Documents

39 views

Detection of 3D Geometric Distortion in MRI

Detection of 3D Geometric Distortion in MRI. Supervisor PMS: Marcel Breeuwer marcel.Breeuwer@philips.com Supervisor TU/e: Bart ter Haar Romeny B.M.terhaarRomeny@tue.nl. F.G.C.M.v.d. Heuvel s446087 F.G.C.M.v.d.Heuvel@student.tue.nl. A local estimation method. Contents. Geometric Distortion
of 64
All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Share
Transcript
Detection of 3D Geometric Distortion in MRISupervisor PMS:Marcel Breeuwermarcel.Breeuwer@philips.comSupervisor TU/e:Bart ter Haar RomenyB.M.terhaarRomeny@tue.nlF.G.C.M.v.d. Heuvels446087F.G.C.M.v.d.Heuvel@student.tue.nlA local estimation methodContents
  • Geometric Distortion
  • State of the art
  • Local Estimation
  • Mathematics
  • Software
  • Validation
  • Discussion
  • Conclusions
  • Future
  • Geometric Distortion 1/5Geometric Distortion Overview:
  • What is geometric distortion ?
  • Types
  • Causes
  • Consequences
  • Geometric Distortion 2/5What is Geometric Distortion?
  • Change of position of anatomical structures
  • Shape change of entire image (global)
  • Shape change of parts of image (local)
  • Characteristic for type of scanner
  • MRI
  • CT
  • Geometric Distortion 3/5Types of Geometric Distortion
  • Expressed as (combinations of) polynomial transformations:
  • 1th order:
  • Rigid  translation, rotation
  • Affine  shear, scaling (, mirror)
  • 2th and higher order:
  • Elastic
  • Both global and/or local
  • Geometric Distortion 4/5Causes
  • Field-in-homogeneity
  • Especially for fast scan protocols
  • Patient induced field changes
  • Watery environment in body plus ionic substances  Eddy current influence on the field
  • Geometric Distortion 5/5Consequences
  • Appearance of structure different from reality 
  • Size
  • Shape
  • Intensity
  • May lead to wrong diagnosis / therapy
  • How to solve the problem
  • State of the art:
  • Creating completely known phantom object
  • Finding transformation from un deformed data set to deformed data set
  • Estimating polynomial parameters for entire dataset  Global estimation
  • But :
  • local and sharp deformation not detected correctly
  • Therefore new approach:
  • Estimating polynomial parameters for parts of data set
  •  Local estimation
  • State of the art 1/13State of the artOverview:
  • Phantom Objects
  • Estimation method
  • Correction method
  • Advantages, Problems & restrictions
  • State of the art 2/13Phantom Objects
  • Number of reference structures with exactly known size and location
  • MR phantom
  • CT phantom
  • State of the art 3/13Phantom Objects
  • MR Phantom for body coil
  • For MR higher order polynomial  more complex structure  future
  • State of the art 4/13Phantom Objects
  • CT Phantom
  • Only up to affine transformation  simple structure
  • State of the art 5/13Phantom ObjectsSynthetically generated phantom scanBreeuwer, Holden, Zylka, Proceedings SPIE Medical Imaging, February 2001, San Diego, USAState of the art 6/13Estimation method
  • Deformation expressed as nth order polynomial transformation
  • Finding transformation for entire dataset
  •  Estimating polynomial parameters State of the art 7/13Estimation method
  • Mathematically expressed as polynomial transformation:
  • with:State of the art 8/13Estimation method
  • Transformations exists of or as combinations of :
  • Rigid:
  • Translation
  • rotation
  • Affine:
  • Scaling
  • Shear
  • Elastic: 2th and higher order transformation matrices
  • State of the art 9/13Estimation method
  • Combine all in system of equations:
  • State of the art 10/13Estimation method
  • Estimating parameters t and a’s using SVD [alg. From Num Rec in C]
  • Will be explained later on…
  • State of the art 11/13Estimation method
  • Schematic representation of estimation and correction procedure
  •  F(x)State of the art 12/13Correction method
  • find position d corresponding to x:
  • Place intensity on d at position x by means of interpolation
  • Trilinear
  • Cubic spline
  • Truncated sinc
  • State of the art 13/13Advantages, Problems & restrictions
  • Advantages
  • Simple continuous description  one polynomial transform
  • Problems & restrictions
  • Unable to describe local deformations
  • Does not work well for “exotic” global deformation fields
  • Local Estimation 1/5Local EstimationOverview:
  • Not entire 3D dataset but sub volume
  • Estimating transformation for every sub volume
  • Expected Advantages
  • Expected Disadvantages
  • Local Estimation 2/5Not entire 3D dataset but sub volume
  • Use of 3D data subsets  overlapping sub volumes
  • Local Estimation 3/5Estimating transformation for every sub volume
  • n sub volumes  n sets of polynomial parameters
  • So a system of equation for every subvolume
  • Local Estimation 4/5Expected Advantages
  • Better estimation of very local or higher-order global deformations
  • Local Estimation 5/5Expected Disadvantages
  • For every n sets of sub-volumes n polynomial estimations needed  more calculation time
  • High order  needs more memory
  • Risk of edge effects  needs large amount of patch-overlap 3Dspace
  • Mathematics 1/12MathematicsOverview:
  • Polynomial transformation
  • Used solution method for Least Squares Problem:
  • Singular Value Decomposition
  • Methods used in SVD computation:
  • Singular values σi: Householder and Givens
  • Left and right eigenvectors using the σi
  • Error calculation and testing
  • as maximum likelihood
  • fit
  • Mathematics 2/12Polynomial TransformationNumber of coordinate combinations and transformation parameters to be estimated as function of order for every volume or sub volume:Mathematics 3/12Used solution method for Least Squares Problem
  • Rewriting transformation as system of equations:
  • A: design matrix, containing the coordinate combinations
  • b: vector with deformed point coordinates
  • Mathematics 4/12Used solution method for Least Squares Problem
  • Singular Value Decomposition
  • U, V: orthogonal,left and right singular vectors resp.
  • W: diagonal matrix with singular values
  • Mathematics 5/12Methods used in SVD computation
  • Computing singular values by using:
  • Householder reduction
  • Givens Rotations
  • Left and right singular vectors
  • Mathematics 6/12Singular values 1/4Householder reduction
  • Matrix :
  • Householder matrix: with:
  • and , ith column of Using this matrix 2 times n-2 times to bi-diagonalize A.Full diagonalization by Givens Rotations:Mathematics 7/12Singular values 2/4Givens Rotations
  • Plane rotation:
  • Mathematics 8/12Singular values 3/4Givens Rotations 2/andthen:Zero by:Mathematics 9/12Singular values 4/4Givens Rotations 2/Now construction of :With elements .Mathematics 10/12Left and right singular vectors
  • Left singular vectors:
  • Right singular vector:
  • Solution:
  • Mathematics 11/12Goodness of Fit estimation
  • as maximum likelihood estimate
  • Goodness-of-Fit by means of incomplete
  • - functionMathematics 12/12Goodness of Fit estimationSolution vector using SVD tot minimize:Goodness of Fit:Chi-square exceedance by chance Software 1/3
  • Overview
  • Software 2/3
  • Estimation loop
  • Software 3/3
  • Application loop
  • Validation 1/17Validation
  • Performance of the local estimator:
  • d = deformed pointrt = retransformed point3D visualization
  • Maxima, minima, st. dev. of Euclidian distance in the patch
  • Goodness of Fit measurement
  • estimate  - fit
  • Validation 2/17Validation
  • Global up to 4th order deformation
  • Origin in center
  • Origin in corner
  • Local deformation
  • Divide space into four parts
  • Validation 3/17Global DeformationApplied to both the cornered as centered data setValidation 4/17Origin in center 1
  • 3D display:
  • Validation 5/17Origin in center 2
  • Histogram of introduced error by initial manual deformation
  • Validation 6/17Origin in center 3
  • Error histogram between initial deformed and globally re-transformed data set
  • Validation 7/17Origin in center 4
  • Error histogram between initial deformed and locally re-transformed data set
  • Validation 8/17Origin in corner 1
  • 3D display:
  • Validation 9/17Origin in corner 2
  • Histogram of introduced error by initial manual deformation
  • Validation 10/17Origin in corner 3
  • Error histogram between initial deformed and globally re-transformed data set
  • Validation 11/17Origin in corner 4
  • Error histogram between initial deformed and locally re-transformed data set
  • Validation 12/17Local Deformation
  • Space divided in four parts
  • Each part another deformation up to third order
  • Validation 13/17Local Deformation
  • Part1  Not deformed
  • Part 2  only 2th order
  • Part 3  only 3th order:
  • Part 4  2th and 3th order:
  • Validation 14/17Division in four parts
  • 3D display
  • Validation 15/17Division in four parts
  • Histogram of introduced error by initial manual deformation
  • Validation 16/17Division in four parts
  • Error histogram between initial deformed and globally re-transformed data set
  • Validation 17/17Division in four parts
  • Error histogram between initial deformed and locally re-transformed data set
  • Discussion
  • Not tested on read MRI data
  • Only a limited amount of tests performed
  • Only one type of patch
  • Only tests used with patch shifts of only 1
  • Conclusions
  • For global deformation not much difference between global and local estimation
  • For local deformation, local estimation gives better description of deformation
  • Discontinuous deformation
  • Global estimation results in very large errors
  • Local estimation also not perfect
  • Future Plans 1/2
  • Better detection of reference structure in real hardware phantom
  • Adaptation of order and patch size to type and amount of local distortion
  • Spherical subvolumes (patches) instead of cubic shaped
  • Future Plans 2/2
  • More dependence on type of deformations
  • First global estimator, then after error analysis, local estimation where necessary
  • Adapted for type of scan protocol (order & patch size)?
  • Perhaps more complex structured phantom for higher order estimation
  • Learning value
  • More business-like environment
  • More performance driven
  • First time use of real programming language  C
  • Learning to use work of other people
  • Useful to see others ideas
  • Very difficult to understand undocumented code, especially encoded mathematics
  • Questions ??
    Advertisement
    Related Documents
    View more
    Related Search
    We Need Your Support
    Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

    Thanks to everyone for your continued support.

    No, Thanks