A Challenging Example Male Pelvis –Bladder – Prostate – Rectum.

Slides:

Advertisements

Similar presentations

1 Registration of 3D Faces Leow Wee Kheng CS6101 AY Semester 1.

Advertisements

Stochastic Systems Group Some Rambling (Müjdat) and Some More Serious Discussion (Ayres, Junmo, Walter) on Shape Priors.

Independent Component Analysis Personal Viewpoint: Directions that maximize independence Motivating Context: Signal Processing “Blind Source Separation”

1/20 Using M-Reps to include a-priori Shape Knowledge into the Mumford-Shah Segmentation Functional FWF - Forschungsschwerpunkt S092 Subproject 7 „Pattern.

System Challenges in Image Analysis for Radiation Therapy Stephen M. Pizer Kenan Professor Medical Image Display & Analysis Group University.

Extended Gaussian Images

Last Time Administrative Matters – Blackboard … Random Variables –Abstract concept Probability distribution Function –Summarizes probability structure.

Provides mathematical tools for shape analysis in both binary and grayscale images Chapter 13 – Mathematical Morphology Usages: (i)Image pre-processing.

Functional Methods for Testing Data. The data Each person a = 1,…,N Each person a = 1,…,N responds to each item i = 1,…,n responds to each item i = 1,…,n.

Model: Parts and Structure. History of Idea Fischler & Elschlager 1973 Yuille ‘91 Brunelli & Poggio ‘93 Lades, v.d. Malsburg et al. ‘93 Cootes, Lanitis,

Shape and Dynamics in Human Movement Analysis Ashok Veeraraghavan.

Medial Object Shape Representations for Image Analysis & Object Synthesis Stephen M. Pizer Kenan Professor Medical Image Display & Analysis Group.

Clustering on Image Boundary Regions for Deformable Model Segmentation Joshua Stough, Stephen M. Pizer, Edward L. Chaney, Manjari Rao Medical Image Display.

Announcements Take home quiz given out Thursday 10/23 –Due 10/30.

Clustering on Local Appearance for Deformable Model Segmentation Joshua V. Stough, Robert E. Broadhurst, Stephen M. Pizer, Edward L. Chaney MIDAG, UNC-Chapel.

ANALYSIS OF A LOCALLY VARYING INTENSITY TEMPLATE FOR SEGMENTATION OF KIDNEYS IN CT IMAGES MANJARI I RAO UNIVERSITY OF NORTH CAROLINA AT CHAPEL HILL.

1 Numerical geometry of non-rigid shapes Non-Euclidean Embedding Non-Euclidean Embedding Lecture 6 © Alexander & Michael Bronstein tosca.cs.technion.ac.il/book.

Towards a Multiscale Figural Geometry Stephen Pizer Andrew Thall, Paul Yushkevich Medical Image Display & Analysis Group.

Statistics of Anatomic Geometry Stephen Pizer, Kenan Professor Medical Image Display & Analysis Group University of North Carolina This tutorial.

Introduction to Geometric Morphometrics

Gender and 3D Facial Symmetry: What’s the Relationship ? Xia BAIQIANG (University Lille1/LIFL) Boulbaba Ben Amor (TELECOM Lille1/LIFL) Hassen Drira (TELECOM.

Object Orie’d Data Analysis, Last Time OODA in Image Analysis –Landmarks, Boundary Rep ’ ns, Medial Rep ’ ns Mildly Non-Euclidean Spaces –M-rep data on.

Object Orie’d Data Analysis, Last Time

Analyzing Configurations of Objects in Images via

S. Kurtek 1, E. Klassen 2, Z. Ding 3, A. Srivastava 1 1 Florida State University Department of Statistics 2 Florida State University Department of Mathematics.

Shape Analysis and Retrieval Structural Shape Descriptors Notes courtesy of Funk et al., SIGGRAPH 2004.

Object Orie’d Data Analysis, Last Time Statistical Smoothing –Histograms – Density Estimation –Scatterplot Smoothing – Nonpar. Regression SiZer Analysis.

Enhanced Correspondence and Statistics for Structural Shape Analysis: Current Research Martin Styner Department of Computer Science and Psychiatry.

1 UNC, Stat & OR Nonnegative Matrix Factorization.

Statistics – O. R. 891 Object Oriented Data Analysis J. S. Marron Dept. of Statistics and Operations Research University of North Carolina.

Generalized Hough Transform

Forward-Scan Sonar Tomographic Reconstruction PHD Filter Multiple Target Tracking Bayesian Multiple Target Tracking in Forward Scan Sonar.

Copyright © 2010 Siemens Medical Solutions USA, Inc. All rights reserved. Hierarchical Segmentation and Identification of Thoracic Vertebra Using Learning-based.

Object Orie’d Data Analysis, Last Time Discrimination for manifold data (Sen) –Simple Tangent plane SVM –Iterated TANgent plane SVM –Manifold SVM Interesting.

1 UNC, Stat & OR Metrics in Curve Space. 2 UNC, Stat & OR Metrics in Curve Quotient Space Above was Invariance for Individual Curves Now extend to: 

1 UNC, Stat & OR Hailuoto Workshop Object Oriented Data Analysis, II J. S. Marron Dept. of Statistics and Operations Research, University of North Carolina.

GRASP Learning a Kernel Matrix for Nonlinear Dimensionality Reduction Kilian Q. Weinberger, Fei Sha and Lawrence K. Saul ICML’04 Department of Computer.

Geometric Modeling using Polygonal Meshes Lecture 3: Discrete Differential Geometry and its Application to Mesh Processing Office: South B-C Global.

Non-Isometric Manifold Learning Analysis and an Algorithm Piotr Dollár, Vincent Rabaud, Serge Belongie University of California, San Diego.

Object Orie’d Data Analysis, Last Time SiZer Analysis –Zooming version, -- Dependent version –Mass flux data, -- Cell cycle data Image Analysis –1 st Generation.

Paper Reading Dalong Du Nov.27, Papers Leon Gu and Takeo Kanade. A Generative Shape Regularization Model for Robust Face Alignment. ECCV08. Yan.

Common Property of Shape Data Objects: Natural Feature Space is Curved I.e. a Manifold (from Differential Geometry) Shapes As Data Objects.

1 UNC, Stat & OR PCA Extensions for Data on Manifolds Fletcher (Principal Geodesic Anal.) Best fit of geodesic to data Constrained to go through geodesic.

Object Orie’d Data Analysis, Last Time SiZer Analysis –Statistical Inference for Histograms & S.P.s Yeast Cell Cycle Data OODA in Image Analysis –Landmarks,

Cone-beam image reconstruction by moving frames Xiaochun Yang, Biovisum, Inc. Berthold K.P. Horn, MIT CSAIL.

1 UNC, Stat & OR ??? Place ??? Object Oriented Data Analysis J. S. Marron Dept. of Statistics and Operations Research, University of North Carolina January.

Math 285 Project Diffusion Maps Xiaoyan Chong Department of Mathematics and Statistics San Jose State University.

Auto-calibration we have just calibrated using a calibration object –another calibration object is the Tsai grid of Figure 7.1 on HZ182, which can be used.

Implicit Active Shape Models for 3D Segmentation in MR Imaging M. Rousson 1, N. Paragio s 2, R. Deriche 1 1 Odyssée Lab., INRIA Sophia Antipolis, France.

Statistical Shape Analysis of Multi-object Complexes June 2007, CVPR 2007 Funding provided by NIH NIBIB grant P01EB and NIH Conte Center MH

1 UNC, Stat & OR U. C. Davis, F. R. G. Workshop Object Oriented Data Analysis J. S. Marron Dept. of Statistics and Operations Research, University of North.

1 UNC, Stat & OR Hailuoto Workshop Object Oriented Data Analysis, I J. S. Marron Dept. of Statistics and Operations Research, University of North Carolina.

Object Orie’d Data Analysis, Last Time PCA Redistribution of Energy - ANOVA PCA Data Representation PCA Simulation Alternate PCA Computation Primal – Dual.

Classification on Manifolds Suman K. Sen joint work with Dr. J. S. Marron & Dr. Mark Foskey.

1 UNC, Stat & OR Hailuoto Workshop Object Oriented Data Analysis, III J. S. Marron Dept. of Statistics and Operations Research, University of North Carolina.

Level Set Segmentation ~ 9.37 Ki-Chang Kwak.

Anatomic Geometry & Deformations and Their Population Statistics (Or Making Big Problems Small) Stephen M. Pizer, Kenan Professor Medical Image.

SigClust Statistical Significance of Clusters in HDLSS Data When is a cluster “really there”? Liu et al (2007), Huang et al (2014)

Manifold Valued Statistics, Exact Principal Geodesic Analysis and the Effect of Linear Approximations ECCV 2010 Stefan Sommer 1, François Lauze 1, Søren.

1 UNC, Stat & OR Place Name OODA of Tree Structured Objects J. S. Marron Dept. of Statistics and Operations Research October 2, 2016.

Clustering on Image Boundary Regions for Deformable Model Segmentation Joshua Stough, Stephen M. Pizer, Edward L. Chaney, Manjari Rao, Gregg.

Landmark Based Shapes As Data Objects

Evgeny Lipovetsky School of Computer Sciences, Tel-Aviv University

Object Orie’d Data Analysis, Last Time

Unsupervised Riemannian Clustering of Probability Density Functions

Images & Objects Input Output Image Objects

Landmark Based Shape Analysis

Principal Nested Spheres Analysis

Today is Last Class Meeting

“good visual impression”

Presentation transcript:

A Challenging Example Male Pelvis –Bladder – Prostate – Rectum

A Challenging Example Male Pelvis –Bladder – Prostate – Rectum –How do they move over time (days)? (all within same person)

A Challenging Example Male Pelvis –Bladder – Prostate – Rectum –How do they move over time (days)? –Critical to Radiation Treatment (cancer)

A Challenging Example Male Pelvis –Bladder – Prostate – Rectum –How do they move over time (days)? –Critical to Radiation Treatment (cancer) Work with 3-d CT (“Computed Tomography”, = 3d version of X-ray)

A Challenging Example Male Pelvis –Bladder – Prostate – Rectum –How do they move over time (days)? –Critical to Radiation Treatment (cancer) Work with 3-d CT –Very Challenging to Segment –Find boundary of each object? –Represent each Object?

Male Pelvis – Raw Data One CT Slice (in 3d image) Like X-ray: White = Dense (Bone) Black = Gas

Male Pelvis – Raw Data One CT Slice (in 3d image) Tail Bone

Male Pelvis – Raw Data One CT Slice (in 3d image) Tail Bone Rectum

Male Pelvis – Raw Data One CT Slice (in 3d image) Tail Bone Rectum Bladder

Male Pelvis – Raw Data One CT Slice (in 3d image) Tail Bone Rectum Bladder Prostate

Male Pelvis – Raw Data Bladder: manual segmentation Slice by slice Reassembled

Male Pelvis – Raw Data Bladder: Slices: Reassembled in 3d How to represent? Thanks: Ja-Yeon Jeong

Object Representation Landmarks (hard to find)

Object Representation Landmarks (hard to find) Boundary Rep’ns (no correspondence)

Object Representation Landmarks (hard to find) Boundary Rep’ns (no correspondence) Medial representations –Find “skeleton” –Discretize as “atoms” called M-reps

3-d m-reps Bladder – Prostate – Rectum (multiple objects, J. Y. Jeong) Medial Atoms provide “skeleton” Implied Boundary from “spokes”  “surface”

3-d m-reps M-rep model fitting Easy, when starting from binary (blue)

3-d m-reps M-rep model fitting Easy, when starting from binary (blue) But very expensive (30 – 40 minutes technician’s time) Want automatic approach

3-d m-reps M-rep model fitting Easy, when starting from binary (blue) But very expensive (30 – 40 minutes technician’s time) Want automatic approach Challenging, because of poor contrast, noise, … Need to borrow information across training sample

3-d m-reps M-rep model fitting Easy, when starting from binary (blue) But very expensive (30 – 40 minutes technician’s time) Want automatic approach Challenging, because of poor contrast, noise, … Need to borrow information across training sample Use Bayes approach: prior & likelihood  posterior (A surrogate for “atomical knowledge”)

3-d m-reps M-rep model fitting Easy, when starting from binary (blue) But very expensive (30 – 40 minutes technician’s time) Want automatic approach Challenging, because of poor contrast, noise, … Need to borrow information across training sample Use Bayes approach: prior & likelihood  posterior ~Conjugate Gaussians (Embarassingly Straightforward?)

3-d m-reps M-rep model fitting Easy, when starting from binary (blue) But very expensive (30 – 40 minutes technician’s time) Want automatic approach Challenging, because of poor contrast, noise, … Need to borrow information across training sample Use Bayes approach: prior & likelihood  posterior ~Conjugate Gaussians, but there are issues: Major HLDSS challenges Manifold aspect of data

3-d m-reps M-rep model fitting Very Successful Jeong (2009)

3-d m-reps M-rep model fitting Very Successful Jeong (2009) Basis of Startup Company: Morphormics

Mildly Non-Euclidean Spaces Statistical Analysis of M-rep Data Recall: Many direct products of: Locations Radii Angles

Mildly Non-Euclidean Spaces Statistical Analysis of M-rep Data Recall: Many direct products of: Locations Radii Angles I.e. points on smooth manifold

Mildly Non-Euclidean Spaces Statistical Analysis of M-rep Data Recall: Many direct products of: Locations Radii Angles I.e. points on smooth manifold Data in non-Euclidean Space But only mildly non-Euclidean

28 UNC, Stat & OR PCA for m-reps, II PCA on non-Euclidean spaces? (i.e. on Lie Groups / Symmetric Spaces)

29 UNC, Stat & OR PCA for m-reps, II PCA on non-Euclidean spaces? (i.e. on Lie Groups / Symmetric Spaces) T. Fletcher: Principal Geodesic Analysis (2004 UNC CS PhD Dissertation)

30 UNC, Stat & OR PCA for m-reps, II PCA on non-Euclidean spaces? (i.e. on Lie Groups / Symmetric Spaces) T. Fletcher: Principal Geodesic Analysis Idea: replace “linear summary of data” With “geodesic summary of data”…

31 UNC, Stat & OR PGA for m-reps, Bladder-Prostate-Rectum Bladder – Prostate – Rectum, 1 person, 17 days PG 1 PG 2 PG 3 (analysis by Ja Yeon Jeong)

32 UNC, Stat & OR PGA for m-reps, Bladder-Prostate-Rectum Bladder – Prostate – Rectum, 1 person, 17 days PG 1 PG 2 PG 3 (analysis by Ja Yeon Jeong)

33 UNC, Stat & OR PGA for m-reps, Bladder-Prostate-Rectum Bladder – Prostate – Rectum, 1 person, 17 days PG 1 PG 2 PG 3 (analysis by Ja Yeon Jeong)

34 UNC, Stat & OR PCA Extensions for Data on Manifolds Fletcher (Principal Geodesic Anal.) Best fit of geodesic to data

35 UNC, Stat & OR PCA Extensions for Data on Manifolds Fletcher (Principal Geodesic Anal.) Best fit of geodesic to data Constrained to go through geodesic mean

36 UNC, Stat & OR PCA Extensions for Data on Manifolds

37 UNC, Stat & OR PCA Extensions for Data on Manifolds Fletcher (Principal Geodesic Anal.) Best fit of geodesic to data Constrained to go through geodesic mean But Not In Non-Euclidean Spaces

38 UNC, Stat & OR PCA Extensions for Data on Manifolds Fletcher (Principal Geodesic Anal.) Best fit of geodesic to data Constrained to go through geodesic mean Counterexample: Data on sphere, along equator

39 UNC, Stat & OR PCA Extensions for Data on Manifolds Fletcher (Principal Geodesic Anal.) Best fit of geodesic to data Constrained to go through geodesic mean Extreme 3 Point Examples

40 UNC, Stat & OR PCA Extensions for Data on Manifolds Fletcher (Principal Geodesic Anal.) Best fit of geodesic to data Constrained to go through geodesic mean Huckemann, Hotz & Munk (Geod. PCA)

41 UNC, Stat & OR PCA Extensions for Data on Manifolds Fletcher (Principal Geodesic Anal.) Best fit of geodesic to data Constrained to go through geodesic mean Huckemann, Hotz & Munk (Geod. PCA) Best fit of any geodesic to data

42 UNC, Stat & OR PCA Extensions for Data on Manifolds Fletcher (Principal Geodesic Anal.) Best fit of geodesic to data Constrained to go through geodesic mean Huckemann, Hotz & Munk (Geod. PCA) Best fit of any geodesic to data Counterexample: Data follows Tropic of Capricorn

43 UNC, Stat & OR PCA Extensions for Data on Manifolds Fletcher (Principal Geodesic Anal.) Best fit of geodesic to data Constrained to go through geodesic mean Huckemann, Hotz & Munk (Geod. PCA) Best fit of any geodesic to data Jung, Foskey & Marron (Princ. Arc Anal.)

44 UNC, Stat & OR PCA Extensions for Data on Manifolds Fletcher (Principal Geodesic Anal.) Best fit of geodesic to data Constrained to go through geodesic mean Huckemann, Hotz & Munk (Geod. PCA) Best fit of any geodesic to data Jung, Foskey & Marron (Princ. Arc Anal.) Best fit of any circle to data (motivated by conformal maps)

45 UNC, Stat & OR PCA Extensions for Data on Manifolds

46 UNC, Stat & OR Principal Arc Analysis Jung, Foskey & Marron (2011) Best fit of any circle to data Can give better fit than geodesics

47 UNC, Stat & OR Principal Arc Analysis Jung, Foskey & Marron (2011) Best fit of any circle to data Can give better fit than geodesics Observed for simulated m-rep example

48 UNC, Stat & OR Challenge being addressed

49 UNC, Stat & OR Composite Nested Spheres

50 UNC, Stat & OR Landmark Based Shape Analysis Kendall Bookstein Dryden & Mardia (recall major monographs)

51 UNC, Stat & OR Landmark Based Shape Analysis Kendall Bookstein Dryden & Mardia Digit 3 Data

52 UNC, Stat & OR Landmark Based Shape Analysis Kendall Bookstein Dryden & Mardia Digit 3 Data

53 UNC, Stat & OR Landmark Based Shape Analysis Kendall Bookstein Dryden & Mardia Digit 3 Data (digitized to 13 landmarks)

54 UNC, Stat & OR Landmark Based Shape Analysis Key Step: mod out Translation Scaling Rotation

55 UNC, Stat & OR Landmark Based Shape Analysis Key Step: mod out Translation Scaling Rotation Result: Data Objects   points on Manifold ( ~ S 2k-4 )

56 UNC, Stat & OR Landmark Based Shape Analysis Currently popular approaches to PCA on S k :  Early: PCA on projections (Tangent Plane Analysis)

57 UNC, Stat & OR Landmark Based Shape Analysis Currently popular approaches to PCA on S k :  Early: PCA on projections  Fletcher: Geodesics through mean

58 UNC, Stat & OR Landmark Based Shape Analysis Currently popular approaches to PCA on S k :  Early: PCA on projections  Fletcher: Geodesics through mean  Huckemann, et al: Any Geodesic

59 UNC, Stat & OR Landmark Based Shape Analysis Currently popular approaches to PCA on S k :  Early: PCA on projections  Fletcher: Geodesics through mean  Huckemann, et al: Any Geodesic New Approach: Principal Nested Sphere Analysis Jung, Dryden & Marron (2012)

60 UNC, Stat & OR Principal Nested Spheres Analysis Main Goal: Extend Principal Arc Analysis (S 2 to S k )