atlas-based registration and tissue segmentation

8/9/2019 Atlas-Based Registration and Tissue Segmentation

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Atlas-Based Tissue Segmentation using Low-Rank

Approaches

Tejas Sudharshan Mathai1

The Robotics Institute, Carnegie Mellon University

Abstract. Multi-modality image registration is a challenging

problem, and it becomes prooundly di!cult "hen the target

image contains large pathologies and deormations# $o"-ran%

based image registration approaches have been very successul

in multiple scenarios such as image registration, image

matching, and atlas-based tissue segmentation# In this report,

atlas-based tissue segmentation is perormed on &$'IR MRI

images# &irst, the lo"-ran% and sparse decomposition o many

&$'IR MRI images is perormed# Then, the lo"-ran% image is

registered "ith a reerence T1 MRI atlas image# &inally, the

sparse portion represents the tissue segmentation prior# The

approach is integrated into a rame"or% that perorms iterative

registration o &$'IR MRI images "ith the T1 atlas, resulting in a

pathology-ree lo"-ran% &$'IR image#

1. Introduction

It is hard to obtain a pure lesion-based segmentation rom multi-modality

images such as &$'IR or S(I# This is especially di!cult during the treatment

o patients "ith large tumors, or traumatic brain injuries, "here there is a big

deormation in brain structure# Multi-modality atlas-based image registration

can be thro"n o) in such cases due to large deormation changes# 'lso, it is

hard to generate an unbiased atlas or segmentation "ith large deormation

present in images# Thereore, it is simpler to register lo"-ran% versions o

these multi-modality images "ith a control atlas, obtain a lesion-speci*c

segmentation, and iteratively improve the segmentation# In this report, the

potential o lo"-ran% image decomposition in addressing these issues is

presented# This report ollo"s the method proposed by $iu et al, +1 and

proves the iterative use o lo"-ran% image decomposition or atlas-based

image segmentation# The iterative algorithm presented here can tolerate

large deormation and the presence o tumors in multi-modality images# It

can also promote unbiased atlas building#


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The approach ollo"ed determines the salient parts o an image that are

consistent "ith each other, and separates the noisy and unli%ely parts o the

image tumors. that do not contribute to the overall consistency o the

image# The result o the registration rame"or% is a /clean0 lo"-ran%

representation o the original input image, and a /noisy0 sparse component

that is speci*c to the lesions present in the original input#

2. ethods

2.1 Low-Rank and Sparse !ecomposition

rincipal Component 'nalysis C'. is used in the *eld o image compression

and analysis# It assumes that the given high-dimensional data can be

e2pressed in terms o a lo"er dimensional subspace, and this can be

computed e!ciently# +3 The intuition is that by estimating the lo"er

dimensional space, the error bet"een the lo"er subspace estimation and theactual data is minimi4ed#

Suppose the given data "ere to be arranged as the columns o a matri2 D 5

Rm 2 n

.The lo"er dimensional subspace can be computed by determining the

lo"-ran% matri2 L, such that the error bet"een L and D is minimi4ed# The

lo"-ran% matri2 can be e2actly recovered by solving the conve2 optimi4ation

problem6

{L, S}=argminL, S

(L+S1)s . t . D=L+S

"here is the positive "eighting parameter, . is the nuclear norm o

the matri2, and .1 is the $1 norm# The e2act lo"-ran% structure can be

obtained even in the presence o large amounts o noise or outliers, and so,

this techni7ue is called Robust C' RC'.# The RC' approach can be sped

up even urther by utili4ing the Ine2act 'ugmented $agrangian Multiplier

I'$M. method#

The idea behind the use o this approach is that the regions o the inputimage, "hich are consistent "ith each other, "ill be pushed into the lo"-ran%

orm o the image, and the portions o the image, "hich cannot be e2plained

by the lo"-ran% structure, "ill be assigned to the sparse component o the

image# The sparse component "ill represent the noisy anomalies present

"ithin the original data matri2# The linear correlation among the columns o


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the image "ill drive the provision o image intensities to each o the t"o

components6 lo"-ran% and sparse#

2.2 Iterati"e Registration #ramework

The lo"-ran% plus sparse decomposition approach has been integrated intoan iterative registration rame"or% "here an input image, possibly

containing large pathological representations, is registered "ith a normal

atlas# It is easier to achieve a registration o the lo"-ran% component "ith

the atlas, in contrast to a direct registration o the input image containing the

pathology to the atlas#

The lo"-ran% portion contains only consistent parts o the input image, and

the inconsistent regions, such as tumors, in the original input are reduced in

this lo"-ran% component# The sparse component speci*cally contains the

inconsistent regions corresponding to the tumor# The lo"-ran% componentcan serve as a prior lesion-ree map o the input, and it can help in the

segmentation o the tumor rom the original image# The algorithm can also

be used or unbiased atlas building8 or each individual input image, the lo"-

ran% plus sparse components are computed# Then, the mean o the lo"-ran%

images is obtained, and the mean image "ould represent the unbiased atlas#

The unbiased atlas "ould be pathology ree and it could serve as a normal

control atlas# It "ould help in registration o ne" input images containing

pathologies "ith the unbiased atlas# The unbiased atlas can be computed as

ollo"s6

UIA=1

ni=1n

Li

"hereL

i are the input lo"-ran% images, andUI

A is the unbiased atlas

obtained ater perorming a mean over ninput lo"-ran% images#

The iterative registration rame"or% is sho"n in *gure 1, and it is detailed as

ollo"s6

1# &or each input image, solve or the a!ne transorm registering the input

image to the atlas#

3# &or each iteration i , compute the lo"-ran% imageL

i by solving

e7uation 1#9# Solve or the :-spline transorm that registers the lo"-ran% image to the

atlas#


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;# Combine the transorms and apply them to the input image#


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&igure 3# Column 16 T1 MRI atlas image# Column 36 Input &$'IR images#

Column 96 $o"-ran% images o the input &$'IR images# Column ;6 Sparse

portion o the input &$'IR images containing most o the pathology# Column


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tissue labels on the lo"-ran% image is displayed in *gures 3, and it sho"s the

successul alignment o the lo"-ran% image "ith the atlas#

$. !iscussion

This report has detailed the algorithm that "as implemented by $iu et al# Thealgorithm is an integrated registration rame"or% that utili4ed a lo"-ran%

plus sparse matri2 decomposition method based on the I'$M-RC' matri2

recovery algorithm# The integrated registration rame"or% serves as a base

or registering an input MRI image "ith large pathology "ith an atlas, and

separating the input into t"o components6 lo"-ran% and sparse# The lo"-ran%

component consists o regions o the image that are consistent in terms o

intensity, and the sparse component consists o regions o the image that do

not correspond to the consistent salient parts o the lo"-ran% image# The

lo"-ran% representation is then registered "ith the atlas, and it can be

urther used as a prior or atlas-based tissue segmentation o the pathology

present in the input image# The algorithm also supports unbiased atlas

building rom the mean o all the lo"-ran% images# The unbiased atlas "ill be

helpul in *ne-tuning the registration o a ne" test input image "ith a large

pathology to the atlas#

Fo"ever, the algorithm that is implemented is a greedy algorithm since it

alternates bet"een lo"-ran% decomposition and registration# &uture "or%

includes the development o a non-greedy implementation o the algorithm#

Re(erences

1# $iu G#, Hiethammer M#, >"itt R#, McCormic% M#, and 'yl"ard S#6 $o"-Ran% to the Rescue

'tlas-:ased 'nalyses in the resence o athologies# In6 MICC'I 3B1;.3# $in, J#, Chen, M#, Ma, K#6 The augmented lagrange multiplier method or e2act recovery o

corrupted lo"-ran% matrices# arGiv preprint arGiv61BBL#

atlas-based registration and tissue segmentation

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