Simulated nonrigid motion field with B-spline parameterization.
2D level set based segmentation results and extracted GOI features from target and reference images: (a) segmented contour with zero level set in agreement with reference kidney boundaries, (b) segmented contour with zero level set agrees with target kidney boundaries, (c) GOIs of the reference image represented by a narrowband LSF, (d) GOIs of the target image represented by a narrowband LSF. The segmented contours of target and reference images are overlaid in (a) (b).
2D motion estimation results in checkerboard presentation and absolute intensity difference maps: (a) checkerboard before registration, (b) checkerboard after registration, showing pronounced improvement of boundary continuity, (c) intensity difference map before registration, (d) intensity difference map after registration, showing significantly improved agreement between the target kidney boundary and reference kidney as well as reduced intensity difference.
Sample slices of reference 3D MR data: T2 weighted MR images with TR = 700ms, TE = 71 ms, FOV = 400 × 400 mm2, array size of 320 × 320 and slice-thickness of 6 mm.
3D segmentation and motion estimation results: (a) left kidney segmentation result overlaid with simulated nonrigid motion field, (b) overlays for reference kidney and target kidney before registration, (c) overlays of reference kidney and target kidney after registration, showing improved alignment.
Simulation workflow for adding contrast and intensity variations and nonrigid deformation to the reference image: Step 1. Changing image contrast by applying the gamma function to the reference image: I 1(x) = I 0(x)γ with γ = 0.6; Step 2. Introducing spatially varying intensity inhomogeneity to I 1(x) by multiplying it with spatially varying function M(x): ; Step 3. Introducing nonrigid motion effect to I 2(x) by deforming it with the simulated motion field T(x): I 3(x) = I 2(x)○T(x).
Performance comparison with benchmark alternatives in terms of mean absolute error (MAE) and standard deviation (SD): when there is no in intensity variations, the proposed method shows slightly inferior result; in the presence of intensity changes, it shows much improved robustness.
Comparison of registration performance in the presence of intensity and contrast variation between benchmark and proposed method: (a) optical flow, (b) mutual information, (c) multimodality demons, (d) proposed. Arrows in (a)–(c) indicate observable misregistration locations and arrows in (d) indicate the corresponding locations for the proposed method with improved registration performance.
Motion estimation results using real MR image sequences: (a) segmented contours (reference in magenta and target in cyan) and estimated motion field, showing downward and expansive motion of the kidneys, consistent with visual examination of the sequence; (b) checkerboard visualization preregistration; (c) checkerboard postregistration, where arrows are used to indicate locations with significant improvement, compared to the same locations indicated in (b).
Temporal evolution of the estimated kidney motion. (a) mean displacement in the superior-inferior direction, (b) mean displacement in the left-right direction, (c) temporal anatomical boundary trajectories reconstructed from estimated motion for the first ten images frames, with corresponding points connected and coded in the same color.
Test of sensitivity to parameter value selections by varying length λ and area β weighting coefficients: the segmentation results vary little for λ ∈ (3, 20) and β ∈ (0, 0.1), indicating the proposed method's insensitivity of parameter selections. (a) λ = 3, β = 0.01, (b) λ = 10, β = 0.01, (c) λ = 20, β = 0.01, (d) λ = 10, β = 0, (e) λ = 10, β = 0.005, (f) λ = 10, β = 0.1.
Test of robustness to intensity variations and noise: the segmented contour only degraded slightly as both intensity variations and significant noise were introduced, when the same fixed optimization parameter values were used. (a) Noise free, (b) with additive gaussian noise, (c) with intensity variations, and (d) with both gaussian noise and intensity variations.
Multiscale scheme for proposed algorithm
Error statistics of 2D experiments on simulated motion showing estimation errors comparable to voxel size (1.52 mm × 1.52 mm).
Error statistics of 3D experiments of simulated nonrigid motion, showing sub-voxel accuracy (voxel size = 0.8 mm × 0.8 mm × 6 mm).
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