A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 1/20 Geometric Morphometrics Feb 27, 2013 Geometric Morphologyd Lecturer: Dr. Keqin Wu

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 2/20 To do work on programming assignment 2 Continue to think about final project Form final group Feb 27, 2013 Geometric Morphologyd

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 3/20 Geometric Morphology What is it? Deals with the study of shape Morphing the Armadillo model (Funck 2006) Feb 27, 2013 Geometric Morphologyd

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 4/20 Set Operations Feb 27, 2013 Geometric Morphologyd

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 5/20 Set Operations Feb 27, 2013 Geometric Morphologyd

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 6/20 Set Operations

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 7/20 Set Operations Feb 27, 2013 Geometric Morphologyd

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 8/20 Set Operations

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 9/20 Set Operations Feb 27, 2013 Geometric Morphologyd

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 10/20 Set Operations

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 11/20 Set Operations Feb 27, 2013 Geometric Morphologyd

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 12/20 Set Operations Feb 27, 2013 Geometric Morphologyd

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 13/20 Set Operations Feb 27, 2013 Geometric Morphologyd

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 14/20 Set Operations Feb 27, 2013 Geometric Morphologyd

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 15/20 Set Operations Feb 27, 2013 Geometric Morphologyd

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 16/20 Set Operations Feb 27, 2013 Geometric Morphologyd

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 17/20 Set Operations Feb 27, 2013 Geometric Morphologyd

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 18/20 As-Rigid-As-Possible Shape Manipulation T. Igarashi, T. Mascovich, J. F. Hughes Presented in SIGGRAPH 2005 Feb 27, 2013 Geometric Morphologyd

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 19/20 Feb 27, 2013 Geometric Morphologyd

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 20/20 Feb 27, 2013 Geometric Morphologyd

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 21/20

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 22/20

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 23/20 Feb 27, 2013 Geometric Morphologyd

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 24/20 Feb 27, 2013 Geometric Morphologyd

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 25/20 Feb 27, 2013 Geometric Morphologyd

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 26/20

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 27/20 Demo ch?v=1M_oyUEOHK8http:// ch?v=1M_oyUEOHK8 Feb 27, 2013 Geometric Morphologyd

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 28/20 Deformable Models in Image Analysis Feb 27, 2013 Geometric Morphologyd

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 29/20 Mathematical Foundations Geometry Physics Approximation theory Feb 27, 2013 Geometric Morphologyd

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 30/20 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

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 31/20 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

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 32/20 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

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 33/20 Image Analysis with Deformable Models Medical image interpretation tasks include segmentation, matching, and motion analysis. Feb 27, 2013 Geometric Morphologyd

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 34/20 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

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 35/20 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

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 36/20 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

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 37/20 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

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 38/20 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

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 39/20 Deformable atlas technique Feb 27, 2013 Geometric Morphologyd

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 40/20 Deformable atlas technique Feb 27, 2013 Geometric Morphologyd

A D V A N C E D C O M P U T E R G R A P H I C S CMSC 635 January 15, 2013 Quadric Error Metrics 41/20 Motion Tracking and Analysis Vector Field Based Shape Deformations (Wolfram von Funck 2006) Demo Demo Feb 27, 2013 Geometric Morphologyd