@article{ab9ab311bde74823a3244948082a2747,

title = "Nonlinear filtering approach to 3-d gray-scale image interpolation",

abstract = "Three-dimensional (3-D) images are now common in radiology. A 3-D image is formed by stacking a contiguous sequence of two-dimensional cross-sectional images, or slices. Typically, the spacing between known slices is greater than the spacing between known points on a slice. Many visualization and image-analysis tasks, however, require the 3-D image to have equal sample spacing in all directions. To meet this requirement, one applies an interpolation technique to the known 3D image to generate a new uniformly sampled 3-D image. We propose a nonlinear-ftlter-based approach to gray-scale interpolation of 3-D images. The method, referred to as column-fitting interpolation, is reminiscent of the maximum-homogeneity filter used for image enhancement. We also draw upon the paradigm of relaxation labeling to devise an improved column-fitting interpolator. Both methods are typically more effecthe than traditional gray-scale interpolation techniques.",

author = "Higgins, {William E.} and Orlick, {Christopher J.} and Ledell, {Brian E.}",

note = "Funding Information: A three-dimensional (3-D) image is formed by stacking a contiguous sequence of two-dimensional (2-D) cross-sectional images. or slices [l], [a].T ypically, the spacing between known slices is greater than the spacing between known points on a slice. Image segmentation and visualization, however, usually require the 3-D image to have equal sample spacing in all directions. To meet this requirement, one applies an interpolation technique to the known 3-D image to generate a new uniformly sampled 3-D image [I]. [3]. Let v denote a 3-D image defined over 3-D Euclidean space R3. Following the notation of 141, let (T. y. 2 ) E s3 denote an image point, or voxel, and P(J.y, 2) be the gray-scale value of voxel (s.y . 2). To define the known finite-extent lattice of a typical 3-D digital image, let A.r, Ay, and Az represent the sample spacings for the known voxels in 7{\textquoteright}. Per the typical circumstances of 3- D imaging scanners, we assume that 1.r = 1 y = 1 and that the slice spacing A t > A. Thus, voxels are spaced further apart in z than in s and y. Let the lattice coordinates for the known voxels be given by .rL = ia, y, = jA, and 2k = x.Ai, where i, ,j, and k are nonnegative integers. Then, the collection of voxels 71(.r(.y ,. ih), i = 0, 1: 2. {\textquoteright}.. - 1, j = 0. 1. 2. .... -1-- 1. k = 0, 1. 2. .... Al - 1, specifies an !U-slice 3-D image I , . The kth slice of 11 at z = zk, denoted 73(., .. s~ j, consists of -1- x -1- voxels .o(.r,, y,. zk),i = 0. 1, . . . , S - 1,. j = 0. 1. 2. . . . . -1-- 1, k. fixed. We wish to compute an interpolated 3-D image F that has voxels specified at equal sampling intervals in .r, y, and ;; i.e., using the known :Wslice 3-D data z{\textquoteright}, we wish to compute Manuscript received January 20, 1995; revised April 30, 1996. This work was supported in part by the National Cancer Institute of the National Institutes of Health under NIH FIRST Award CA-53607. The Associate Editor responsible lor coordinating the review of this paper and recommending its publication was H. K. Huang. Asterisk indicates corresponding author. *W. E. Higgins is with the Department of{\textquoteright}Electrica1 Engineering, Computer Science and Engineering, and the Bioengineering Program, The Pennsylvania State University, 12 I Electrical Engineering East, University Park, PA 16802 USA (e-mail: weh@ruth.ece.psu.edu). C. J. Orlick and B. E. Ledell are with the Department of Electrical Engineering, The Pennsylvania State University, University Park, PA 16802 USA. Publishcr Itcm Identifier S 0278-0062(96)0575 1-5.",

year = "1996",

doi = "10.1109/42.511761",

language = "English (US)",

volume = "15",

pages = "580--587",

journal = "IEEE Transactions on Medical Imaging",

issn = "0278-0062",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

number = "4",

}