Assembling Image Stacks for Sectioned Tissue into Coherent 3D Images

1
Assembling Image Stacks for Sectioned Tissue into
Coherent 3D Images
Baylor College of Medicine Gregor Eichele,
Ph.D. Wah Chiu, Ph.D. Christina Thaller,
Ph.D. Dawna Armstrong, M.D. James Carson, Ph.D.
Rice University Joe Warren, Ph.D. David Scott,
Ph.D. Scott Schaefer Tao Ju
University of Houston Ioannis Kakadiaris,
Ph.D. Musodiq Bello
2
Spatial Database of Gene Expressions

• Genes expressions
• Genes are blue prints of creating proteins
• Gene expressions are where genes are synthesizing
  proteins
• Gene expression images
• High-throughput in situ hybridization Eichele
• Cellular-resolution images using light microscopy
• 500 images/brain for 2,000 genes

3
High-throughput ISH Images

• Sagittal ISH images for genes Hnt, Rorb, Calb and
  Sst

4
2D Brain Atlas

• Geneatlas.org 2D database of gene expressions
• Consists of 2D atlases using quad subdivision
  meshes
• Supports queries restricted to selected planes

5
Constructing a 3D Brain Atlas

• Ultimate goal 3D database supports fully spatial
  queries and computations
• Core a 3D volumetric brain atlas using
  subdivision
• Construct a smooth, high-resolution stack of
  brain images (Tao)
• Construct 3D brain atlas (Scott)

6
Input Data and Problems

• 500 coronally-sectioned images per brain
• Problems
• Variation of image intensity
• Translation and rotation during imaging
• Non-linear tissue distortion due to sectioning

Slice 77
Slice 140
Slice 141
7
Goal

• Goal A smooth 3D image volume that represents
  the natural shape of a brain

Output
Input
8
Image Assembly Pipeline

• Pre-processing
• Equalizes image intensity
• 2D orientation
• Undo rotation and shifting during imaging
• Warping and smoothing
• Undo sectioning error and Obtain a smooth volume
• New image warping method
• Validation of 3D alignment
• Compute orientation of sectioning

9
Image Processing and 2D Orientation

• Intensity equalization
• Histogram transformation
• Undo tissue rotation and shifting
• Detect and align line of symmetry
• Align vertical locations

10
Warping and Smoothing

• Warping
• A mapping (re-parameterization) from one image to
  another
• Minimizing a selected distance norm
• Smoothing
• Deform each image based on its warps to the
  neighboring images
• Mapped features in consecutive images form smooth
  curves in the stacking direction

11
Image Warping

• Warping methods
• Optimization
• Dynamic programming
• Dynamic Time Warping
• Standard 1D warping method Sakoe and Chiba
• To warp from vectors si to tj (of length n)
• Compute error table eij for all pairs (i, j),
  where
• eij(si-tj)2
• Compute minimal error path from e11 to enn, which
  encodes a re-parameterization from s into t.

12
1D Warping Example
s(u)
t(x)
x f(u)
Before
Error table eij and re-parameterization
After
13
2D Dynamic Time Warping

• Fully 2D warping is NP-Complete Keysers and
  Unger
• Existing extensions of 1D DTW only handles low
  resolution images Uchida Sakoe
• Our approach Decompose into 1D DTW
• Sectioning errors lie in a small space of warps
• The warp from image s(u,v) to t(x,y) can be
  modeled as
• xf(u), yg(u,v)

14
2D Dynamic Time Warping

• Algorithm
• Compute the error eij of the minimal warp from
  the ith column of s to the jth column of t for
  all (i, j) pairs. (1D DTW)
• Use error table eij to find the best warp between
  columns of s and columns of t. (1D DTW)
• Warp inside pairs of matching columns from s and
  t. (1D DTW)

15
Coherent Warping

• Compute coherent warps for neighboring columns
• Compute a sub-set of minimal energy warps for
  each column
• Use dynamic programming to select the column
  warps that minimize energy and maximize coherence

16
Image Warping Example
A
B
C A to B
A B
C B
17
Constructing A Smooth Volume

• Key trace and smooth parameter lines connecting
  corresponding points on consecutive images

Before
After
18
Image Filtering

• Local normalization of image intensity
• Use a majority filter for neighboring pixels on a
  same parameter line

Before
After
19
Validation of 3D Alignment

• Compare synthetic sections to standard sections
• 3D orientation of the stacked images is uncertain

Paxino (Correct)
Eichele (tilted)
20
Computing 3D Orientation

• Determine image slice number si for approx 8-10
  landmarks with position (xi,yi,zi) in model brain
• Compute plane equation axbyczd0 of frontmost
  coronal image by minimizing Si(axibyiczid-si)2

21
Comparison
22
Acknowledgements

• Keck Center
• Allen Institute of Brain Science
• Baylor College of Medicine
• University of Houston

23
Brain Atlas

• What is an atlas
• A deformable model of the brain
• A common reference system for storing and
  comparing image data
• Subdivision meshes as brain atlas
• Explicit partitioning models anatomical regions
• Smooth parameterization induces smooth
  deformations
• Multi-resolution structure supports fast
  computation

24
Image Pre-processing

• Segmentation
• Clear background noises
• Use flood-filling with thresholding
• Histogram normalization
• Undo variation of image intensity due to staining
• Equalize mediums of histograms

Before
After
25
2D Image Orientation

• Undo tissue rotation and shifting
• Detect line of symmetry
• Rotate and translate tissue to the center of the
  image

26
2D Image Orientation

• Recover vertical tissue position
• The brain is not a cylinder
• Align centers of masses of all images using a
  real sagittal section