BAYESIAN INFERENCE AND/OR OPTIMIZATION STRATEGIES FOR
SOME DETECTION, TRACKING AND DECONVOLUTION
PROBLEMS IN MEDICAL IMAGES
Max Mignotte & Jean Meunier
       
DIRO
The authors thank INRIA (Institut National de la Recherche en
Informatique et Automatique, France) and NSERC (Natural Sciences
and Engineering Research Council of Canada) for financial support
of this work (postdoctoral grant) respectively from September 1998
until August 1999 and from September 1999 until August 2000. The
authors are also grateful to Jean-Paul Soucy and Christian Janicki
(CHUM, University of Montreal) for having provided the SPECT images.
DETECTION AND TRACKING OF ANATOMICAL STRUCTURES USING DEFORMABLE
TEMPLATES AND A NOISE MODEL ESTIMATION IN AN ECHOGRAPHIC SEQUENCE
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In this work, we present a new method to shape-based segmentation of
deformable anatomical structures in medical images and validate this
approach by detecting and tracking the endocardial border in an
echographic image sequence. To this end, a global prior knowledge of
the endocardial contour is captured by a prototype template with a set
of admissible deformations to take into account its inherent natural
variability over time. In this approach, the data likelihood model
rely on an accurate statistical modeling of the grey level
distribution of each class present in the image. The parameters of
this distribution mixture are given by a preliminary estimation step
which takes into account the distribution shape of each class. Then
the tracking problem is stated in a Bayesian framework where it ends
up as an optimization problem. This one is then efficiently solved by
a genetic algorithm combined with a steepest ascent procedure. This
technique has been successfully applied on synthetic images and on a
real echocardiographic image sequence. This method seems to be
particularly well suited to handle ultrasound images with strong
speckle noise on which edge information cannot be exploited.
Finally, the local and global minimization procedure we propose is
fast, robust and do not require initialization of the template close
to the desired solution. Initialization may be defined at random,
leading to segmentation and tracking procedure that are completely
data driven.
(slides)
Figure 1:
Tracking of the endocardial contour in a medical
echographic sequence
at different time frames during the cardiac cycle. From top left to
bottom right : frame 1, 4, 6, 9, 12, 13, 18, 20, 27, 30, 35, 40, 41,
44, 46.
A MULTISCALE OPTIMIZATION APPROACH FOR THE DYNAMIC CONTOUR-BASED
BOUNDARY DETECTION ISSUE
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In this work, we present a new multiscale approach for deformable contour
optimization. The method relies on a multigrid minimization method and
a coarse-to-fine relaxation algorithm. This approach consists in
minimizing a cascade of optimization problems of reduced and
increasing complexity instead of considering the minimization problem
on the full and original configuration space. Contrary to classical
multiresolution algorithms, no reduction of image is applied. The
family of defined energy functions are derived from the original (full
resolution) objective function, ensuring that the same function is
handled at each scale and that the energy decreases at each step of
the deformable contour minimization process. The efficiency and the
speed of this multiscale optimization strategy is demonstrated in the
difficult context of the minimization of a region-based contour energy
function ensuring the boundary detection of anatomical structures in
ultrasound medical imagery. In this context, the proposed multiscale
segmentation method is compared to other classical region-based
segmentation approaches such as Maximum Likelihood or Markov Random
Field-based segmentation techniques. We also extend this multiscale
segmentation strategy to active contour models using a classical
edge-based likelihood approach. Finally, time and performance
analysis of this approach, compared to the (commonly used) dynamic
programming-based optimization procedure, is given and allows to
attest the accuracy and the speed of the proposed method.
(demo)
(slides)
Figure 2:
ML blocky segmentation
at different resolution levels and estimated snakes at different
resolution levels.
Figure 3:
Radiography medical image of a bone. Initial snake position
at coarsest level and estimated optimal snakes obtained by
the DP-based optimization procedure at different resolution
levels.
THREE-DIMENSIONAL BLIND DECONVOLUTION OF SPECT IMAGES
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Contrary to other clinical medical imaging techniques, 3D
SPECT imagery remains unique in its ability to yield functionally
rather than anatomically-based information. This visualization method
has become a great help in the diagnostic of cerebrovascular diseases
which are the third most common cause of death in the USA and
Europe. Nevertheless, 3D SPECT images (or SPECT volume) are very
blurred and consequently their interpretation is difficult. In order
to improve the spatial resolution of each cross-sectional image from
a given SPECT volume and then to facilitate their interpretation by
the clinician, we propose to implement and to compare the
effectiveness of twelve different existing 2D blind or ``supervised''
deconvolution methods. To this end, we present an accurate
distribution mixture parameter estimation procedure which takes into
account the diversity of the laws in the distribution mixture of a
SPECT image. In our application, parameters of this distribution
mixture are efficiently exploited in order to prevent overfitting of
the noisy data for the iterative deconvolution techniques without
regularization term or to determine the exact support of the object to
be restored when this one is needed. Recent 2D blind deconvolution
techniques such as the NAS-RIF algorithm combined with this estimation
procedure can be efficiently applied in SPECT imagery and yield very
promising restoration results.
In order to restore more accurately these 3D SPECT images
and to take into account the inter-slice blur in the restoration
procedure, we have proposed to extend the abovementioned 2D blind in
the deblurring 3D case. This technique requires to find, in a
preliminary step, the support of the object to be restored. In this
work, we propose to solve this problem thanks to an unsupervised 3D
Markovian segmentation technique. This method has been successfully
tested on numerous real brain SPECT volumes, yielding very promising
restoration results. We have also shown that this 3D blind
deconvolution technique gives superior performance than its 2D
version. Finally, This 3D blind deconvolution technique combined with
this unsupervised segmentation leads to a restoration procedure that
is completely data driven and really compatible with an automatic
processing of massive amounts of 3D SPECT data.
(slides)
Figure 4:
Examples of human brain SPECT volume deconvolution given by the 3D-extended version
of the NAS-RIF algorithm combined with the Markovian segmentation-based support
finding algorithm. From top to bottom and left to right, respectively cross-sectional
slice number: 27, 28, 29, 30, 31, 32, 33, 34, 35, 36.
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M. Mignotte, J. Meunier, J.-C. Tardif.
Endocardial Boundary estimation and tracking in echocardiographic images
using deformable templates and Markov Random Fields. Pattern Analysis and
Applications, 4(4):256-271, November 2001.
(postscript)
(pdf)
(abstract)
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M. Mignotte, J. Meunier. A multiscale optimization approach for
the dynamic contour-based boundary detection issue. Computerized
Medical Imaging and Graphics, 25(3):265-275, May 2001.
(postscript)
(pdf)
(abstract)
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M. Mignotte, J. Meunier.Three-dimensional blind deconvolution of SPECT images.
IEEE Transactions on Biomedical Engineering, 47(2):274-281, February 2000.
(postscript)
(pdf)
(abstract)
Postdoctoral Report
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M. Mignotte. Bayesian inference and/or optimization strategies for some
detection, traking, and deconvolution problems in medical images. INRIA
postdoctoral Report, DIRO, Montreal University, Canada, Québec,
September 1999.
(postscript)
(pdf)