ECSE6963, BMED 6961 Cell

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ECSE-6963, BMED 6961Cell Tissue Image Analysis

• Lecture 14 Blob Segmentation Basics (Contd)
• Badri Roysam
• Rensselaer Polytechnic Institute, Troy, New York
  12180.

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Recap Distance Maps

• Distance maps another classic and
  super-versatile tool that can be put to use in
  diverse ways
• Similar in versatility to connected components
  labeling
• Applications only limited by our imagination
• Many variations available nearest neighbor
  maps, signed distance maps, etc.
• D,L bwdist(BW,method) in MATLAB
• Many more waiting to be developed!
• The watershed algorithm is a work horse for blob
  segmentation
• L watershed(A,conn) in MATLAB
• Variations of this algorithm are used widely for
  segmenting nuclei, punctae, foci, particles,
  etc.
• Today
• Modifications to the watershed to improve
  performance

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Classic Watershed Tends to OversegmentImproving
Markers Improves Watershed Results
Distance Transform
Eliminate closely spaced markers
Classical Watershed
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3-D Example Liver cells
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Can we do Better?

• Indeed, there are lots of ideas out there!
• Idea 1
• Use other algorithms instead of watershed (e.g.,
  clustering)
• Idea 2
• Touching cells have a membrane between them. If
  the membrane is labeled fluorescently, we have an
  additional cue.
• Idea 3
• Touching cells often exhibit some edges. The
  watershed algorithm does not exploit them.
• Idea 4
• If the touching cells have shapes that can be
  modeled, we can exploit that information to
  improve object separation

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Idea 1 Use cluster analysis instead

• Perform a cluster analysis in (x, y, z, I(x,y,z))
• Conceptually simple
• Computationally more expensive than using a
  strong model
• The object shape is implicitly modeled by choice
  of clustering algorithm
• Choice of distance measure, especially

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When to use this method

• Neo-natal rat brain
• (weak model)

Well-formed nuclei (strong model)
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Simplest Distance Measure
P
C

• Need to recognize that spatial and intensity
  distances are like apples and oranges
• Need scale factors to provide appropriate
  weightage

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Initialization Seeds

• The k-means cluster analysis procedure assumes
  that we know the number of clusters k .
• This is actually the hardest problem in cluster
  analysis!
• One method
• Ask user to specify approximate size S
• Threshold the image
• Scan foreground labels from top left to bottom
  right
• Select every S voxels as a seed point

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Example
Background Clutter
Neurons in rat substantia nigra immunostained for
tyrosine hydroxylase
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Idea 2 Exploit Membrane Information
Hepatocyte (liver cell) Proliferation Analysis
by Dual-label Imaging
Data Courtesy Dr. Gregg Ridder, Procter and
Gamble Co.
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Modified Distance Measures
P
C

• Consider non-metric distance (pseudo) measures
• Example
• Line integrals from P to C can take into account
  intervening edges

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Idea 3 Exploiting Edge Cues
Cilium in the rat gut
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Apples and Oranges

• The distance transform, and the intensity
  gradient represent dissimilar quantities!
• Expressed in different units
• Cant be combined directly
• Idea Invent an ad hoc combining formula

Modified Distance transform
Distance transform
Normalized gradient
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Its intuitive

• The modified distance value D' is high in places
  that are
• Closer to the center of objects, and
• Having lower gradient values

Normalized gradient
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Example
Thresholding Connected components On red channel
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Comparing D and D'
D
D'
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Recap of Steps
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Analogous idea Exploit region-based cues from
another fluor/color
Watershed Segmentation
SHE Cell Colonies
Hybrid Watershed Cluster Analysis
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Idea 4 Use object model
Fact Even with the gradient-weighted distance,
the watershed algorithm tends to over segment,
i.e., break up objects more often than it
should. Idea Why not examine adjacent
fragments and see if merging them may help?
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Model-Based Merging
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Model-based Object Merging

• Basic idea
• Ask the user to identify examples of valid
  objects
• Compute a vector X of n features for each object
• Features such as volume, texture (standard
  deviation of intensity), convexity, shape factor,
  circularity,
• Find the mean and standard deviations of the
  features
• If the features are Gaussian distributed, we
  build the following mathematical model for
  objects!

Use other formulas other distributions
covariance
mean
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Putting the Model to Use

• Basic idea
• Given a vector Xi for an object i, we can
  compute the probability p(Xi) that it belongs to
  the model.
• This is like a score that indicates how
  confident we are that the object is a valid
  nucleus

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Model-Based Merging
For each watershed, we need to decide whether or
not to break it (i.e., merge the two
components). Breaking the watershed w means
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Merging Criterion
Bigger number means its better to merge!
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Another Criterion

• Usually, the intensity gradient across two
  objects is greater than the gradient within
  either object

Gradient along watershed line
Average gradient within object
Bigger number means better to break
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Handling Complex Clusters
Break?
Break?
Use a combined score on each watershed
Threshold Typically ? 1.2
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Homework

• Read the following paper, and answer the
  following questions
• http//www.ecse.rpi.edu/roysam/PDF/J42.pdf
• What type of smoothing algorithm was used in this
  work? Why was it chosen over others?
• How were holes in the thresholding result
  eliminated?
• What is the purpose of the kernels shown in
  Figure 3?
• List the limitations of the classical watershed
  algorithm.
• How is the image intensity gradient G computed?
• How do the authors handle the anisotropy of
  confocal microscope images?
• Why is it necessary to add 1 to the inverse
  distance map prior to the watershed step?
• Critique the manner in which the shape feature
  was computed for the nuclei.
• What considerations did the authors note for the
  problem of choosing the features to use?
• What features of objects are most valuable for
  modeling purposes?
• Case 1 for 2-D images?
• Case 2 for 3-D images?

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Summary

• Many ideas on object separation
• When we encounter a new application, a
  combination of these ideas can be used
• Of course, new ideas continue to emerge
• E.g., use multiple object models to handle
  diversity of cell types
• Term Projects
• Need to meet/talk?
• Next Class
• Feature Selection
• Introduction to tube tracing algorithms

Final segmentation
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Instructor Contact Information

• Badri Roysam
• Professor of Electrical, Computer, Systems
  Engineering
• Office JEC 7010
• Rensselaer Polytechnic Institute
• 110, 8th Street, Troy, New York 12180
• Phone [phone]
• Fax [phone]
• Email roysam_at_ecse.rpi.edu
• Website http//www.ecse.rpi.edu/roysam
• Course website http//www.ecse.rpi.edu/roysam/CT
  IA
• Secretary Laraine Michaelides, JEC 7012, (518)
  276 8525, michal_at_.rpi.edu
• Grader Ying Chen (cheny9_at_rpi.edu, Office JEC
  6308, 518-276-8207)

Center for Sub-Surface Imaging Sensing