ECSE6963, BMED 6961 Cell

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ECSE-6963, BMED 6961Cell Tissue Image Analysis

• Lecture 13 Blob Segmentation Basics (Contd)
• Badri Roysam
• Rensselaer Polytechnic Institute, Troy, New York
  12180.

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Recap Labeling Connected Components
Adaptive Smoothing Thresholding
Connected Components Labeling
Binary image
Regions labeled
image
Image
Connected Components Labeling
Binary Segmentation
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CC labeling A Versatile Tool

• MATLAB Function
• L,num bwlabel(BW,n) for 2-D images only
• BW binarized image
• n 4 or 8 (default) connectivity
• L label array, same size as BW
• num number of connected components
• L,NUM bwlabeln(BW,CONN) for n-dimensional
  images
• CONN 6/18/26 connectivity in 3-D space
• RGB label2rgb(L,map,zerocolor) for displaying
  the CC labels
• Can use CC labeling in diverse ways limited only
  by our imagination
• Find the background
• Count components
• Measure size (area, volume, radius), extent
  (feret box, diameter), location, shape
  (convexity, circularity), and orientation (min.
  enclosing rectangle) features
• Filter components by size shape
• Find and fill holes
• Cleanup results of edge detection

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Recap Features of Connected Components

• Area
• Feret box, and minimum enclosing rectangle
• Diameter
• Centroid
• Convexity
• Radius Circularity

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Radius Circularity

• The circularity, C, is defined as the variance of
  the distances around the radius

Circularity of a circular object is zero, and for
non-circular objects, it is greater than 0
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Example Compactness
Compact
Invariant to linear image transformations,
but Watch for scale-dependent error in perimeter
estimate
Not so compact
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Perimeter

• Simplest Definition Count the number of boundary
  pixels
• Boundaries often associated with membranes
• Extremely important sites of biochemical activity
• CC pixels with at least one 4-connected
  background neighbor are boundary pixels
• In MATLAB, BW2 bwperim(BW1,CONN) identifies
  perimeter pixels
• Two types of boundary pixels
• Type I only one 4-connected background neighbor
• Type II Two 4-connected background neighbors
• For a more accurate estimation, necessary to
  perform contour following
• Freemans algorithm
• Weight for Type I pixels 1
• Weight for Type II pixels ??2

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2
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Accurate Estimation of Perimeter

• Kulpas Algorithm
• Start with 8-connected contour
• Scale Freemans estimate by 0.948
• Many other formulas discussed in the literature
• 3-D case is analogous
• Surface area of a connected component

Correction factor for closed surfaces
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Contours External Internal

• Usually, external contours are better behaved
• Form closed curves when object contains no holes
• Even if parts of object are just 1 pixel wide

Practical notes 1. Internal contour would work
better if we had a single-pixel-wide tunnel 2.
Often convenient to either erode or widen
single-pixel-wide structures to 2 pixels
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Contour Following
Starting Point

• Need a way to represent a contour
• Need algorithms to
• Find a starting point
• Find the next point on contour
• Recognize when contour following is complete

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Neighbor Labeling

• A contour can be written as a series of 3-bit
  numbers
• Chain code directions
• Invented by Herb Freeman in the 60s
• An RPI professor

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Finding the Starting Point

• Just scan from upper left to bottom right
• The first background pixel that has a foreground
  neighbor to the right is our starting point for
  contour following
• Pixel (2, 6) in this example

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Finding the Second Point

• Search the neighbors that have not been tested
  before (from 4 to 7)
• Look for first transition from background to
  foreground
• Pick the background pixel as the next point on
  the external contour
• Will always yield counter-clockwise contour

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Subsequent Points

• We need a way to keep track of whats already
  been traced and whats not
• P Previous pixel
• C Current pixel
• N Next pixel

Directions
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The invert() function
Directions
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Finding Subsequent Points

• Starting from , search the neighborhood
  counter clockwise for contour candidates,
  including the previous point
• Allows algorithm to enter and leave a tunnel
• Pick the last candidate as the next direction

Directions
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Finding Subsequent Points

• Note that the previous pixel is also a candidate
  in the search
• Need that to handle single-pixel wide entrances
• Taken only when there are no other candidates to
  avoid getting stuck

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End Point

• Stop when you encounter the start point while
  finding the subsequent points
• Works when you dont have holes

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Doing this in MATLAB
(x, y) sequences, one for each object
Label Matrix
No. of objects
Boundary Array
Adjacency matrix

• B,L,N,A bwboundaries (BW, CONN, options)

Binarized image
How holes should be treated holes or noholes
Type of Connectivity (4 or 8)
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Freemans Perimeter Estimate - Revisited
Directions
Number of odd direction codes in contour
Number of even direction codes in contour
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Perimeter Comments

• Perimeters, surface areas, and curve lengths are
  notoriously susceptible to estimation errors
• Small segmentation errors can cause big changes
• The fractal nature of object perimeters
• Often more meaningful to define these
  measurements at a specific scale
• We would like to smooth the contour and then
  measure

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Perimeter Based Features
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Curvature

• Basic Concept
• Curvature is the rate of change of the slope of a
  curve
• Positive curvature means convex, and vice versa
• Using curvature, we can locate special points of
  interest

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Curvature Estimation

• The derivatives can be approximated by differences

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Practical Method
m is a scale parameter Notwithstanding m, we
still need to smooth the boundary
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Shape Complexity Feature

• Find the nearest distance of each pixel to the
  boundary
• Efficient algorithms, known as Distance
  Transforms are available to do this (shortly)
• Find the average ? of the above distances

Suppose the two shapes had the same area, which
one will have more complexity?
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Using CC labels as cookie cutters

• Keep in mind that the original image data is
  available, and spatially aligned with
  segmentation labels
• CC labels can help define regions of interest in
  the image
• Make spatially selective measurements over the
  original image
• Fluorescence intensity measurements
• Optical density measurements

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Example Absorption features
Feret Box

• Important for transmitted-light images
• Total Optical Density
• Measure background within a local neighborhood,
  usually a slightly expanded Feret box, or a
  rounder approximation
• Mean Optical Density
• Variance of optical density
• A texture measure

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Reference

• Shape analysis Classification Theory and
  Practice by Luciano da Fontura Costa
• Available on-line through the RPI library catalog
• Chapter 5.2 describes the contour following
  algorithm

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Summary

• Connected components labeling is a versatile tool
• Applications only limited by our imagination
• We looked at more features of regions
• We looked at shape features of regions
• Term Projects
• Need more time? Need to meet/talk?
• Next Class
• Invariance of Features
• More object features
• Distance transforms separation of connected
  components

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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