Matthews, I.[Iain], and Baker, S.[Simon],
Evaluating Error Functions for Robust Active Appearance Models,
FGR06(149-154).
IEEE DOI Link
HTML Version. 0604
BibRef

Hu, C., Xiao, J., Matthews, I., Baker, S., Cohn, J.F., Kanade, T.,
Fitting a Single Active Appearance Model Simultaneously to Multiple Images,
BMVC04(xx-yy).
HTML Version. 0508
BibRef

Batur, A.U., Hayes, III, M.H.,
Adaptive Active Appearance Models,
IP(14), No. 11, November 2005, pp. 1707-1721.
IEEE DOI Link 0510
BibRef
Earlier:
A novel convergence scheme for active appearance models,
CVPR03(I: 359-366).
IEEE Abstract. 0307
BibRef

Doretto, G.[Gianfranco], Soatto, S.[Stefano],
Dynamic Shape and Appearance Models,
PAMI(28), No. 12, December 2006, pp. 2006-2019.
IEEE DOI Link 0611
Joint variation of shape and appearence. BibRef

Doretto, G.[Gianfranco],
Modeling Dynamic Scenes with Active Appearance,
CVPR05(I: 66-73).
IEEE DOI Link 0507
Rathern than only appearence, only shape, or only motion, model all three together. Extension of AAM ( See also Active Appearance Models. ) to temporal domain. BibRef

Wang, X.G.[Xiao-Gang], Doretto, G.[Gianfranco], Sebastian, T.[Thomas], Rittscher, J.[Jens], Tu, P.[Peter],
Shape and Appearance Context Modeling,
ICCV07(1-8).
IEEE DOI Link 0710
BibRef

Beichel, R., Bischof, H., Leberl, F., Sonka, M.,
Robust Active Appearance Models and Their Application to Medical Image Analysis,
MedImg(24), No. 9, September 2005, pp. 1151-1169.
IEEE DOI Link 0509
BibRef

Beichel, R., Mitchell, S., Sorantin, E., Leberl, F., Goshtasby, A., Sonka, M.,
Shape- and Appearance-based Segmentation of Volumetric Medical Images,
ICIP01(II: 589-592).
IEEE Abstract. 0108
BibRef

Duta, N.[Nicolae], Sonka, M.[Milan],
An improved active shape model: Handling occlusion and outliers,
CIAP97(I: 398-405).
WWW Version. 9709
BibRef

Christoudias, C.M.[Chris Mario], Morency, L.P.[Louis-Philippe], Darrell, T.J.[Trevor J.],
Non-parametric and light-field deformable models,
CVIU(104), No. 1, October 2006, pp. 16-35.
WWW Version. 0609
BibRef
Earlier:
Light Field Morphable Models,
MIT AIMAIM-2003-010, April 18, 2003.
WWW Version. Image morphing; PCA; Shape-and-texture appearance model; Deformable model; Active appearance model; Multidimensional morphable model; Light-field; Non-Lambertian surface reflectance; Nonlinear appearance manifold. We describe how to construct a manifold of the multi-view appearance of an object class using light fields and show how to match a 2D image of an object to a point on this manifold. In turn we use the reconstructed light field to render novel views of the object 0306
BibRef

Christoudias, C.M.[C. Mario], Darrell, T.J.[Trevor J.],
On Modelling Nonlinear Shape-and-Texture Appearance Manifolds,
CVPR05(II: 1067-1074).
IEEE DOI Link 0507
BibRef

Ramnath, K.[Krishnan], Koterba, S.[Seth], Xiao, J.[Jing], Hu, C.B.[Chang-Bo], Matthews, I.[Iain], Baker, S.[Simon], Cohn, J.F.[Jeffrey F.], Kanade, T.[Takeo],
Multi-View AAM Fitting and Construction,
IJCV(76), No. 2, February 2008, pp. 183-204.
Springer DOI Link 0801
BibRef
Earlier: A2, A6, A5, A4, A3, A7, A8, Only:
Multi-View AAM Fitting and Camera Calibration,
ICCV05(I: 511-518).
IEEE DOI Link 0510
Calibration. AAM: Active Appearance Model. Essentially use the face as the calibration grid. BibRef

Xiao, J.[Jing], Baker, S., Matthews, I., Kanade, T.,
Real-time combined 2D+3D active appearance models,
CVPR04(II: 535-542).
IEEE Abstract. 0408
Show 2D AAM can model faces as well as 3D Morphable Models. See also Multi-View AAM Fitting and Construction. BibRef

am_tools,
2007.
HTML Version. Code, Active Appearance Model. A set of tools to build and play with Appearance Models and AAMs. See also University of Manchester, Medicine.

AAM Building,
February, 2007.
WWW Version. Code, Active Appearance Model. Code, Open Source.

Stegmann, M.B.[Mikkel B.],
Active Appearance Models,
Online2007.
WWW Version. Code, Active Appearance Model. Dataset, Active Appearance Model. AAM code and information. See also Technical University of Denmark. BibRef 0700

Sung, J.W.[Jae-Won], Kanade, T.[Takeo], Kim, D.J.[Dai-Jin],
A Unified Gradient-Based Approach for Combining ASM into AAM,
IJCV(75), No. 2, November 2007, pp. 297-309.
Springer DOI Link 0710
BibRef
Earlier: A1, A3, Only:
A Unified Approach for Combining ASM into AAM,
PSIVT06(353-362).
Springer DOI Link 0612
See also STAAM: Fitting a 2D+3D AAM to Stereo Images. BibRef

Lee, S.J.[Sang-Jae], Sung, J.W.[Jae-Won], Kim, D.J.[Dai-Jin],
Incremental Update of Linear Appearance Models and Its Application to AAM: Incremental AAM,
ICIAR07(538-547).
Springer DOI Link 0708
BibRef

Lee, H.S.[Hyung-Soo], Kim, D.J.[Dai-Jin],
Tensor-Based AAM with Continuous Variation Estimation: Application to Variation-Robust Face Recognition,
PAMI(31), No. 6, June 2009, pp. 1102-1116.
IEEE DOI Link 0904
Tensor based to handle face pose, illumination, expression variations. BibRef

Donner, R.[Rene], Reiter, M.[Michael], Langs, G.[Georg], Peloschek, P., Bischof, H.[Horst],
Fast Active Appearance Model Search Using Canonical Correlation Analysis,
PAMI(28), No. 10, October 2006, pp. 1690-1694.
IEEE DOI Link 0609
Combine Texture and model. See also Appearance Models Based on Kernel Canonical Correlation Analysis. BibRef

Langs, G.[Georg], Peloschek, P.[Philipp], Donner, R.[Rene], Bischof, H.[Horst],
Multiple appearance models,
PR(40), No. 9, September 2007, pp. 2485-2495.
WWW Version. 0705
BibRef
Earlier:
A Clique of Active Appearance Models by Minimum Description Length,
BMVC05(xx-yy).
HTML Version. 0509
MDL; Model building; Active appearance models; Medical imaging; Eigenimages BibRef

Donner, R.[Rene], Micusik, B., Langs, G.[Georg], Bischof, H.[Horst],
Sparse MRF Appearance Models for Fast Anatomical Structure Localisation,
BMVC07(xx-yy).
PDF Version. 0709
BibRef

Langs, G.[Georg], Peloschek, P.[Philipp], Bischof, H.[Horst],
Optimal Sub-Shape Models by Minimum Description Length,
CVPR05(II: 310-315).
IEEE DOI Link 0507
BibRef

Langs, G.[Georg], Peloschek, P.[Philipp], Donner, R.[Rene], Reiter, M.[Michael], Bischof, H.[Horst],
Active Feature Models,
ICPR06(I: 417-420).
WWW Version. 0609
BibRef

Ketchantang, W., Derrode, S., Martin, L., Bourennane, S.[Salah],
Pearson-based mixture model for color object tracking,
MVA(19), No. 5-6, October 2008, pp. xx-yy.
Springer DOI Link 0810
Dynamically updates mixture model to appearance changes. BibRef

Zhu, J.K.[Jian-Ke], Lyu, M.R.[Michael R.], Huang, T.S.[Thomas S.],
A Fast 2D Shape Recovery Approach by Fusing Features and Appearance,
PAMI(31), No. 7, July 2009, pp. 1210-1224.
IEEE DOI Link 0905
Both appearance and local features. Linear solution for surface detection. Deformable Lucas-Kanade to contstain the deformation. BibRef

Zhu, J.K.[Jian-Ke], Hoi, S.C.H.[Steven C.H.], Lyu, M.R.[Michael R.],
Face Annotation Using Transductive Kernel Fisher Discriminant,
MultMed(10), No. 1, January 2008, pp. 86-96.
IEEE DOI Link 0905
BibRef
Earlier:
Real-Time Non-rigid Shape Recovery Via Active Appearance Models for Augmented Reality,
ECCV06(I: 186-197).
Springer DOI Link 0608
BibRef

Ionita, M.C., Corcoran, P., Buzuloiu, V.,
On Color Texture Normalization for Active Appearance Models,
IP(18), No. 6, June 2009, pp. 1372-1378.
IEEE DOI Link 0905
BibRef

Saragih, J.M.[Jason M.], Goecke, R.[Roland],
Learning AAM fitting through simulation,
PR(42), No. 11, November 2009, pp. 2628-2636.
Elsevier DOI Link
WWW Version. 0907
BibRef
Earlier:
A Nonlinear Discriminative Approach to AAM Fitting,
ICCV07(1-8).
IEEE DOI Link 0710
BibRef
And:
Monocular and Stereo Methods for AAM Learning from Video,
CVPR07(1-8).
IEEE DOI Link 0706
BibRef
Earlier:
Iterative Error Bound Minimisation for AAM Alignment,
ICPR06(II: 1192-1195).
WWW Version. 0609
Active appearance model; Fitting; Discriminative; Linear model BibRef

Asthana, A.[Akshay], Sanderson, C.[Conrad], Gedeon, T.[Tom], Goecke, R.[Roland],
Learning-based Face Synthesis for Pose-robust Recognition from Single Image,
BMVC09(xx-yy).
PDF Version.
PDF Version. 0909
BibRef

Asthana, A.[Akshay], Khwaja, A.[Asim], Goecke, R.[Roland],
Automatic frontal face annotation and AAM building for arbitrary expressions from a single frontal image only,
ICIP09(2445-2448).
IEEE DOI Link 0911
BibRef

Asthana, A.[Akshay], Goecke, R.[Roland], Quadrianto, N.[Novi], Gedeon, T.[Tom],
Learning based automatic face annotation for arbitrary poses and expressions from frontal images only,
CVPR09(1635-1642).
IEEE DOI Link 0906
BibRef

Lee, S.J.[Sung Joo], Park, K.R.[Kang Ryoung], Kim, J.H.[Jai-Hie],
A comparative study of facial appearance modeling methods for active appearance models,
PRL(30), No. 14, 15 October 2009, pp. 1335-1346,.
Elsevier DOI Link
WWW Version. 0909
Active appearance model; Non-negative matrix factorization; Facial appearance modeling; Local non-negative matrix factorization; Non-smooth non-negative matrix factorization BibRef

Noceti, N.[Nicoletta], Delponte, E.[Elisabetta], Odone, F.[Francesca],
Spatio-temporal constraints for on-line 3D object recognition in videos,
CVIU(113), No. 12, Decmeber 2009, pp. 1198-1209,.
Elsevier DOI Link
WWW Version. 0911
View-based 3D object recognition; Local keypoints; Space-time coherence; Continuous views; Interactive recognition; On-line recognition; Real-time recognition BibRef

Noceti, N.[Nicoletta], Destrero, A.[Augusto], Lovato, A.[Alberto], Odone, F.[Francesca],
Combined Motion and Appearance Models for Robust Object Tracking in Real-Time,
AVSBS09(412-417).
IEEE DOI Link 0909
BibRef

Delponte, E., Noceti, N., Odone, F., Verri, A.,
Appearance-based 3D object recognition with time-invariant features,
CIAP07(467-474).
IEEE DOI Link 0709
BibRef

Séguier, R.[Renaud], Le Gallou, S.[Sylvain], Breton, G.[Gaspard], Garcia, C.[Christophe],
Adapted Active Appearance Models,
JIVP(2009), No. 2009, pp. xx-yy.
WWW Version. 1002
BibRef

Butakoff, C.[Constantine], Frangi, A.F.[Alejandro F.],
Multi-view face segmentation using fusion of statistical shape and appearance models,
CVIU(114), No. 3, March 2010, pp. 311-321.
Elsevier DOI Link
WWW Version. 1003
AAM; ASM; Model fusion; Statistical model; Shape model; Face segmentation; Multi-view segmentation BibRef

Gao, X., Su, Y., Li, X., Tao, D.,
A Review of Active Appearance Models,
SMC-C(40), No. 2, March 2010, pp. 145-158.
IEEE DOI Link 1003
Survey, AAM. Survey, Active Appearance Models. BibRef

Ye, N.[Ning], Sim, T.[Terence],
Combining Facial Appearance and Dynamics for Face Recognition,
CAIP09(133-140).
Springer DOI Link 0909
BibRef

Yang, J.Y.[Jun-Yeong], Byun, H.R.[Hye-Ran],
Multi Subspaces Active Appearance Models,
FG08(1-6).
IEEE DOI Link 0809
BibRef

Castelli, I., Maggini, M., Melacci, S., Sarti, L.,
Auto Associative Neural Network based Active Shape Models,
FG08(1-6).
IEEE DOI Link 0809
BibRef

Wimmer, M.[Matthias], Fujie, S.[Shinya], Stulp, F.[Freek], Kobayashi, T.[Tetsunori], Radig, B.[Bernd],
An ASM fitting method based on machine learning that provides a robust parameter initialization for AAM fitting,
FG08(1-6).
IEEE DOI Link 0809
BibRef

Sattar, A.[Abdul], Seguier, R.[Renaud],
MVAAM (multi-view active appearance model) optimized by multi-objective genetic algorithm,
FG08(1-8).
IEEE DOI Link 0809
BibRef

Nandi, S.[Sudipto], Guha, P.[Prithwijit], Venkatesh, K.S.,
Objects from Animacy: Joint Discovery in Shape and Haar Feature Space,
ICCVGIP08(730-737).
IEEE DOI Link 0812
Appearance models from full sequence. BibRef

Netzell, K.[Karl], Solem, J.E.[Jan Erik],
Efficient image inner products applied to active appearance models,
ICPR08(1-4).
IEEE DOI Link 0812
BibRef

Aidarous, Y.[Yasser], Séguier, R.[Renaud],
Fast Simplex Optimization for Active Appearance Model,
PSIVT09(106-117).
Springer DOI Link 0901
BibRef

Sattar, A.[Abdul], Aidarous, Y.[Yasser], Seguier, R.[Renaud],
GAGM-AAM: A genetic optimization with Gaussian mixtures for Active Appearance Models,
ICIP08(3220-3223).
IEEE DOI Link 0810
BibRef

Lui, Y.M.[Yui Man], Beveridge, J.R.[J. Ross],
Grassmann Registration Manifolds for Face Recognition,
ECCV08(II: 44-57).
Springer DOI Link 0810
BibRef

Lui, Y.M.[Yui Man], Beveridge, J.R., Howe, A.E., Whitley, L.D.,
Evolution Strategies for Matching Active Appearance Models to Human Faces,
BTAS07(1-7).
IEEE DOI Link 0709
BibRef

Peyras, J., Bartoli, A.E., Khoualed, S.K.,
Pools of AAMs: Towards Automatically Fitting any Face Image,
BMVC08(xx-yy).
PDF Version. 0809
BibRef

Papandreou, G.[George], Maragos, P.[Petros],
Adaptive and constrained algorithms for inverse compositional Active Appearance Model fitting,
CVPR08(1-8).
IEEE DOI Link 0806
BibRef

Pizarro, D.[Daniel], Peyras, J.[Julien], Bartoli, A.E.[Adrien E.],
Light-invariant fitting of active appearance models,
CVPR08(1-6).
IEEE DOI Link 0806
BibRef

Ramnath, K.[Krishnan], Baker, S.[Simon], Matthews, I.D.[Iain D.], Ramanan, D.[Deva],
Increasing the density of Active Appearance Models,
CVPR08(1-8).
IEEE DOI Link 0806
BibRef

Yu, X.[Xin], Tian, J.W.[Jin-Wen], Liu, J.[Jian],
Active Appearance Models Fitting with Occlusion,
EMMCVPR07(137-144).
Springer DOI Link 0708
BibRef

Peyras, J.,
Segmented AAMs Improve Person-Indepedent Face Fitting,
BMVC07(xx-yy).
PDF Version. 0709
BibRef

Mercier, H., Peyras, J., Dalle, P.,
Toward an Efficient and Accurate AAM Fitting on Appearance Varying Faces,
FGR06(363-368).
IEEE DOI Link 0604
BibRef

Huisman, P., van Munster, R., Moro-Ellenberger, S., Veldhuis, R.N.J., Bazen, A.M.,
Making 2D Face Recognition More Robust Using AAMs for Pose Compensation,
FGR06(108-113).
IEEE DOI Link 0604
BibRef

Kittipanya-Ngam, P., Cootes, T.F.,
The effect of texture representations on AAM performance,
ICPR06(II: 328-331).
WWW Version. 0609
BibRef
Earlier: A2, A1:
Comparing Variations on the Active Appearance Model Algorithm,
BMVC02(Face and Gesture Processing). 0208
BibRef

Liebelt, J.[Joerg], Xiao, J.[Jing], Yang, J.[Jie],
Robust AAM Fitting by Fusion of Images and Disparity Data,
CVPR06(II: 2483-2490).
IEEE DOI Link 0606
BibRef

Choi, K.T.[Kwon-Taeg], Ahn, J.H.[Jung-Ho], Byun, H.R.[Hye-Ran],
Face Alignment Using Segmentation and a Combined AAM in a PTZ Camera,
ICPR06(III: 1191-1194).
WWW Version. 0609
BibRef

Faggian, N.[Nathan], Paplinski, A.P.[Andrew P.], Sherrah, J.[Jamie],
3D Morphable Model fitting from multiple views,
FG08(1-6).
IEEE DOI Link 0809
BibRef
Earlier:
Active Appearance Models for Automatic Fitting of 3D Morphable Models,
AVSBS06(90-90).
IEEE DOI Link 0611
BibRef

Faggian, N.[Nathan], Paplinski, A.P.[Andrew P.], Chin, T.J.[Tat-Jun],
Face Recognition From Video using Active Appearance Model Segmentation,
ICPR06(I: 287-290).
WWW Version. 0609
BibRef

Schreiber, S., Stormer, A., Rigoll, G.,
A Hierarchical ASM/AAM Approach in a Stochastic Framework for Fully Automatic Tracking and Recognition,
ICIP06(1773-1776). 0610

IEEE DOI Link BibRef

Zhang, C.P.[Cui-Ping], Cohen, F.S.[Fernand S.],
Component-Based Active Appearance Models for Face Modelling,
ICB06(206-212).
Springer DOI Link 0601
BibRef
Earlier:
A Constrained Hybrid Optimization Algorithm for Morphable Appearance Models,
EMMCVPR05(568-583).
Springer DOI Link 0601
BibRef

Jones, E.[Eagle], Soatto, S.[Stefano],
Layered Active Appearance Models,
ICCV05(II: 1097-1102).
IEEE DOI Link 0510
(AAM) Model the joint shape and texture. Layered allows for missing features. BibRef

Andreopoulos, A.[Alexander], Tsotsos, J.K.[John K.],
A Novel Algorithm for Fitting 3-D Active Appearance Models: Applications to Cardiac MRI Segmentation,
SCIA05(729-739).
Springer DOI Link 0506
BibRef

Chapter on Matching and Recognition Using Volumes, High Level Vision Techniques, Invariants continues in
Invariants -- Principal Component Analysis .