Zhujiang Cao1, Shiyan Pan2, Rui Li3, Ramya Balachandran3,

1
Registration of Medical Images Using an
Interpolated Closest Point Transform Method and
Validation

• Zhujiang Cao1, Shiyan Pan2, Rui Li3, Ramya
  Balachandran3,
• Michael J. Fitzpatrick3, William C. Chapman4,
  Benoit M. Dawant3
• 1Department of Biomedical Engineering, Vanderbilt
  University, Nashville, TN
• 2Broadband Codec Software Engineering, LSI Logic
  Corporation, Milpitas, CA
• 3Department of Electrical Engineering and
  Computer Science, Vanderbilt University,
  Nashville, TN
• 4Surgery and Cell Biology, School of Medicine,
  Washington University, St. Louis, MO

2
Contents

• Introduction
• Method
• Computation of closest point transform (CPT).
• Comparison between standard CPT and interpolated
  CPT.
• Simulated image Results
• Real image results
• Discussion and Conclusion

3
Introduction

• Previously Proposed Surface-based registration
  methods
• Iterative closest point algorithm (ICP)
  withray-casting.
• Distance Transform algorithm (DT)
• ICP with Closest Point transform (CPT)

4
Closest point transform (CPT)

• Eikonal equation
• (1)
• Solved using the Fast Marching method
• proposed by Sethian.
• Algorithm has been modified to propagate
• closest point coordinates as well as
  distance.
• JA Sethian, Level Set Methods and Fast
  Marching Methods Evolving Interfaces in
  Computational Geometry, Fluid Mechanics, Computer
  Vision, and Materials Science, Cambridge
  University Press, 1999

5
CPT cont.

• Fast Marching method
• Label all points on the initial boundary as
  Known, all points that are one grid away as Trial
  and all the other points as Far.
• Begin loop let A be the Trial points with the
  smallest T value.
• Add the point A to Known and remove it from
  Trial.
• Label as Trial all neighbors of A that are not
  Known. If the neighbor is in Far, remove it , and
  add it to the Trial set.
• Recompute the values of T at all Trial neighbors
  of A according to (1)
• Return to top of loop

6
CPT cont.

• Propagate closest point information along
  distance
• In the initialization phase, we compute and store
  the Euclidean distance between the points in the
  Trial set and their closest neighbor in the Known
  set as well as the coordinates of this closest
  neighbor.
• During the loop phase, we compute the Euclidean
  distance between all the neighbors of A in the
  Trial set and A,s closest point. If this distance
  is smaller than the distance currently associated
  with the neighbor, we update this distance and
  the closest point to this neighbor is set to the
  closest point of A.

7
Standard CPT

• Use CPT as a lookup Table for
• ICP algorithm
• Spatial quantization of the CPT causes a residual
  error.

Original contours
Shifted/registered contours
8
Residual Error
Original contours
Shifted/registered contours
9
Explanation of Residual Error
10
Interpolation of CPT
11
Illustration of ICPT
Original contours
Shifted/registered contours
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Results Simulated data

• Two synthetic images (3D) were used.
• Closest point map was calculated from
  theseimages.
• Random noise was added to the x, y, and z
  coordinates of the points comprising these
  shapes to generate corrupted shapes.
• Registration was performed 300 times with
  normally distributed 050 rotation angles in
  the x, y, and z directions and normally
  distributed 05 voxel translation vectors.

13
Simulated data cont.
14
Simulated data cont.

• Results show that if noise in the order of
  0.3-0.4 voxels is added to the
• shapes, the interpolated and non-interpolated
  methods behave similarly.

• The noise breaks the periodicity introduced by
  the regular grid on which the patterns are
  defined.
• This periodicity could also be broken by
  resampling as proposed by Pluim for MI based
  registration algorithm.

JPW Pluim, JBA Maintz, and M.A Viergever.
Interpolation artifacts in mutual-information-base
d image registration. Computer Vision and Image
Understanding, 77(2) 211-232, 2000
15
Patient Data Sets

• Data sets provided by Retrospective Registration
• Evaluation Project (RREP) headed by Dr.
  Fitzpatrick at Vanderbilt University.
• CT and MR volumes of 7 different patients were
  acquired from the data sets.
• MR image data sets are composed of T1, T2
• and proton density-weighted volumes and their
  respective rectified versions.
• Registration method was performed between CT and
  the various MR volumes.
• A total of 6 registration results for each
  patient were validated.

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Surface Extraction

• Surfaces were extracted with a fully automatic
  level set algorithm.
• Skin/air interface was found.
• MR-T2 images were preprocessed with a Total
  Variation filter and a median filter.

SY Pan and BM Dawant, Automatic 3D segmentation
of the liver from abdominal CT images a level
set approach, Medical Imaging 2001 Image
Processing, Proc. SPIE Vol. 4322, p. 128-138,
2001. TF Chan, S Osher and JH Shen. The digital
TV filter and nonlinear denoising. IEEE
Transactions on Image Processing, Vol. 10,
pp.231-241, 2001.
17
Surface Extraction Cont.
Figure 5. Extraction air/skin surfaces.
18
Surface Extraction Cont.

• Before extraction, MR-T2 images were preprocessed
  with a Total variation (TV) filter followed by
  amedian filter with coefficient as follows
  ?25, iteration 50 and S 3X3 (size for
  median filter).

Figure 6. Effect of TV filter and median filter.
19
Simulated data cont.

• The noise we have introduced breaks the
  periodicity introduced by the regular grid on
  which the patterns are defined.
• It should be noted that this periodicity could
  also be broken by
• resampling the rotated and translated shapes in
  such a way that the dimensions of the voxels in
  the volume from which the closest point map is
  computed and the dimension of the voxels in the
  rotated/translated image are not an integer
  number of each other. This is similar to the
  strategy advocated by Pluim to reduce the effect
  of regular grids on local extrema when performing
  Mutual Information-based image registration.

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Results Real data
21
Results Real data cont.
22
Discussion and conclusion

• CPT-based methods can lead to a registration
  accuracy that is comparable to the accuracy
  achieved with voxel-based methods.
• This is the first CPT based method that was
  validated on RREP
• data set and the accuracy of this method is
  substantially better than other surface-based
  methods.
• Maybe important for applications for which
  voxel-based methods are not applicable such as
  computer-aided surgery.
• The simulation results suggest that the main
  source of difference between the interpolated and
  non-interpolated version of the algorithm is a
  discretization-related artifact. Other possible
  ways to reduce this artifact are to either add
  noise or to resample one of the images.

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Discussion and conclusion cont.

• The smaller difference between the interpolated
  and non-interpolated algorithms in real images is
  attributed to two main causes
• Imprecision in the localization of the surfaces.
• Registration is performed between two
  different surfaces (MR and CT). Differences in
  skin surface shapes may mask the
  quantization-related artifact.

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Acknowledgement
This work has been supported, in parts by NIH
grant CA-91352 R01-CS89323-01.