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Title: Probabilistic Characterization of Partial Volume Effects in Imaging of Rectangular Objects

In imaging, a partial volume effect refers to the problem that arises when the system resolution is low relative to the size of the object being imaged [1, 2]. In this setting, it is likely that most voxels occupied by the object are only partially covered, and that the fraction covered in each voxel is low. This makes the problem of object detection and image segmentation very difficult because the algorithms designed for these purposes rely on pixel summary statistics. If the area covered by the object is very low in relatively many of the total number of the voxels the object occupies, these summary statistics may not reach the thresholds required to detect this object. It is thus important to understand the extent of partial volume effect for a given object size and resolution. This technical report focuses on rectangular objects and derives the probability distributions for three quantities for such objects: 1) the number of fully covered voxels, 2) the number of partially covered voxels, and 3) the fractions of the total volume covered in the partially covered voxels. The derivations are first shown for 2-D settings and are then extended to 3-D settings.
Authors:
 [1]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
OSTI Identifier:
1184185
Report Number(s):
LLNL-TR--670422
DOE Contract Number:
DE-AC52-07NA27344
Resource Type:
Technical Report
Research Org:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE