Order bessel function a out of focus distance h u v

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Unformatted text preview: r Bessel function a out-of-focus 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 least-squares 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 Z-series 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 Z-travel, 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 depth-of-field (microscopy) Image series of out-of-focus images (large microscopy magnification) Extended depth-of-field 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 depth-of-field 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 depth-of-field 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 non-uniform illumination Multiplicative illumination-model 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.

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