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Unformatted text preview: r Bessel function a outoffocus distance (
H ( u, v ) = e − c u 2 + v2 19.05.2009 ) 5 6 c degree of turbulence
Dr. Pierre Elbischger  MIP1/ISAP'SS09 52 E19 Wiener filter
Degradation
Filter u (t ) s (t ) + m(t ) u (t ) Reconstruction
Filter H(f) W(f) n(t ) The optimal reconstruction filter in the
leastsquares sense is the Wiener filter
– It copes with image that are distorted
by the linear system H(f), and is
corrupted by additive noise. −1 W( f ) = H ( f ) corrupted image u (t ) reconstruced signal S( f ) 2 S( f ) + N( f )
2 2 inverse filter Wiener filter increased noise level u (t ) original signal
s (t ) regraded signal Whereby S(f) and N(f) denote the signal
power density spectrum and the noise
power density spectrum respectively.
19.05.2009 Dr. Pierre Elbischger  MIP1/ISAP'SS09 53 Example  Wiener filter – 3D widefield microscopy
When taking a Zseries of images using a widefield fluorescence microscope, it does not discriminate
between light emanating from inside or outside your plane of focus. In fact, you need only to focus the
object near the center of the region of interest to you, and then tell the microscope the upper and lower
limits of Ztravel, the number of images to take in this range, and how far apart (with a resolution
capability of 0.1 micrometers in Z) the images should be. You can the let the microscope take the series
of images, many of which will be completely out of focus. A proper deconvolution software then does its
magic and reallocates light to the correct pixels, and lo and behold, the images suddenly make sense
again, or most of them will make much more sense than they did before, anyway. raw image
19.05.2009 deconvolution result
Dr. Pierre Elbischger  MIP1/ISAP'SS09 54 Extended depthoffield (microscopy) Image series of outoffocus images (large microscopy magnification) Extended depthoffield image
19.05.2009 Dr. Pierre Elbischger  MIP1/ISAP'SS09 55 Solution: Exploiting the local contrast / variance local histogram
in a region of interest (ROI) frequency
Strong texture information
Sahrp image large standard deviation / variance
Weak texture information
unsharp image small standard deviation / variance gray value
19.05.2009 Dr. Pierre Elbischger  MIP1/ISAP'SS09 56 Extended depthoffield exploiting the local contrast 1. For each pixel in the image the local
variance in a certain neighborhood is
computed.
2. An image of extented depthoffield
is created by combining the pixel
values corresponding to sharp regions
in the input images, thus regions of
large local variance. 19.05.2009 Dr. Pierre Elbischger  MIP1/ISAP'SS09 57 Shading correction  Correction of nonuniform illumination
Multiplicative illuminationmodel f(i,j) = e(i,j)g(i,j)
g(i,j) ... undisturbed image
e(i,j) ... disturbance
f(i,j) ... corrupted image
Use a reference image c(i,j) to
compute the disturbance. In the
simplest case c may be a constant
(e.g., for images that are expected to
have a constant gray value –
homogeneous background, no
objects). g (i, j ) = c
f c (i, j ) = e(i, j )c
e(i, j ) =
19.05.2009 f c (i, j )
c Dr. Pierre Elbischger  MIP1/ISAP'SS09 Illumination correction g (i, j ) = f (i, j ) cf (i, j )
=
e(i, j )
f c (i, j )
58...
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This note was uploaded on 07/09/2009 for the course MEDIT 1 taught by Professor Pierreelschbinger during the Spring '09 term at Carinthia University of Applied Sciences.
 Spring '09
 PIERREELSCHBINGER

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