A Statespace Model for a Sequence of Image Characteristics

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A State-space Model for a Sequence of Image
Characteristics

• Claus DethlefsenMartin Bøgsted HansenSøren
  Lundbye-ChristensenAalborg University, 1997

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Medicine Coronary Arteries

• Coronary arteries supply the heart muscle with
  oxygen
• Obstructions in the coronary arteries causes
  insufficient oxygen supply
• Insufficient oxygen supply leads to chest pains
  etc.
• Obstructions may be due to calcification or low
  flexibility in the arteries

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Coronary Angiography

• Catheter inserted in blood vessels and guided to
  the coronary arteries
• Contrast fluid and X-ray images lead to an
  outside view of arteries
• Calcifications can be detected, but not low
  elasticity

Stenosis
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Intracoronary ultrasound imaging
Transducer
Catheter

• Again, a catheter inserted in blood vessels and
  guided to the coronary arteries
• An ultrasonic transducer in the head of the
  catheder leads to an inside view of the
  arteries
• Both calcifications and low elasticity may be
  detected (locally)

Coronary artery wall
Plaque
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Medical Problem

• From a sequence of ultrasonic images, determine
  the evolution of the cross-sectional area of a
  coronary atery
• This is very cumbersome and a trained operator is
  needed. Reproduction of results is still nearly
  unretrievable
• An automated method is needed yielding estimates
  of areas with a measure of precision

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Statistical Problem

• Observed images matrices of real
  valued pixels
• Idealized image One or more moving/deforming
  objects as time goes by
• Idealized image at time t can be parametrized by
  a low-dimensional vector of image
  characteristics,

Our idea
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Related work

• Besag. On the statistical analysis of dirty
  pictures, 1986
• Geman Geman. Stochastic Relaxation, Gibbs
  Distributions, and the Bayesian Restoration of
  Images, 1984
• Harrison Stevens. Bayesian Forecasting, 1976
• Green Titterington. Recursive methods in image
  processing, 1987
• Metropolis, Equations of state calculations by
  fast computing machine, 1953
• Gilks et al. Markov Chain Monte Carlo in
  practice, 1996

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Proposed state-space model
Idealized image
Observational noise
Observation Eq System Eq
Random fluctuation
Systematic movement
Independent
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Image Generating Function
Observed image
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Image Characteristics

• Idealized image parametrized by - a center,
  moving around a reference center AR(1)- a
  radius, fluctuating semi-periodically around
  reference radius

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Kalman Filtering

• Suppose that is linear
• Then the Kalman filter yields updating equations
  for

Posterior Prior Forecast
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A simple Kalman filter
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Kalman Filtering - non-linear

• is not linear
• Generate sample from
• Then obtain

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Metropolis-Hastings algorithm

• Goal generate sample from
• 1) Choose
• 2) Proposal
• 3)where

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Sample from N(0,1)
Proposal N(0,0.5)
Proposal N(0,0.1)
Proposal N(0,10.0)
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Future work

• Compare results with 1) clinicians results
  2) engineering
  methods
• Use ECG-information in estimation of
• Transform images to polar coordinates
• Put a window around the estimated circle
• Templates (polygons)