A MAP framework for tag line detection in SPAMM data using Markov random fields on the B-spline solid

Yasheng Chen, Amir A. Amini

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


Magnetic resonance (MR) tagging is a technique for measuring heart deformations through creation of a stripe grid pattern on cardiac images. In this paper, we present a maximum a posteriori (MAP) framework for detecting tag lines using a Markov random field (MRF) defined on the lattice generated by three-dimensional (3-D) and four-dimensional (4-D) (3-D+t) uniform sampling of B-spline models. In the 3-D case, MAP estimation is cast for detecting present tag features in the current image given an initial solid from the previous frame (the initial undeformed solid is manually positioned by clicking on corner points of a cube). The method also allows the parameters of the solid model, including the number of knots and the spline order, to he adjusted within the same framework. Fitting can start with a solid with less knots and lower spline order and proceed to one with more knots and/or higher order so as to achieve more accuracy and/or higher order of smoothness. In the 4-D case, the initial model is considered to be the linear interpolation of a sequence of optimal solids obtained from 3-D tracking. The same framework proposed for the 3-D case can once again be applied to arrive at a 4-D B-spline model with a higher temporal order.

Original languageEnglish
Pages (from-to)1110-1122
Number of pages13
JournalIEEE Transactions on Medical Imaging
Issue number9
StatePublished - Sep 2002


  • B-splines
  • Deformable models
  • Markov random fields
  • Tagged magnetic resonance imaging (MRI)


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