COMP 790-06 Shape Representation & Statistics

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Lecture Recordings

Lecture 1

Course Overview, Both Administratively and Contents

Lecture 2

Course Overview Concl., Shape Representations through Points and Normals

Lecture 3

Skeletal and Diffeomorphism Shape Representations, Local Surface Curvatures

Lecture 4

Object Topology, Curve Geometry, Shape Spaces, Alignmen

Lecture 5

Metric Tensor, Best Ellipsoid, PCA, Principal Nested Sphere

Lecture 6

Statistics on Other Manifolds, Spherical Harmonics (suspended due to technical difficulties)

Lecture 7

Spherical Harmonics, Correspondence, Thin-Plate Splines, Diffeomorphism Optimization

Lecture 8

Correspondence by Diffeomorphisms, by Skeletal Models. Shape Distances Modulo Reparametrizations and Alignment Group

Lecture 9

Surface representations Modulo Correspondence, Blum Medial Geometry in 2D and 3D.

Lecture 10

Radial Geometry, incl. Radial Coordinate System. Diffeomorphism From Ellipsoid

Lecture 11

Skeletal Coordinates and Fitted Frames. Diffeomorphisms from Ellipsoid to Objects

Lecture 12

S-reps, Fitting to Boundaries, Multi-Object S-reps

Lecture 13

Paul Yushkevich, Cm-reps, PDE Approach and Applicatons

Lecture 14

Paul Yushkevich, Cm-reps, Medially-Guided Deformation Approach and Application

Lecture 15

Multi-Figure S-reps, Swept-Plane S-reps, Straightening S-reps, Finite Element Modeling Via S-reps

Lecture 16

Tom Fletcher: regression on manifolds: pseudo-linear, pseudo-polynomial, pseudo-kernel, pseudo-longitudinal

Lecture 17

Shape stats topics overview, means and spread measures on manifolds

Lecture 18

Means, modes, principal variances, entropy on manifolds, incl. HDLSS, intro to segmentation by posterior optimization

Lecture 19

Image intensity and shape analysis stats, quantile function statistics, # of eigenmodes to use, Marchenko-Pastur analysis

Lecture 20

Gaussians, Hypothesis testing by permutation tests: on single features, on multiple GOPs

Lecture 21

Hypothesis testing on multiple shape features. ROC and area under ROC (AUC)

Lecture 22

Improvement on method for hypothesis testing on shape features, AUC production, classification methods producing separating directions: SVM and DWD

Lecture 23

Generalization and specificity of estimated pdf’s, multi-entity statistical analysis

Lecture 24.

Multi-entity statistical analysis, concl. Longitudinal shape statistics

Lecture 25

Course Summary pt 1

Lecture 26

Course Summary pt 2

PDFs of the Slide Deck:

1.Course Overview

2.shape reps overview

3. Math

4. statistics on pdms

5. Non-pdm repesentaions

6. Statistics of shape

7. Other shape representations

course summary