SU-F-J-83: Estimation of Deformation Field with Two-Scale Supervoxel Equations

Authors


Abstract

Purpose:

To circumvent the ill-posedness in the problem to estimate inhomogeneous motion or deformation field without resorting to global regularization conditions.

Methods:

We present a novel method for deformable registration. First, we estimate the deformation field at a coarse resolution level, with super-voxels as the spatial elements, keeping the target/reference image remains at the fine resolution. The resultant system of nonlinear equations are no longer under-determined. Next we establish local systems of 2-scale equations to determine the difference in deformation between the coarser level and the fine level, namely, the relative deformation between each super-voxel and its 8 sub-pixels. The equations are set up as follows. Consider an arbitrarily fixed super-voxel, we refer to it as the pivot voxel to be refined. Partition the other super-voxels as its near neighbors or far neighbors. In the local equations, the deformation at far neighbors are fixed as that obtained at the coarse resolution. The relative deformation at the sub-voxels within the pivot voxel is unknown and to be estimated. The deformation at the near neighbors is allowed to undergo changes, acting as elastic variables bridging the deformation associated with sub-pixels within the pivot voxel and that over the far neighbors. Each local system is not under-determined. The refinement is regularized by the principle of strong near-neighbor influence and weak far-neighbor influence, inspired primarily by the celebrated numerical Fast Multiple Method.

Results:

We demonstrate the viability and efficacy of the new method using 2D XCAT lung images. We provide comparisons to two other commonly used iterative methods.

Conclusion:

The proposed method is essentially a self-regularization mechanism, which is adaptive, non-parametric, non-global, in the sense that the solution at the finer resolution is regulated by the deformation structure itself at multiple resolution scale.

NIH Grant No: R01-184173

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