ShapeBased Interpolation of Multidimensional GreyLevel Images

1
Shape-Based Interpolation of Multidimensional
Grey-Level Images

• George J. Grevera et al.
• IEEE Transactions on Medical Imaging
• Volume 15, Number 6
• September 1996

2
Motivation
3
Outline

• Introduction
• Scene-based interpolation
• Object-based interpolation
• Methods
• 5 (6) step process
• Evaluation
• Qualitative
• Quantitative

4
Introduction

• Scene-based interpolation
• final intensity values determined directly from
  input intensity values
• Nearest-neighbor, linear, spline
• Object-based interpolation
• object information extracted from a given scene
  guides the interpolation process
• first method designed for binary images

5
Binary Image Example

• Calculate distance map
• Interpolate distance maps using scene-based
  interpolation
• Threshold at 0

6
Myocardium Segmentation
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Methods Step 1 Lifting

• nD image is converted to a binary (n1)D image

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Step 2 Distance Map

• Chamfer distance approximation

-ve values
ve values
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Step 3 Interpolation

• Use scene-based interpolation (linear) to obtain
  distance maps with increased resolution

-ve values
ve values
-5
5
9
5
0
7
10
Step 4 Convert to Binary

• Threshold interpolated distance map (d gt 0 set m
  to 1, d lt 0 set m to 0)
• What is m if d is exactly 0?
• Randomly assign 0 or 1 to m
• Always select 0 for m
• Always select 1 for m
• Set m to 1 if majority of neighbors have d gt 0,
  set m to 0 otherwise. If number of neighbors
  with d gt 0 number of neighbors with d lt 0,
  choose randomly

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Step 5 Collapsing

• Convert the interpolated (n1)D lifted image back
  to a nD real image

12
Step 6 Averaging (optional)

• Reconstruct 2 nD, real images
• always setting m to 1 if d 0
• always setting m to 0 if d 0
• Average the two real images

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2D Image Example
1. Lifted binary (3D)
2. Distance map (m 50)
Slice from 3D image
4. and 5. Interpolated lifted binary and real 2D
images
6. Avg. interpolated slice
3. Interpolated map
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Heart MR Example
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Validation - Quantitative

• 3D example
• Take 3 consecutive slices of data
• interpolate the middle slice using the two
  extreme slices
• Compare interpolated versus original middle slice
• Measures of Accuracy
• msd
• nsd of disagreement sites within some
  tolerance
• ldiff largest difference in intensities
• sdiff total signed difference
• udiff total unsigned difference

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Validation - Quantitative
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Validation - Qualitative
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Validation - Qualitative