Marr's Framework for Computational Vision:

1
Marr's Framework for Computational
Vision Computational theory What are
we computing? Why are we computing it?
What assumptions are needed to solve the
problem? Algorithm and representation
Details of computational strategy?
Sequential or parallel? How are assumptions
used in computation? Implementation How is
computation implemented in specific hardware?
(e.g. computer program, electronic hardware,
neurons)
2
Detecting Intensity Changes

• Smooth the image intensities
• reduces effect of noise
• sets resolution or scale of analysis
• Differentiate the smoothed intensities
• Transforms image into a representation that
  facilitates detection of intensity changes
• Detect and describe features in the transformed
  image
• (e.g. peaks or zero-crossings)

3
Smoothing the intensities
Intensity
Smoothing
More Smoothing
4
Intensity Derivative
Smoothed Intensity
First Derivative
(note that sign Is reversed)
Second Derivative
5
Analyzing a 2D image
Image after smoothing and second derivative
Image
Black Negative White Positive
Zero-Crossings
6
Smoothing the image intensities
Strategy 1 compute the average of the intensity
values in a neighborhood around each image
position Strategy 2 compute a weighted average
of the intensity values in a neighborhood around
each image position, using a smooth function that
weighs nearby intensities more heavily A Gaussian
function works well for this weighting. In one
dimension, the Gaussian function can be written
as
Smoothing can be performed using the convolution
operation
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The Derivative of a Convolution
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Smoothing a 2D Image
To smooth an image, I(x,y), we can convolve with
a 2D Gaussian
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Differentiation in 2D
To differentiate the smoothed 2D image, we will
use the Laplacian operator

We can again combine the smoothing and derivative
operations
(displayed with sign reversed)
10
Detecting intensity changes at multiple scales


11
Computing the contrast of intensity changes