1 / 41

Geometric Morphometrics

Geometric Morphometrics. Lecturer: Dr. Keqin Wu. Feb 27, 2013 Geometric Morphology d. To do. work on programming assignment 2 Continue to think about final project Form final group. Feb 27, 2013 Geometric Morphology d. Geometric Morphology What is it?. Deals with the study of shape.

ilario
Download Presentation

Geometric Morphometrics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Geometric Morphometrics Lecturer: Dr. Keqin Wu Feb 27, 2013 Geometric Morphologyd

  2. To do • work on programming assignment 2 • Continue to think about final project • Form final group Feb 27, 2013 Geometric Morphologyd

  3. Geometric MorphologyWhat is it? • Deals with the study of shape Morphing the Armadillo model (Funck 2006) Feb 27, 2013 Geometric Morphologyd

  4. Set Operations Feb 27, 2013 Geometric Morphologyd

  5. Set Operations Feb 27, 2013 Geometric Morphologyd

  6. Set Operations

  7. Set Operations Feb 27, 2013 Geometric Morphologyd

  8. Set Operations

  9. Set Operations Feb 27, 2013 Geometric Morphologyd

  10. Set Operations

  11. Set Operations Feb 27, 2013 Geometric Morphologyd

  12. Set Operations Feb 27, 2013 Geometric Morphologyd

  13. Set Operations Feb 27, 2013 Geometric Morphologyd

  14. Set Operations Feb 27, 2013 Geometric Morphologyd

  15. Set Operations Feb 27, 2013 Geometric Morphologyd

  16. Set Operations Feb 27, 2013 Geometric Morphologyd

  17. Set Operations Feb 27, 2013 Geometric Morphologyd

  18. As-Rigid-As-Possible Shape Manipulation T. Igarashi, T. Mascovich, J. F. Hughes Presented in SIGGRAPH 2005 Feb 27, 2013 Geometric Morphologyd

  19. Feb 27, 2013 Geometric Morphologyd Feb 27, 2013 Geometric Morphologyd

  20. Feb 27, 2013 Geometric Morphologyd

  21. Feb 27, 2013 Geometric Morphologyd

  22. Feb 27, 2013 Geometric Morphologyd

  23. Feb 27, 2013 Geometric Morphologyd

  24. Demo • http://www.youtube.com/watch?v=1M_oyUEOHK8 Feb 27, 2013 Geometric Morphologyd

  25. Deformable Models in Image Analysis Feb 27, 2013 Geometric Morphologyd

  26. Mathematical Foundations • Geometry • Physics • Approximation theory Feb 27, 2013 Geometric Morphologyd

  27. Mathematical Foundations • Geometry • Broad shape coverage by employing geometric representations that involve many degrees of freedom, such as splines. • The model remains manageable because the degrees of freedom are generally not permitted to evolve independently Feb 27, 2013 Geometric Morphologyd

  28. Mathematical Foundations • Physics • The physical interpretation views deformable models as elastic bodies which respond naturally to applied forces and constraints. • The energy grows monotonically as the model deforms away from a specified natural or “rest shape” • Often includes terms that constrain the smoothness or symmetry of the model • The deformation energy gives rise to elastic forces internal to the model. Feb 27, 2013 Geometric Morphologyd

  29. Deformable model geometry • Approximation theory • In physics-based view of classical optimal approximation, external potential energy functions are defined in terms of the data of interest to which the model is to be fitted. • These potential energies give rise to external forces which deform the model such that it fits the data Feb 27, 2013 Geometric Morphologyd

  30. Image Analysis with Deformable Models • Medical image interpretation tasks include segmentation, matching, and motion analysis. Feb 27, 2013 Geometric Morphologyd

  31. Snakes: Active Contour Models (MICHAEL KASS, 1988) • A snake is an energy-minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges. • The interface allows a user to select starting points and exert forces on snakes interactively as they minimize their energy. Feb 27, 2013 Geometric Morphologyd

  32. Image Segmentation with Deformable Curve • Algorithm: • Initial Points defined around Feature to be extracted • Explicitly defined • Approximation of an Ellipse • Pre-defined number of Points generated • Points are moved through an Iterative Process • “Energy Function” for each point in the Local Neighbourhood is calculated • Move to point with lowest Energy Function • Repeat for every point • Iterate until Termination Condition met • Defined number of iterations • Stability of the position of the points Feb 27, 2013 Geometric Morphologyd

  33. Volume Image Segmentation with Deformable Surfaces • Medical image interpretation tasks including segmentation, matching, and motion analysis. • On matching deformable models to images. (D. Terzopoulos, 1986) Feb 27, 2013 Geometric Morphologyd

  34. Matching • Matching of regions in images can be performed between • the representation of a region and a model (labeling) or be- tween the representation of two distinct regions (registration). • Incorporating Priori Knowledge • Deformable atlas technique Feb 27, 2013 Geometric Morphologyd

  35. Deformable atlas technique A General Scheme for Automatically Building 3D Morphometric Anatomical Atlases: application to a Skull Atlas (Ge rard Subsol, 1995) Feb 27, 2013 Geometric Morphologyd

  36. Deformable atlas technique Feb 27, 2013 Geometric Morphologyd

  37. Deformable atlas technique Feb 27, 2013 Geometric Morphologyd

  38. Motion Tracking and Analysis • Vector Field Based Shape Deformations (Wolfram von Funck 2006) Demo Feb 27, 2013 Geometric Morphologyd

More Related