Outline
Motivation and Problem Definition
Deterministic Perspective
Stochastic Perspective
Summary
Location Prediction of Moving Target
Dan Ruan
Department of Radiation Oncology
Stanford University
AAPM 2009
Dan Ruan
Prediction
Outline
Motivation and Problem Definition
Deterministic Perspective
Stochastic Perspective
Summary
Outline of Topics
1 Motivation and Problem Definition
Motivation
Problem Description
Two Perspectives
Dan Ruan
Prediction
Outline
Motivation and Problem Definition
Deterministic Perspective
Stochastic Perspective
Summary
Outline of Topics
1 Motivation and Problem Definition
Motivation
Problem Description
Two Perspectives
2 Deterministic Perspective
Sample Path Estimation via Motion Modeling
Deterministic regression
Dan Ruan
Prediction
Outline
Motivation and Problem Definition
Deterministic Perspective
Stochastic Perspective
Summary
Outline of Topics
1 Motivation and Problem Definition
Motivation
Problem Description
Two Perspectives
2 Deterministic Perspective
Sample Path Estimation via Motion Modeling
Deterministic regression
3 Stochastic Perspective
Estimation of Stochastic Process
Stochastic Regression: Recent Development
Dan Ruan
Prediction
Outline
Motivation and Problem Definition
Deterministic Perspective
Stochastic Perspective
Summary
Outline of Topics
1 Motivation and Problem Definition
Motivation
Problem Description
Two Perspectives
2 Deterministic Perspective
Sample Path Estimation via Motion Modeling
Deterministic regression
3 Stochastic Perspective
Estimation of Stochastic Process
Stochastic Regression: Recent Development
4 Summary
Disclaimer: unless indicated otherwise, the views in this talk represent
personal opinion, not an official statement of AAPM or Stanford
University.
Dan Ruan
Prediction
Outline
Motivation and Problem Definition
Deterministic Perspective
Stochastic Perspective
Summary
Motivation
Problem Description
Two Perspectives
Outline
1 Motivation and Problem Definition
Motivation
Problem Description
Two Perspectives
2 Deterministic Perspective
Sample Path Estimation via Motion Modeling
Deterministic regression
3 Stochastic Perspective
Estimation of Stochastic Process
Stochastic Regression: Recent Development
4 Summary
Dan Ruan
Prediction
Outline
Motivation and Problem Definition
Deterministic Perspective
Stochastic Perspective
Summary
Motivation
Problem Description
Two Perspectives
Motivation
• Adaptive therapy with online motion compensation
At each time instant, requires
Target localization ⇒ Treatment adaptation.
• System latency is ubiquitous: necessitates prediction (estimation
with delayed observations).
[Motion Monitoring + Prediction] ⇒ Treatment adaptation
• From a filtering perspective, prediction (extrapolation) is a
viable option for handling asynchronous multiple observation
streams in hybrid systems.
Dan Ruan
Prediction
Outline
Motivation and Problem Definition
Deterministic Perspective
Stochastic Perspective
Summary
Motivation
Problem Description
Two Perspectives
Problem description
Observation Event I
Observation Event II
Processing I
Observation Event III
Processing III
Processing II
Treatment II
Treatment I
Treatment III
Time
System Latency
Observation Interval
Goal: given an observed sample path {si }K
i=1 , to causally estimate
the underlying state sK +L at a future time (times).
Talk will focus on intra-fraction respiratory motion, idea generalizes.
Dan Ruan
Prediction
Outline
Motivation and Problem Definition
Deterministic Perspective
Stochastic Perspective
Summary
Motivation
Problem Description
Two Perspectives
Key factors
observation (sample path) mode - usually discrete {si }.
◦ sampling pattern (uniform v.s. non-, rate)
◦ uncertainty
◦ missing samples/outliers? detectable?
prediction requirement:
◦ setup: prediction horizon pattern (fixed length, varying,
continuous)
◦ accuracy requirement
state definition:
◦ instantaneous target dynamics (location, velocity, etc.,
with possibly categorical classification).
◦ instantaneous anatomical configuration.
Dan Ruan
Prediction
Outline
Motivation and Problem Definition
Deterministic Perspective
Stochastic Perspective
Summary
Motivation
Problem Description
Two Perspectives
Two perspectives
• Deterministic perspective
Consider the underlying state as deterministic unknown ⇒
estimate its value , explicitly seek ŝ.
◦ sample path modeling: most intuitive.
◦ deterministic regression: estimates a deterministic
input/output map from the observed portion of sample path.
Dan Ruan
Prediction
Outline
Motivation and Problem Definition
Deterministic Perspective
Stochastic Perspective
Summary
Motivation
Problem Description
Two Perspectives
Two perspectives
• Deterministic perspective
Consider the underlying state as deterministic unknown ⇒
estimate its value , explicitly seek ŝ.
◦ sample path modeling: most intuitive.
◦ deterministic regression: estimates a deterministic
input/output map from the observed portion of sample path.
• Stochastic perspective
Consider the underlying state as stochastic unknown ⇒
estimate its distribution.
◦ random process modeling: most stochastic filtering
schemes
◦ ...
Dan Ruan
Prediction
Outline
Motivation and Problem Definition
Deterministic Perspective
Stochastic Perspective
Summary
Motivation
Problem Description
Two Perspectives
Categorization of Prediction Schemes
Sample Path Est.
Deterministic
Stochastic
Dan Ruan
Prediction
Regression
Outline
Motivation and Problem Definition
Deterministic Perspective
Stochastic Perspective
Summary
Motivation
Problem Description
Two Perspectives
Categorization of Prediction Schemes
Sample Path Est.
Deterministic
Stochastic
Cosine, Fourier, Wavelet,
Piecewise Linear, ARMA
Stochastic filter,
KF, PF
Dan Ruan
e.g.,
Prediction
Regression
ANN, SVM, LOESS
...
Outline
Motivation and Problem Definition
Deterministic Perspective
Stochastic Perspective
Summary
Sample Path Estimation via Motion Modeling
Deterministic regression
Outline
1 Motivation and Problem Definition
Motivation
Problem Description
Two Perspectives
2 Deterministic Perspective
Sample Path Estimation via Motion Modeling
Deterministic regression
3 Stochastic Perspective
Estimation of Stochastic Process
Stochastic Regression: Recent Development
4 Summary
Dan Ruan
Prediction
Outline
Motivation and Problem Definition
Deterministic Perspective
Stochastic Perspective
Summary
Sample Path Estimation via Motion Modeling
Deterministic regression
Sample path estimation via motion modeling
• Sample path modeling: generally seeks a complete
temporal-spatial description of the underlying evolving state by
modeling the feasible sample path.
Any method that reminds you of a sketching procedure...
• Major playground: representation
e.g. modified cosine model[Lujan 94], local linear model[Wu 04],
wavelet + AR[Ernst 07], real-time profiling[Ruan 09]
Dan Ruan
Prediction
Outline
Motivation and Problem Definition
Deterministic Perspective
Stochastic Perspective
Summary
Sample Path Estimation via Motion Modeling
Deterministic regression
Local linear representation
• A normal breathing cycle is decomposed into three stages:
inhale(IN), exhale(EX), and end of exhale (EOE).
• Periodic progression in/out of each linear segment is modeled
with a discrete set of rules, local parameters estimated.
• Potential local continuous prediction capability.
Dan Ruan
Prediction
Outline
Motivation and Problem Definition
Deterministic Perspective
Stochastic Perspective
Summary
Sample Path Estimation via Motion Modeling
Deterministic regression
Profiling representation
• The observations are considered as noisy discrete samples from
a periodic shape subject to phase warping and baseline drift.
si = [fT (φ(t)) + b(t) + w (t)]|t=ti .
• The online profiling system estimates the instantaneous shape
fT , phase warping φ (thus frequency variation) and baseline
drift b in real-time.
Dan Ruan
Prediction
Outline
Motivation and Problem Definition
Deterministic Perspective
Stochastic Perspective
Summary
Sample Path Estimation via Motion Modeling
Deterministic regression
Profiling schematic
• robust to nonuniform samples, high observation noise, outliers.
• provides functional descriptor with natural continuous horizon
prediction.
Dan Ruan
Prediction
Outline
Motivation and Problem Definition
Deterministic Perspective
Stochastic Perspective
Summary
Sample Path Estimation via Motion Modeling
Deterministic regression
Profiling applied to prediction (cont.)
10
8
6
5
displacement
displacement
4
0
−5
2
0
−2
−4
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−10
−8
−15
0
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Time (sec)
20
25
−10
0
30
5
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Time (sec)
20
25
30
5
10
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Time (sec)
20
25
30
20
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15
10
displacement
displacement
10
5
0
5
0
−5
−5
−10
−10
0
−15
5
10
15
Time (sec)
20
25
30
0
available observation, unknown observation, prediction with profiling
extrapolation.
Dan Ruan
Prediction
Outline
Motivation and Problem Definition
Deterministic Perspective
Stochastic Perspective
Summary
Sample Path Estimation via Motion Modeling
Deterministic regression
Profiling applied to prediction
6
2
4
−2
displacement
displacement
0
−4
−6
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0
−2
−4
−10
−12
0
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−6
5
10
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Time (sec)
20
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0
30
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Time (sec)
20
25
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Time (sec)
20
25
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5
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0
displacement
displacement
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0
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−10
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−15
−20
−20
0
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15
Time (sec)
20
25
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−25
0
5
10
available observation, unknown observation, prediction with profiling
extrapolation.
Dan Ruan
Prediction
Outline
Motivation and Problem Definition
Deterministic Perspective
Stochastic Perspective
Summary
Sample Path Estimation via Motion Modeling
Deterministic regression
Deterministic regression for state prediction
• Location prediction with deterministic regression: assumes a
consistent relationship between a recent observed temporal
segment and the state after a fixed latency. The goal is to
estimate such a consistent map.
Any method that deterministically “learns” from input-output
pairs.
• Major playground: functional approximation and estimation.
e.g. LOESS [Ruan 06], ANN[Murphy 06], SVM[Ernst 08], ANFIS
[Kakar, 05]
Dan Ruan
Prediction
Outline
Motivation and Problem Definition
Deterministic Perspective
Stochastic Perspective
Summary
Sample Path Estimation via Motion Modeling
Deterministic regression
Generating input-output pairs for regression
Lookahead Length
Response
Unavailable
Current SK
Delay SK−∆
250
1
200
0.8
150
0.6
100
0.4
50
0
0
0.2
2
4
6
8
10
Time (seconds)
12
14
16
Regression Weights
Distance in State Space
Current State xK
Actual yK
(unavailable)
0
18
Dan Ruan
• input
xi = [si−(p−1)∆ , . . . , si−∆ , si ],
concatenation of p delayed
samples
• output yi = si+L , discrete lag L
corresponds to prediction length
• With most current sample sK ,
training set {(xi , yi )}i<K −L .
Testing input: xK , want ŷK .
• Goal: learn map g : <p → <,
y ≈ g (x) from training set,
especially around input xK .
Prediction
Outline
Motivation and Problem Definition
Deterministic Perspective
Stochastic Perspective
Summary
Sample Path Estimation via Motion Modeling
Deterministic regression
Functional estimation
Parametric: LOESSP
• assume g (x) = Q
q=1 βq zq (x)
with tensor basis zq .
• determine local inference weight
Nonparametric: ANN, ANFIS
−1
wi = κ(hK
kxi − xK k).
• estimate the coefficient β via
WLS.
β̂ = arg min
β
K
−L
X
i=1
Q
X
wi (yi −
βq zq (xi ))2 .
q=1
Dan Ruan
Prediction
Outline
Motivation and Problem Definition
Deterministic Perspective
Stochastic Perspective
Summary
Sample Path Estimation via Motion Modeling
Deterministic regression
Performance of deterministic regression
600ms lookahead length, RPM relative displacement.
• ANN: more flexible, favorable with abundant training samples.
• LOESS: more specific functional form, more robust with sparse
samples, computationally efficient.
Dan Ruan
Prediction
Outline
Motivation and Problem Definition
Deterministic Perspective
Stochastic Perspective
Summary
Estimation of Stochastic Process
Stochastic Regression: Recent Development
Outline
1 Motivation and Problem Definition
Motivation
Problem Description
Two Perspectives
2 Deterministic Perspective
Sample Path Estimation via Motion Modeling
Deterministic regression
3 Stochastic Perspective
Estimation of Stochastic Process
Stochastic Regression: Recent Development
4 Summary
Dan Ruan
Prediction
Outline
Motivation and Problem Definition
Deterministic Perspective
Stochastic Perspective
Summary
Estimation of Stochastic Process
Stochastic Regression: Recent Development
Starting from KF
• iterates between predicting and
updating the R.V. dist.
• the performance limitation of KF
in respiratory prediction lies in
linearity, NOT its stochastic
nature.
• motivates stochastic estimation
with more general dynamic model
promising.
Dan Ruan
Prediction
Outline
Motivation and Problem Definition
Deterministic Perspective
Stochastic Perspective
Summary
Estimation of Stochastic Process
Stochastic Regression: Recent Development
What about stochastic regression
A recent development
• admits the random state, relaxes requirement for map
consistency.
• nonparametrically learns distribution.
4.5
4
3.5
RMSE
3
2.5
2
MRS
Linear
1.5
1
ANN
Kernel
0.5
0
5
10
15
20
sampling frequency (Hz)
Dan Ruan
Prediction
25
30
Outline
Motivation and Problem Definition
Deterministic Perspective
Stochastic Perspective
Summary
Outline
1 Motivation and Problem Definition
Motivation
Problem Description
Two Perspectives
2 Deterministic Perspective
Sample Path Estimation via Motion Modeling
Deterministic regression
3 Stochastic Perspective
Estimation of Stochastic Process
Stochastic Regression: Recent Development
4 Summary
Dan Ruan
Prediction
Outline
Motivation and Problem Definition
Deterministic Perspective
Stochastic Perspective
Summary
deterministic
samp. path regression
utilize periodicity
nonunif. sample
local variation
cont. prediction
accuracy
needs work
Y
needs work
Y
Y
Dan Ruan
Y
N
N
N
Y
Prediction
stochastic
process
regression
needs work
Y
Y
Y
needs work
Y
N
Y
N
Y
Outline
Motivation and Problem Definition
Deterministic Perspective
Stochastic Perspective
Summary
Summary
• Motion prediction is a challenging problem - a lot of room for
improvement.
• Different interpretations/perspectives offer new opportunities.
• Proper choice depends on specific applicationl
• Play with different modifications, combinations and have fun!
Thank you!
Dan Ruan
Prediction