Detecting regions of intrest

1
Detecting regions of intrest

• Tresholdig
• Region growing
• Edge detection
• -Convolution masks
• -Hough transfrom
• -References

2
Why?

• Images are not homogenous, and the information
  is represtented by inhomogenousity. Thus if we
  can divede image in to parts, we can often ease
  the information aquiring process, whether it is
  performed by human eye or automated machine.
• Examples of uses in brain area include, but not
  limited to
• - Tresholding grey/white matter from MRI
  image
• - Evaluating lesion size
• - Mapping out arteries before cranial
  surgery

3
How

• By detecting discontuinity
• convolution masks
• Hough trasform
• By detecting similarity
• region growing
• adaptive region growing
• tresholding

4
Considerations

• Circumstances vary
• Segmentation system used in hospital X with good
  results my be lacking in hosptal Y
• There is no perfect segmentation
• Inter- and intra-expert diffirence
• Doctors are humans
• While clinical scientists use segmentation, the
  main customers are still normal radiologists.
  Even if you are sure that your system is perfect,
  you should leave space for manual correction.

5
Tresholding

• -In the most simplest form, it means that
• for pixel in x,y if f(x,y) lt L, we set it to
  0
• otherwise we give it value 255. (in 8-bit
  images)
• -We can also leave the f(x,y) unchanged if its
  equal or grater than L
• -We can also treshold on N levels, with
  treshold limits approximated for the needs of the
  application in question
• -Approximation from histograms
• -Optimal treshold via Otsu-method

6
Histograms
images and histograms corresponding to them
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Tresholding 1
Normal MBA-picture Picture in the left
tresholded to two levels
http//www.nazarethimaging.com/services.html
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Tresholding 2
Normal MBA-picture Picture in the lefy
tresholded to so that values above
treshold remain unchanged
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Tresholding 3
Normal MRI-picture Left picture tresholded
to three levels, ideally separating WM from
GM.
10
Optimal tresholding

• -Several methods exists
• - approximation from histogram
• - Gaussian PDF based optimization
• - Otsus method
• Two principal intensities P1,P2, both blurred
  by gaussian PDFs p1
• and p2. The image grey level PDF is then

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Optimal tresholding
Probability of erroneous classification is
To find optimal treshold, we may differantiate
this with respect to T and equate it to 0. This
leads to
Which can be written open as
Sure its not pretty, but its solvable, though
the possibility of two solutions indicates that
it may require two tresholds to obtain optimal
threshold
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Otsus method

• Image is 2D intensity function and contains N
  pixels with grey levels from 0 to L.
• Probability of grey level i in image is p(i)
  f(i)/N, where f(i) is the amount of pixels with
  intesity i.
• If we have to pixels divided to two classes C1
  (grey levels 1,2...,t) and C2 (grey levels
  t1,...,L) Then the PDs for the classes are
• C1 (p(1)p(2)...p(t))/
• C2 (p(t1)p(t2)...p(L))/
• where and

Means for the classes C1 and C2 are thus
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Otsus method

• If intenisty of whole image is
  
  
• then it can be shown that
• Using discriminant analysis, Otsu defined
  between-class
• variance of tresholded image as
• for two level tresholding. He also verfied that
  optimal treshold t is chosen so
• that between-class variance is maximized. This
  can be expanded to M-1
• tresholds with M classes.
• As we need to check all possible tresholds, this
  is computationally costly
• operation, but faster algotrithm exists. 3

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Otsus method
From left to right, orginal image, tresholded
image with Otsu(M3), tresholded image with
Otsu(M5)
15
Region growing

• We can choose seed pixel(s) from the image, and
  increase the area by certain rule
• This approach lead to reagion growing by additive
  tolerance or by running mean
• HVS and fuzzy based RG-techniques also exist.
• Split and merge method

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Region growing

• Idea is to grow the reagion by selecting one seed
  pixel that sure is part of the ROI in the image,
  and then comparing the neighbour pixels to the
  seed. If the neightbours pass the criteria, then
  they too are added to
• Criteria might be f(i,j) S T, where S is
  seed pixel value, f(i,j) the value of neighbout
  pixel and T some beforehand determined constant

From up left to down right, region growing by
additive tolerance (T1)
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Region growing

• Other possible criterion is f(i,j) C T,
  where C is running mean, calculated from the
  already included pixels, f(i,j) the value of
  neighbour pixel and T some beforehand determined
  constant

Region growing performed on tumor region, seed
(155,365)
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Region growing

• The other method is to split the image to
  consequently
• smaller reqions until all reqions are homogenous
  and then
• combining split reqions of similiar intensity to
  larger
• homogeous pieces.

19
Edge detection

• Edges are important feature when we want to
  recognize and/or separate areas form the image
• Even human visual system has enhanced
  edge-detection filter
• Based on convolution masks that react to change
• Hough transform maps lines to parameter space

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Convolution masks for edge detection

• Change is physically measured as derivate df/dx
• Discrete derivate is of form fx-fx-1
• When this is intepreted as 3x3 masks we get so
  called Prewitt masks

Most common Prewitt masks, upper left for change
in y direction, upper right for change in x
direction, lower two for changes in angles 45 and
135 degrees.
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Prewitt masking
Original MBA image
Angiogram convolved with x-directional Prewitt
mask
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Prewitt masking
Angiogram convolved with y-directional Prewitt
mask
Sum of x and y directional images
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Sobel masks

• Formulated as Prewitt masks, but have stronger
  weight on middle
• Magnitude and direction of the gradient can be
  expressed as

http//en.wikipedia.org/wiki/Sobel_operator
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Sobel masks
Original Sobel in x-direction Sobel in
y-direction
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Laplacian masks

• Second derivative tells about change in change
• Discrete second derivative in discreet form can
  be modelled as fx-2fx-1fx-2
• Second derivate is also known as Laplacian, hence
  the name Laplacian masks for mask that intepret
  second derivative
• Laplacian masks are omnidirectional, that is they
  detect edges in all directions
• Laplacian masks are very sensitive to noise,
  which is a double edged blade, as it makes them
  good at detecting sinlge pixels, but makes them
  less than agreeable edge detectors if noise is
  present in the image

Left two most common Lapacian masks
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Laplacian pixel detection
left image has one pixels slightly brighter than
the rest. Laplacian makes it clearly visible
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Laplacian of an image
Left Original image, right Laplacian of the
image
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Laplacian of an image
Left Original image, right Laplacian of the
image
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Laplacian of an image
Left Original image with SP noise, right
Laplacian of the image
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Laplacian of a Gaussian

• Normal Laplacian as high pass enphasis function
  also enchances the noise.
• This effect can be reduced by blurring the image
  first by 2D Gaussian function
• Due convolution theorem we can apply the
  Laplacian to Gaussian and then operate the image
  with operator thus created
• Consider Gaussian

. Laplacian of said function is
where
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Laplacian of a Gaussian
Formulation above leads to so called mexican hat
function, that can be approximated e.g. by
following 5x5 mask
While the LoG reduces the effects of the noise,
it naturally also causes some loss of detail and
blurring of edges
http//bp3.blogger.com/_wj-w-YeraxI/Rg8OrGOKuQI/AA
AAAAAAACU/3-NJz_FIP8M/s1600-h/ai_mexican-hat-funct
ion.JPG
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Laplacian of a Gaussian
Left Original image, right LoG of the image
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Hough transform

• For each data point, a number of lines are
  plotted going through it, all at different
  angles. These are shown here as solid lines.
• For each solid line a line is plotted which is
  perpendicular to it and which intersects the
  origin. These are shown as dashed lines.
• The length and angle of each dashed line is
  measured. In the diagram above, the results are
  shown in tables.
• This is repeated for each data point.
• A graph of length against angle, known as a Hough
  space graph, is then created.

http//en.wikipedia.org/wiki/Hough_transform
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Hough transform
Thus the intersection point in the Hough space
tells us the parameters of the line in real
space. This parameterization is also suitable for
curve and the idea can be expanded for circles
35
References

• 1 Biomedical Image Analysis by R.M Rangayyan
• 2 Digital Image Processing by R.C Gonzalez and
  R.E Woods
• 3 A fast algorithm for multilevel tresholding
• Ping-Sung Liao and Tse-Sheng Chen and Pau-Choo
  Chung (2001). "A Fast Algorithm for Multilevel
  Thresholding". J. Inf. Sci. Eng. 17 713-727.
• 4 http//en.wikipedia.org/wiki/Hough_transform
• 5 http//en.wikipedia.org/wiki/Sobel_operator