paper2 - A Model for Arbitrary Plane Imaging 223 A Model...

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Unformatted text preview: A Model for Arbitrary Plane Imaging 223 A Model for Arbitrary Plane Imaging, or the Brain in Pain Falls Mainly on the Plane Jeff Miller Dylan Helliwell Thaddeus Ladd Harvey Mudd College 1250 N. Dartmouth Ave. Claremont, CA 91711 { jmiller, dhelliwe, tladd } @math.hmc.edu Advisor: Michael Moody Summary We present an algorithm for imaging arbitrary oblique slices of a three- dimensionaldensityfunction, basedonarectilineararrayofuniformlysampled MRI data. We develop a linear interpolation scheme to determine densities of points in the image plane, incorporate a discrete convolution &lter to compensate for unwanted blur- ring caused by the interpolation, and provide an edge-detecting component based on &nite differencing. The resulting algorithm is suf&ciently fast for use on personal computers and allows control of parameters by the user. We exhibit the results of testing the algorithm on simulated MRI scans of a typical human brain and on contrived data structures designed to test the limitations of the model. Filtering distortions and inaccurate modeling due to interpolation appear in certain extreme scenarios. Nonetheless, we &nd that our algorithm is suitable for use in real-world medical imaging. The UMAP Journal 19 (3) (1998) 223236. c Copyright 1998 by COMAP, Inc. All rights reserved. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for pro&t or commercial advantage and that copies bear this notice. Abstracting with credit is permitted, but copyrights for components of this work owned by others than COMAP must be honored. To copy otherwise, to republish, to post on servers, or to redistribute to lists requires prior permission from COMAP. 224 The UMAP Journal 19.3 Constructing the Model Our model consists of four main parts: First, we develop a technique for positioning a plane anywhere in R 3 . Then we interpolate data from the region in R 3 that contains data onto the plane. Next, we use a sharpening technique to remove extra blur caused by the interpolation. Finally, we construct a difference array and use it to create a line drawing representing edges in the image. Assumptions Density variations in the source object are reasonably well behaved and continuous. Discontinuities such as sharp edges will be approximated in the model but only if they are isolated on a scale of several array elements. Similarly, erratic behavior and wild &uctuations can be accurately modeled only if they exist on a scale of several pixels. The model should image the source of the data array, not the array itself; but the accuracy of the oblique slice images depends on the accuracy of the data in the array....
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This note was uploaded on 01/16/2012 for the course MAD 4103 taught by Professor Li during the Spring '11 term at University of Central Florida.

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paper2 - A Model for Arbitrary Plane Imaging 223 A Model...

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