Algorithms to automatically quantify the geometric similarity of anatomical surfaces

Proceedings of the National Academy of Sciences of the United States of America

Volumn 108, Issue 45, 2011, Pages 18221-18226

  Boyer, Doug M ^a,b   Lipman, Yaron ^c   St Clair, Elizabeth ^b   Puente, Jesus ^d   Patel, Biren A ^b   Funkhouser, Thomas ^e   Jernvall, Jukka ^b,f   Daubechies, Ingrid ^g  

^a CITY UNIVERSITY OF NEW YORK   (United States)

^b STONY BROOK UNIVERSITY   (United States)

^c WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^d PRINCETON UNIVERSITY   (United States)

^e Princeton University   (United States)

^f UNIVERSITY OF HELSINKI   (Finland)

^g DUKE UNIVERSITY   (United States)

Author keywords

Homology; Mobius transformations; Morphometrics; Procrustes

Indexed keywords

ANATOMICAL VARIATION; ARTICLE; BONE; COMPARATIVE STUDY; EVOLUTIONARY ALGORITHM; EVOLUTIONARY DEVELOPMENTAL BIOLOGY; EXTINCT SPECIES; FEASIBILITY STUDY; GEOMETRY; HUMAN; MORPHOMETRICS; NATURAL SCIENCE; NONHUMAN; PRIMATE; PRIORITY JOURNAL; SURFACE PROPERTY; TOOTH;

ALGORITHMS; MODELS, ANATOMIC;

ANIMALIA; PRIMATES;

EID: 81055141406     PISSN: 00278424     EISSN: 10916490     Source Type: Journal    
DOI: 10.1073/pnas.1112822108     Document Type: Article

References (44)

1. Sargis EJ, Boyer DM, Bloch JI, Silcox MT (2007) Evolution of pedal grasping in primates. J Hum Evol 53:103-107. (Pubitemid 46840238)
2. Schwartz JH, Tattersall I (1985) Evolutionary Relationships of Living Lemurs and Lorises (Mammalia, Primates) and Their Potential Affinities with European Eocene Adapidae (Am Museum Natural History, New York).
3. MacLeod N (1999) Generalizing and extending the eigenshape method of shape visualization and analysis. Paleobiology 25:107-138.
4. Bookstein FL (2007) Morphometrics and Computed Homology: An Old Theme Revisited. Automated Taxon Identification in Systematics, ed N MacLeod (CRC, London), pp 69-82.
5. Liu K, Raghavan S, Nelesen S, Linder CR, Warnow T (2009) Rapid and accurate large-scale coestimation of sequence alignments and phylogenetic trees. Science 324:1561-1564.
6. Murphy WJ, et al. (2001) Resolution of the early placental mammal radiation using bayesian phylogenetics. Science 294:2348-2351. (Pubitemid 33140557)
7. Mitteroecker P, Gunz P (2009) Advances in geometric morphometrics. Evol Biol 36:235-247.
8. Simpson GG (1936) Studies of the earliest mammalian dentitions. Dent Cosmos 78:791-800 940-953.
9. Wiley DF, et al. (2005) Evolutionary morphing. Proc IEEE Visualization, .
10. Polly PD, MacLeod N (2008) Locomotion in fossil carnivora: An application of eigensurface analysis for morphometric comparison of 3D surfaces. Palaeontol Electron 11.2.8A:1-13.
11. Zelditch ML, Swiderski DL, Sheets DH, Fink WL (2004) Geometric Morphometrics for Biologists (Elsevier Academic, San Diego).
12. Lohmann GP (1983) Eigenshape analysis of microfossils: A general morphometric method for describing changes in shape. Math Geol 15:659-672.
13. Thirion JP, Gourdon A (1996) The 3D marching lines algorithm. Graph Model Im Proc 58:503-509.
14. Subsol G, Thirion JP, Ayache N (1998) A general scheme for automatically building 3D morphometric anatomical atlases: Application to a skull atlas. Med Image Anal 2:37-60. (Pubitemid 128500720)
15. Subsol G, Mafart B, Silvestre A, de Lumley MA (2002) 3d image processing for the study of the evolution of the shape of the human skull: presentation of the tools and preliminary results. Three-Dimensional Imaging in Paleoanthropology and Prehistoric Archaeology, British Archeological Reports International Series, eds B Mafart, H Delingette, and G Subsol (Archeopress, Oxford), 1049, pp 37-45.
16. Gaston KJ, O'Neill MA (2004) Automated species identification - why not? Philos Trans R Soc Lond B Biol Sci 359:655-667. (Pubitemid 38504155)
17. Weeks PJD, O'Neill MA, Gaston KJ, Gauld ID (1999) Species-identification of wasps using principal component associative memories. Image Vision Comput 17:861-866.
18. Besl PJ, McKay ND (1992) A method for registration of 3-D shapes. IEEE Trans Pattern Anal Mach Intell 14:239-256.
19. Mémoli F, Guillermo Sapiro (2005) A theoretical and computational framework for isometry invariant recognition of point cloud data. Found Comput Math 5:313-347.
20. Bronstein AM, Bronstein MM, Kimmel R (2006) Generalized multidimensional scaling: A framework for isometry-invariant partial surface matching. Proc Natl Acad Sci USA 103:1168-1172. (Pubitemid 43191136)
21. Schmidt EJ, et al. (2010) Micro-computed tomography-based phenotypic approaches in embryology: Procedural artifacts on assessments of embryonic craniofacial growth and development. BMC Dev Biol 10:18.
22. Abbott A (2010) Mouse project to find each gene's role. Nature 465:410.
23. Salazar-Ciudad I, Jernvall J (2010) A computational model of teeth and the developmental origins of morphological variation. Nature 464:583-586.
24. Gu X, Yau ST (2008) Computational Conformal Geometry (Intl Press, Boston).
25. Gu X, Wang Y, Chan TF, Thompson PM, Yau ST (2004) Genus zero surface conformal mapping and its application to brain surface mapping. IEEE Trans Med Imaging 23:949-958.
26. Rubner Y, Tomasi C, Guibas LJ (2000) The Earth mover's distance as a metric for image retrieval. Int J Comput Vis 40:99-121. (Pubitemid 32136368)
27. Haker S, Zhu L, Tannenbaum A, Angenent S (2004) Optimal mass transport for registration and warping. Int J Comput Vis 60:225-240.
28. Dominitz A, Tannenbaum A (2010) Texture mapping via optimal mass transport. IEEE Trans Vis Comput Graph 16:419-433.
29. Mémoli F (2007) On the use of Gromov-Hausdorff distances for shape comparison. Proc Point Based Graphics, edsMBotsch, P Parajola, B Chen, andMZwicker (AK Peters, Boston), pp 81-90.
30. Lipman Y, Puente J, Daubechies I (2011) Conformal Wasserstein distances: Comparing disk and sphere-type surfaces in polynomial time II: Computational aspects. Math Comput arXiv:1103.4681.
31. Lipman Y, Funkhouser T (2009) Mobius voting for surface correspondence. ACM Trans Graph 28:72.1-12 Proc SIGGRAPH.
32. Villani C (2003) Topics in optimal transportation. Graduate Studies in Mathematics, (Am Math Soc, New Providence, RI), 58.
33. Lipman Y, Daubechies I (2011) Conformal wasserstein distances: Comparing surfaces in polynomial time. Adv Math 227:1047-1077.
34. Lipman Y, Daubechies I (2010) Surface comparison with mass transportation. arXiv:0912.3488v2.
35. Lipman Y, Al-Aifari R, Daubechies I (2011) The continuous Procrustes distance between two surfaces. Communication on Pure and Applied Mathematics arXiv:1106:4588.
36. Mémoli F (2008) Gromov-Hausdorff distances in Euclidean spaces., Computer Vision and Pattern Recognition Workshop (IEEE Computer Society); 10.1109/CVPRW.2008.4563074.
37. Moser J (1965) On the volume elements on a manifold. Trans Am Math Soc 120:286-294.
38. Mantel N (1967) The detection of disease clustering and a generalized regression approach. Cancer Res 27:209-220.
39. MacLeod N, ed. (2007) Automated Taxon Identification in Systematics: Theory, Approaches, and Applications (CRC, London) p 339.
40. MacLeod N (2008) Understanding morphology in systematic contexts: 3D specimen ordination and 3D specimen recognition. The New Taxonomy, ed Q Wheeler (CRC, London), pp 143-210.
41. Swindler (2002) Primate Dentition: An Introduction to the Teeth of Non-Human Primates (Cambridge Univ Press, Cambridge, UK) p 312.
42. Patterson C (1982) Morphological characters and homology. Systematics Association Special Volume No 21 21-74.
43. Osborn HF (1907) Evolution of Mammalian Molar Teeth: To and From the Tritubercular Type (Macmillan, New York).
44. Van Valen L (1982) Homology and causes. J Morphol 173:305-312.