Multilevel
Segmentation and
Integrated Bayesian
Model Classification
Jason J. Corso
Postdoctoral Research Fellow
Laboratory of Neuro Imaging
Center for Computational Biology
Center for Imaging and Vision Science
Departments of Neuroscience and Statistics
University of California, Los Angeles
jcorso@ucla.edu
Motivation
Segmentation of Brain Tumor is Important but Difficult.
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Enhancement
Important
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Would quantify tumor growth.
Currently, only manual or interactive.
Aid in surgical planning.
Provide data for treatment analysis.
Difficult
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Necrosis
Ring
Glioblastoma multiforme.
Debris
Edema
Highly varying in appearance,
size and shape.
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Can deform nearby structures.
Impossible with simple thresholding.
Multiple modalities necessary.
© Jason Corso
UCLA LONI/CCB and CIVS
2
Motivation
Two Typical Examples
© Jason Corso
UCLA LONI/CCB and CIVS
3
Graph Affinity-Based Segmentation
2
case that distinct feature distributions can be learned for
heterogeneous
regions.the
To demonstrate
suchon
an application,
Define
problem
a graph:
experiment with the task of detecting and segmenting
n tumors. Our method combines
the most effective
G = two
{V,of E}
oaches to segmentation. The first approach, exemplified
are[4],sparse,
neighbors.
he work of Edges
Tu et al.
[5], usestoclass
models to
icitly represent the different heterogeneous processes. The
Eachand
pixel
voxel is aestimation
node. are
s of segmentation
class/membership
ed jointly by sampling from a posterior distribution of
ible problem
solutions. nodes,
The goal offor
thesev methods
∈ V is
Augment
ompute samples that maximize the posterior distribution,
ch is often statistics:
represented as savproduct
. distribution over Fig. 2. An example graph from brain MR showing the measurable node
rative models on sets of pixels, or segments. Hense, properties as squares and the random, model variables are circles. A 2D graph
call these methods
. type of approach is shown for presentation only; all processing occurs in 3D.
class model-based.
label: cv This
ery powerful as the samples are guaranteed to be from
atistical distribution
has beenbetween
learned from u,
training
v ∈ Vdiscuss the application of our method to the problem of
Define that
affinity
but the algorithms for obtaining these estimates are
segmenting brain tumor in multichannel MR. We describe the
paratively slow and the model choice problem is difficult.
w
=
exp
(−D(s
,
s
;
θ))
,
specific class models and probability functions used in the
uv
u
v
e techniques have been studied to improve the efficiency
experimental results.
he inference where
task, e.g. D
Swendsen-Wang
sampling
[6],
but
is some non-negative
e methods still remain comparatively inefficient.
distance function and θ are some
II. BACKGROUND
he second approach is based on the concept of normalized
predetermined
values.
[7] on graphs.
In these graph-based
methods, the input
In this section, we first make the definitions and describe
induces a sparse graph, and each edge in the graph is the notation necessary for the technical discussion. Then, we
Regions
are
cuts.
n an affinity
measurement
thatdefined
characterizesby
the cuts
similarity introduce the necessary background concepts for the use of
he two neighboring nodes in some predefined feature generative models in segmentation.
e. Cuts are sets of edges that separate the graph into
subsets, typically
analyzing
eigen-spectrum
[7],
© Jasonby
Corso
UCLA the
LONI/CCB
and CIVS
4
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Graph Affinity-Based Segmentation
Segmentation by Affinities
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Define a region saliency measure
!
u∈R,v ∈R
/
•
Γ(R) = !
wuv
.
Low Γ(R) means good saliency:
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•
u,v∈R
wuv
low affinity on boundaries,
high affinity in interior.
Normalized Cut (Shi & Malik)
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Affinities at a pixel scale only.
Can take filters of varying size
but erroneous at borders.
© Jason Corso
UCLA LONI/CCB and CIVS
5
Graph Affinity-Based Segmentation
Segmentation by Weighted Aggregation
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Invented in natural image domain by Sharon et al. (CVPR 2000, 2001).
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Affinities are calculated at each level of the graph.
First extended to medical imaging domain by Akselrod-Ballrin (CVPR 2006)
Efficient, multiscale process.
Results in a pyramid of recursively coarsened graphs that capture multiscale
properties of the data.
Statistics in each graph node are agglomerated up the hierarchy.
WU V
G1
U
sU
sV
V
puU
G0
u
su
© Jason Corso
wuv s
v
v
UCLA LONI/CCB and CIVS
6
Segmentation with Generative Models
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Define a likelihood function P ({su }|{cu }) ,
And define priors on the class labels (models): P ({cu }) .
Goal is to seek estimates of class labels that maximize the
posterior:
P ({cu }|{su }) ∝ P ({su }|{cu })P ({cu }) .
Segmentation and classification solved jointly.
Exemplified by the DDMCMC algorithm of Tu and Zhu.
4
EDEMA
NECROTIC
4
ACTIVE
NEC
EDEMA
4UMOR/UTLINE
Image From Tu et al. IJCV 2005
© Jason Corso
UCLA LONI/CCB and CIVS
4OPOLOGYWITH'RAMMATICAL2ELATIONS
Stochastic grammars are another example.
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Comparison
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Graph Affinity-Based Methods
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Rapid, feed-forward methods giving quick results.
Evidence of much power in these methods.
Not guaranteed to get meaningful answers.
Very memory intensive (especially with 3D medical data).
Model-Based MAP Methods
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Guaranteed to get answer from posterior.
Very computationally expensive.
The models are hard to design and train.
Suggests a combination of the two.
Research Agenda: leverage the efficiency of graph-based
bottom-up methods with the power and optimality of top-down
generative models.
© Jason Corso
UCLA LONI/CCB and CIVS
8
Combining Affinities and Models
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Define class dependent affinities in terms of probabilities:
P̂ (Xuv |su , sv ) = wuv .
•
Xuv is the binary event that both u and v are in the same region.
Xuv = 0
•
u
Xuv
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Xuv = 1
v
u
is not deterministic on class labels (cu , cv ):
v
pixels in same region may have different labels,
pixels in different regions may have same labels.
© Jason Corso
UCLA LONI/CCB and CIVS
9
Combining Affinities and Models
The Conventional Affinity Function
wuv = exp (−D(su , sv ; θ))
© Jason Corso
UCLA LONI/CCB and CIVS
10
Combining Affinities and Models
Model-Aware Affinity
Node Likelihoods
Model Specific
Measurements
The node likelihoods weigh the model specific measurements.
© Jason Corso
UCLA LONI/CCB and CIVS
11
Combining Affinities and Models
Model-Aware Affinity
•
Treat class labels as hidden variables and sum them out:
P (Xuv |su , sv ) =
∝
=
!!
cu
cv
!!
cu
cv
!!
cu
cv
P (Xuv |su , sv , cu , cv )P (cu , cv |su , sv ) ,
P (Xuv |su , sv , cu , cv )P (su , sv |cu , cv )P (cu , cv ) ,
P (Xuv |su , sv , cu , cv )P (su |cu )P (sv |cv )P (cu , cv ) .
Model Specific Measurement
© Jason Corso
UCLA LONI/CCB and CIVS
Node Likelihoods
Class Prior
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Combining Affinities and Models
Model-Aware Affinity
!
"
P (Xuv |su , sv , cu , cv ) = exp −D (su , sv ; θ[cu , cv ])
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Defined as a function of class label pairs θ[cu , cv ] .
Suitable for heterogeneous data.
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Model-aware affinities modulated by evidence:
P (su |cu ) .
At pixel scales, evidence for any class is low.
At coarser scales, evidence is high and models improve affinities.
© Jason Corso
UCLA LONI/CCB and CIVS
13
Segmentation by Weighted Aggregation
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Overview
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Multiscale graph-based algorithm.
Inspired by methods in Algebraic Multigrid.
First extended to 3D medical domain by Akselrod-Ballrin (2006)
Again, define a graph Gt = (V t , E t )
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Superscript denotes level in a pyramid of graphs
Finest layer induced by voxel lattice
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G = {G : t = 0, . . . , T }
t
6-neighbor connectivity
sv set according to multimodal image intensities.
Affinities initialized by L1-distance: wuv = exp (−θ |su − sv |1 ) .
Node properties
G0
u
su
© Jason Corso
wuv s
v
v
UCLA LONI/CCB and CIVS
14
Segmentation by Weighted Aggregation
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Select a representative set of nodes satisfying
!
v∈Rt
•
wuv ≥ β
!
wuv
v∈V t
i.e., all nodes in finer level have strong affinity to nodes in coarser.
G0
u
su
© Jason Corso
wuv s
v
v
UCLA LONI/CCB and CIVS
15
Segmentation by Weighted Aggregation
•
Select a representative set of nodes satisfying
!
v∈Rt
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wuv ≥ β
!
wuv
v∈V t
i.e., all nodes in finer level have strong affinity to nodes in coarser.
Begin to define graph G = (V , E )
1
G
1
1
1
G0
u
su
© Jason Corso
wuv s
v
v
UCLA LONI/CCB and CIVS
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Segmentation by Weighted Aggregation
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Compute interpolation weights between coarse and fine levels
puU = !
wuU
V ∈V t+1
G
1
U
wuV
V
puU
G0
u
su
© Jason Corso
wuv s
v
v
UCLA LONI/CCB and CIVS
17
Segmentation by Weighted Aggregation
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Compute interpolation weights between coarse and fine levels
puU = !
wuU
V ∈V t+1
wuV
Accumulate statistics at the coarse level
sU =
!
u∈V t
G
1
U
sU
puU su
"
v∈V t pvU
sV
V
puU
G0
u
su
© Jason Corso
wuv s
v
v
UCLA LONI/CCB and CIVS
18
Segmentation by Weighted Aggregation
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Interpolate affinity from finer levels
ŵU V =
!
puU wuv pvV
(u!=v)∈V t
G
1
U
sU
ŵU V
sV
V
puU
G0
u
su
© Jason Corso
wuv s
v
v
UCLA LONI/CCB and CIVS
19
Segmentation by Weighted Aggregation
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Interpolate affinity from finer levels
ŵU V =
!
puU wuv pvV
(u!=v)∈V t
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Use coarse affinity to modulate the interpolated affinity
WU V = ŵU V exp (−D(sU , sV ; θ))
WU V
G
1
U
sU
sV
V
puU
G0
u
su
© Jason Corso
wuv s
v
v
UCLA LONI/CCB and CIVS
20
Segmentation by Weighted Aggregation
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Repeat ...
WU V
G
1
U
sU
sV
V
puU
G0
u
su
© Jason Corso
wuv s
v
v
UCLA LONI/CCB and CIVS
21
Segmentation by Weighted Aggregation
Incorporating Model-Aware Affinities
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Alter the way coarse affinities are modulated.
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Change to
Currently
WU V = ŵU V exp (−D(sU , sV ; θ)) .
WU V = ŵU V P (XU V |sU , sV ) .
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Associate the most-likely class with each node:
∗
cU
© Jason Corso
= arg max P (sU |c) .
UCLA LONI/CCB and CIVS
c∈C
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Example of the Segmentation Pyramid
© Jason Corso
UCLA LONI/CCB and CIVS
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Extracting Information from the Hierarchy
The Problem:
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Gives hierarchy, need final answer.
Original SWA suggests saliency.
Model information provides more
information for extraction.
Current Model-Based Extraction
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Compute class for each voxel for
each level in the pyramid.
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Use interpolation weights.
Accumulate class membership.
Assign class the voxel was for most
of the levels.
© Jason Corso
UCLA LONI/CCB and CIVS
24
Extracting Information from the Hierarchy
Energy Based Methods -- Saliency Only
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Treat hierarchy as an input datum to a minimizer.
Define a set of level variables {lv }, v ∈ V over voxel lattice.
A final segmentation is induced by an instance.
Hs ({l}) = α1
!
(li )
Γ(vi )
{i}
− α2
“External” Potential
•
!
1 (li = lj )
<i,j>
Pair Potential
Can be minimized various techniques
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Formulate as Gibbs Field and use simulated annealing.
Use popular min-cut/max-flow graph cuts method.
© Jason Corso
UCLA LONI/CCB and CIVS
25
Extracting Information from the Hierarchy
Energy Based Methods -- Model-Based
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Models provide stronger information for extraction.
Define a set of model variables {mv }, v ∈ V over voxel lattice.
Bayesian estimate of model likelihood over hierarchy:
!
P (mi , ŝi ) =
P (ŝi , mi , t)
t={0,...,T }
!
=
t={0,...,T }
P (sv(t) |mi )E(ŝi , t)
i
• E(ŝi , t) is level evidence, computed by entropy of likelihood dist:
#
exp −κ m∈M P (sv(t) |m) ln P (sv(t) |m)
i
i
!
#
E(ŝi , t) = "
"
z={0,...,T } exp −κ
m∈M P (sv (z) |m) ln P (sv (z) |m)
!
"
i
© Jason Corso
UCLA LONI/CCB and CIVS
i
26
Extracting Information from the Hierarchy
Energy Based Methods -- Model-Based
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Define a similar Potts-type energy model:
Hm (M) = −α1
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!
{i}
P (mi , ŝi ) − α2
!
1 (mi = mj )
<i,j>
Use energy minimization or stochastic optimization techniques
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Min-flow/max-cut methods.
Simulated annealing on Gibbs field:
!
"
1
ΠM (M) = exp −τ H({l})
Z
Swendseng-Wang cuts similar to Barbu and Zhu.
© Jason Corso
UCLA LONI/CCB and CIVS
27
Extracting Information from the Hierarchy
Activate Top-Down Generative Models
Treat the hierarchy as a set of model “proposals.”
Becomes plausible to use global object properties (e.g., shape).
Towards a comprehensive medical image parsing framework.
Keys to making these methods more robust and efficient.
Integrate Top-Down Generative Models
Drive hierarchical agglomeration by the top-down models.
Need to define a new multiscale generative model incorporating
appearance and shape properties.
New learning algorithms for the models and agglomeration.
© Jason Corso
UCLA LONI/CCB and CIVS
28
Application
Brain Tumor
Segmentation
On theto
Dimensionality
of Enhancing
Brain Tumor Appearance in
Multimodal MR Images
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Jason J. Corso PhD
Informatics, multiforme
University of California,
Los Angeles, CA 90024
DatasetMedical
of 20Imaging
glioblastoma
patients.
3D, 256x256x25.
Images
Pre-processed:
Abstract
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noise
Medical removal
data presents complex high dimensional signals to the informatician. Understanding this data is
skull
removal
paramount
to achieving robustness and efficiency in the
solution to many medical informatics problems. In this
spatial
registration
paper, we perform a statistical analysis of the appearance of brain standardization.
tumor and edema. A maximum
intensity
likelihood and minimum description length methodology is
adopted
using mixture models to capture the distribuUse
4 modalities
tions. The data consists of 30 manually contoured enhancing
tumor studies analyzed
both inT2.
single
T1,
T1brain
w/contrast,
Flair, and
modalities and jointly in four modalities.
•
Expert
annotated.
1 Introduction
Understanding
the data isprovided
paramount to achieving
Data
graciously
by robustness and efficiency in the solution to many medDr.
Cloughesy
UCLA
Henry
ical informatics
problems.ofEven
though medical
data E.
Figure 1: Example slices for brain tumor (left-column)
is
typically
constrained
due
to
the
domain,
be
it
natSingleton
Brain Cancer Research and
Program
edema (right-column).
ural language reports, imaging studies, intra-operative
(swelling).
Multiple
modalities are necessary to
video preprocessed
recordings, or doctor-patient
it can be
and
byqueries,
Shishir
Dubeedema
using
FSL
tools.
very complex and sampled from some unknown highdimensional, qualitative or quantitative space. Studying the underlying statistics of this data is important not
in Corso
its own right,
also because
of the potential
©only
Jason
UCLAbut
LONI/CCB
and CIVS
perform a full analysis of the imaging study: the T1
modality with a contrast agent (referred to as T1 Post)
is typically used to discriminate enhancing tumor regions from normal brain, and T2 or FLAIR modality is
29
Model-Aware Affinity and Class Prior
•
For model-aware affinity, use class-dependent weighted distance:
!
P (Xuv |su , sv , cu , cv ) = exp −
•
Coefficients
θcmu cv
θcmu cv
m=1
# m
#
#su − sm
#
v
.
7
are set based on expert, domain knowledge.
!!
!! m
T1
cu , cv !!!
!
ND, Brain
Brain, Brain
Brain, Tumor
Tumor, Tumor
Brain, Edema
Tumor, Edema
Edema, Edema
•
•
M
"
$
1/4
1/4
0
0
0
0
0
T1CE
FLAIR
T2
1/4
1/4
1
1
0
1/2
0
1/4
1/4
0
0
1/2
1/4
1/2
1/4
1/4
0
0
1/2
1/4
1/2
TABLE I
Feature statistic is simply average intensity.
C OEFFICIENTS USED IN MODEL - AWARE AFFINITY CALCULATION . ROWS
The class prior term
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ARE ( SYMMETRIC ) CLASS PAIRS AND COLUMNS ARE MODALITIES .
encodes obvious hard constraints (e.g. tumor cannot be next to non-data),
remaining set to uniform.
© Jason Corso
UCLA LONI/CCB and CIVS
30
Class Likelihood Model
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Each class is modeled with a
Gaussian mixture model.
•
Likelihood is computed directly
against this model.
•
!!
For some structures more node
statistics must be used:
•
•
•
•
!
cu , c v
ND
Brai
Brain
Tumo
Brain
Tumo
Edem
T1
T2
FLAIR
T1CE
C OEFFICIENTS U
ARE ( SYMMET
(a) Tumor Class
E. Implementa
Shape moments
Surface curvature
Location
T1
Relational
T2
FLAIR
T1CE
(b) Edema Class
Fig. 5.
Class intensity histograms in each channel independently.
D. Model-Aware Affinity Definition
© Jason Corso
UCLA LONI/CCB and CIVS
For the model-aware affinity term (5), we use a class
dependent weighted distance:
The multilev
weighted aggre
#
input pixels (#V
model-aware a
the number of
typically small
not greatly affe
However, the
rithm is great. T
typically numb
cuts the numbe
is maintaining
is huge, even i
al. [11] give su
In our implem
buffer to store t
hierarchy.
The algorith
native bindings
31
Example of the Segmentation Pyramid
© Jason Corso
UCLA LONI/CCB and CIVS
32
Example of the Segmentation Pyramid
Caudate
4
5
6
7
8
9
10
11
12
Ventricle
Putamen
Can see the relevant structures emerging.
Preliminary results from sub-cortical project (began Sept. 2006).
© Jason Corso
UCLA LONI/CCB and CIVS
33
Example of the Segmentation Pyramid
5
6
7
8
Hippocampus
Hard to segment structures emerging too.
© Jason Corso
UCLA LONI/CCB and CIVS
34
Quantitative Results
Volume Overlap Comparison
Algorithm
Single Voxel Classifier
Saliency-Based Extractor
Model-Based Extractor
Algorithm
Single Voxel Classifier
Saliency-Based Extractor
Model-Based Extractor
Results on Training Set
Tumor
Jac
Prec
Rec
42% 48%
85%
44% 51%
64%
62% 75%
81%
Results on Testing Set
Tumor
Jac
Prec
Rec
49% 55%
81%
48% 61%
63%
66% 80%
79%
8
Jac
43%
47%
54%
Edema
Prec
49%
55%
66%
Rec
78%
76%
72%
Jac
56%
56%
61%
Edema
Prec
66%
66%
78%
Rec
76%
71%
71%
TABLE II
VOLUME OVERLAP RESULTS ( MEAN SCORES ).
© Jason Corso
UCLA LONI/CCB and CIVS
35
Quantitative
Results
Fig. 8. Example hierarchy on image TE01 from the test set. The top row is comprised of the
Volume Measurement
Study ID
TR01
TR02
TR03
TR04
TR05
TR06
TR07
TR08
TR09
TR10
TE01
TE02
TE03
TE04
TE05
TE06
TE07
TE08
TE09
TE10
Tumor
Truth
Auto
93335
79894
17344
12516
71211
30769
798
1552
25411
34776
7643
13826
31829
34699
24594
26570
64486
79718
220243
227251
24851
38817
54352
51054
46651
41242
10499
8177
46783
57454
41395
39328
36826
24079
52256
39348
16503
19989
95422
92311
mm III
TABLE
Edema
Truth
Auto
138972
151524
20709
38145
122168
188732
10143
11730
122829
118247
10768
16470
34733
38670
134487
162264
253682
268981
90120
36970
262421
213046
171869
153000
65919
70784
81740
74495
101198
84437
37355
29709
72625
36251
140799
146390
220270
241509
183315
186080
Stu
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
T
3
© Jason Corso
UCLA LONI/CCB and CIVS
36
Quantitative
Results
t. The top row is comprised of the following channels: T1, T1 with contrast, FLAIR, and T2.
Surface Measurement
Auto
1524
8145
8732
1730
8247
6470
8670
2264
8981
6970
3046
3000
0784
4495
4437
9709
6251
6390
1509
6080
Study ID
TR01
TR02
TR03
TR04
TR05
TR06
TR07
TR08
TR09
TR10
TE01
TE02
TE03
TE04
TE05
TE06
TE07
TE08
TE09
TE10
© Jason Corso
Tumor
Mean
Median
1.23
0
7.73
0
3.71
1.8
5.11
0.86
1.56
0
7.63
1.22
10.28
0
1.17
0
4.11
0
0.68
0
29.97
0.78
1.56
0
1.12
0
0.39
0
1.02
0
0.74
0
20.23
2.32
2.23
0
2.14
0
4.54
0
UCLA LONI/CCB and CIVS
mm IV
TABLE
Edema
Mean
Median
1.01
0
76.40
97.68
3.03
0
1.95
0
0.56
0
13.60
6.5
7.02
0
1.12
0
0.71
0
5.57
1.72
2.52
0
2.49
0
0.54
0
1.24
0
0.77
0
19.69
26.78
10.25
1.83
1.63
0
2.04
0
3.36
0
37
Classification Comparison
2
3
4
5
6
Models
Saliency
Single
Voxel
Manual
1
© Jason Corso
UCLA LONI/CCB and CIVS
38
Classification Comparison
8
9
10
11
Models
Saliency
Single
Voxel
Manual
7
© Jason Corso
UCLA LONI/CCB and CIVS
39
Results
Comparing SWA with Model-Aware Affinities to Original SWA
Model-Aware
Original
© Jason Corso
UCLA LONI/CCB and CIVS
40
Implementation Details
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Built with Java and Swing.
Uses ImageIO: supports many image formats using the LONI
medical image plugins.
Developed new core data structures to support transparent outof-core data manipulation, which is often necessary when
working with medical imaging (especially hierarchical).
Developed with principled OO techniques:
Polymorphic Model-Class design for “plug-and-play” affinity
function and likelihood measurements based on specific
application.
Design patterns to make it easy to generate an application
specific segmentation algorithm built with atop same core
software.
Computational time: 90x60x90 volume segmented in about 2
minutes on a 2Ghz PowerPC G5.
Extraction time depends on method.
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© Jason Corso
UCLA LONI/CCB and CIVS
41
Results - Tool for Interactive Analysis Using Models
Select Slices to View (3 axes)
Select Modality
Axial
Sagittal
Select
Hierarchy Level
Select
Transparency
Overlay Manual
Contours
© Jason Corso
UCLA LONI/CCB and CIVS
Coronal
3D
Rendering
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Conclusions
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Main contribution:
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Classes as hidden variables for bridging graph-based affinities and modelbased techniques.
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Incorporated into the SWA algorithm.
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Software contribution:
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Computational time: 90x60x90 volume segmented & classified in
about 2 minutes on a PowerPC G5 (in Java).
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A complete system for experimenting with the Bayesian computational
methods, including learning, segmentation, visualization, and analysis.
Future:
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Better models with more feature statistics,
Learning the model-aware affinity class dependent parameters,
Leverage the efficiency of graph-based bottom-up methods with the
comprehensive and optimality of top-down generative models.
Thanks for listening.
© Jason Corso
UCLA LONI/CCB and CIVS
43
Acknowledgements
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Funding by NLM Medical Informatics Training Grant #LM07356
and NIH NCBC Center for Computational Biology (LONI).
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Dr. Cloughesy of the Henry E. Singleton Brain Cancer Research
Program, University of California, Los Angeles, for providing the
data.
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Shishir Dube for helping with and performing the data
preprocessing.
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Drs. Yuille, Sharon, Taira and Sinha for guidance.
© Jason Corso
UCLA LONI/CCB and CIVS
44
Research Overview
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Concepts
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Automatic Knowledge discovery
Domain expert knowledge
Models
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Statistical
Learning
Bayesian methodology (generative modeling)
Manual creation
Model discovery (e.g. learning grammars, manifold learning)
Inference
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Estimate the models (find instances of the concepts) in data
Efficient and robust
Integrate bottom-up, feed-forward with top-down models
Applications
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Medical Informatics
Surgical planning
Various related biomedical application (e.g. tissue microarrays)
© Jason Corso
UCLA LONI/CCB and CIVS
45