ECSE6963 Biological Image Analysis

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ECSE-6963Biological Image Analysis

• Lecture 12
• Image Edges
• Badri Roysam
• Rensselaer Polytechnic Institute, Troy, New York
  12180.

Center for Sub-Surface Imaging Sensing
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Recap Image Enhancement

• Goes beyond defect correction to deliberate image
  modification
• The resulting image is understood to not
  necessarily depict physical reality
• Histogram Modification Analysis
• Equalization, Inversion, Stretching,etc
• Today Edges and how to detect them

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Assignment 3

• Write a program to perform adaptive histogram
  equalization, and test that on the retina image
  for window sizes of 20x20 pixels and 50x50
  pixels. Comment on the observed differences.
• Write a program to perform the Sobel edge filter
  at each pixel. Calculate the magnitude and angle
  at each pixel, and display it.
• Then extract all edge pixels that have a
  comparably strong edge with the opposite angle
  within a neighborhood of N pixels. Display the
  result for N 10 and 20 pixels for the retina
  image. Comment on your results.

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Edges

• Boundaries between different objects in the image
• Locations of abrupt change in image properties
• Gray level edges
• Texture edges
• Color edges

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Edges and Edgels

• The term edge is also used to refer to
  connected chains of edge points, i.e., fragments
  of object contours
• Edge points are also called edgels (for edge
  elements)
• The term boundary is used for the real thing
• Edges are a fragment of the boundary

Biggest Problem Finding the edges that really
correspond to object boundaries from edges caused
by texture and/or noise
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Edge Models
Noisy observation
True intensity
Step
Ramp
Roof
Ridge
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Basic Steps to Edge Detection

• Noise Smoothing Pre-processing
• Suppress as much of the image noise as possible
  without destroying the true edges
• Edge Enhancement
• Make the edges stand out, using suitable filters
• Edge Localization
• Process the filters output to decide where the
  edges are, and where they are not.
• Usually two steps
• 1. Thinning or non-maximum suppression
• 2. Thresholding
• Post Processing
• Best to avoid in the first place. If absolutely
  necessary, use morphological operations /
  connected components / curvature size
  constraints.

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Edge Enhancement

• Edges usually associated with regions having high
  derivatives
• Usually, thats where the action is
• Regions that have high edges are sharp
• One way to enhance is to suppress the unsharp
  regions
• Need to understand derivatives first

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Gradient Magnitude Angle
The square root takes time!
The arctangent takes time!
Same math works in 3-D as well
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Discrete Approximation
Central Difference Approximation

• Finite-difference approximation to gradient
• Inherently, a noise enhancing operation
• Responds to every little change in I(x,y)

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Example
y
x
Gradient Magnitude
Angle
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Ways to Combat Noise
Averaging along the edge (Prewitt operator)
Weighted Averaging (Sobel operator)
Another idea Fit a plane
to a local neighborhood of pixels
Then,
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Another Noise Combating Method

• Just suppress weak edges!
• Non-maximum suppression
• At each pixel (x,y), look within a small
  neighborhood
• Find the maximum gradient magnitude
• If the gradient magnitude at (x,y) is less than
  the maximum, simply attenuate it, or set it to
  zero!
• Better
• Find the local gradient direction
• Do the suppression just along this direction

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Smoothing Before Differentiation
Approximate Gaussian Smoothing Filter
Differentiator
Single operation that combines both
(scale factor)
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Adding Smoothing Along Edge
Note If image brightness goes up from left to
right, the result response is positive ? The
sign of the response can be put to good use
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Ways to Achieve Speed

• Kirsch Operator
• Discretize the angles into a small set of values
• Use a directional gradient at each discretized
  angle
• Keep the one that gives the maximum value
• Avoids arctangent and square root!
• There are numerous operators in the literature,
  but the principles are similar

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Thresholding

• Really, another noise combating method
• Non-maximum suppression still leaves noise-caused
  local maxima
• If the gradient magnitude is greater than a
  threshold T, set edgel to 1
• Else, set edgel to 0.
• Choosing a threshold
• T too low ? Pick up too many noisy edgels
• T too high ? Miss real edgels, making boundaries
  discontinuous.

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Thresholding

• One Solution
• Adaptive thresholding
• Define a N?M window at each pixel
• Use (hopefully bi-modal) histogram to select a
  threshold
• Better Solution
• Define two thresholds Tlow and Thigh
• Follow object boundaries
• Locate next un-visited pixel with gradient gt
  Thigh
• Follow chains of connected local maxima in both
  directions along the edge direction (i.e.,
  perpendicular to the gradient direction)
• Accept as edgels points where the gradient is
  higher than Tlow

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Ideas

• The best edge detectors have the following
  properties
• They are based on a valid model of the types of
  edges that are expected
• Model for how intensity changes across the
  boundary
• Model for the underlying objects and the
  structure of their boundary
• Example smoothness constraints on boundaries are
  helpful
• Model for the noise
• They treat the gradient direction and the
  direction perpendicular to it differently
• Smooth along boundaries
• Smoothing differentiation across boundaries

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Another Powerful Idea

• Connected groups of edges often exhibit
  properties that are very different from
  noise/texture
• object level constraints
• Big Question How do we recognize and exploit
  these properties to do more selective edge
  detection?

Long Chains of parallel edges with low curvature
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Example Tracing Blood Vessels

• Problem Trace blood vessels in 2D and 3D images
• Why bother?
• Vessel morphometry is of direct interest to
  biologists doctors
• Vessels provide landmarks for image registration
• Change detection
• Mosaicing
• Instrument control

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• Practical Challenges
• High image variability, need for reliability
• Presence of clutter (e.g., pathologies)
• Live data
• cannot prevent partial views, dark/overexposed
  images, variable contrast, variable illumination,
  noise, glare etc....
• Strong need for highly selective edge detection

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Related Application

• Fluoroscopic Cardiac X-Ray Image

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Related Application

• Neurons grown on a treated nano-fabricated surface

Clutter does not exhibit the properties that the
neuron does
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Related Application

• Angiogenesis Research

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A 1-D Cross Section
Image Gray Level
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Detecting Edges of Blood Vessels
LEFT
RIGHT
Sum these responses (could also find the median)
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Edges at Many Discrete Angles
LEFT
RIGHT
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A Model For Vasculature
? M

• Parallel edges,
• ? M pixels wide

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Locating the Boundaries
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Application Vessel Tracing
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Tracing Algorithm
Compute Right Left Responses
Search for Best Response
Strongest Response Sets the Direction
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Unsharp Masking

• An age old trick used by photographers
• Capture two images,
• I1 Normal, in focus
• I2 Blurred by a known amount
• Calculate I1 I2 photographic process
• Place positive of one image, negative of other
  image together before printing
• Rejects smooth variations, and highlights sharp
  variations

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Galaxy Example

• This idea of using controlled blurs prior to
  differentiation is extremely powerful!
• More on this next class!

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Mammogram Example
Mammogram with Calcifications
Gaussian Blur, Radius 10
Difference
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Summary

• Edges
• Edges, Edgels, and the Real Boundary
• Gradient operators
• Ways to combat noise
• Model-Based Edge Detection
• Next Class
• More about Edges
• Edge location and Scale Space Methods
• Basics of Image 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]/2433
• Email roysam_at_ecse.rpi.edu
• Website http//www.rpi.edu/roysab
• Course Material Website http//www.ecse.rpi.edu/c
  enssis/BioCourse
• New Weekly Teleconference Schedule Thursdays at
  3-4pm.
• Dial 1-888-872-2038 and use the guest passcode
  0611.
• NetMeeting ID (for off-campus students)
  128.113.61.80
• Assistant Betty Lawson, JEC 6049, (518) 276
  8525, lawsob_at_rpi.edu