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Rigid Slice-To-Volume Medical Image Registration through Markov Random Fields
Roque Porchetto, Franco Stramana, Nikos Paragios, Enzo Ferrante
TL;DR
Rigid slice-to-volume registration is commonly treated as a continuous optimization problem, and the paper notes that discrete methods had not yet been demonstrated for the rigid case. The authors formulate it as a pairwise graph-labeling problem and report more accurate, robust estimates than simplex, with further improvement from simplex refinement.
Problem
The paper addresses rigid slice-to-volume registration, usually solved with continuous optimization, for which the authors say discrete methods had not been shown to work.
Source: §1 · pp. 1–2Method
The method formulates single-slice, single-volume rigid registration as a discrete pairwise graph-labeling problem over six rigid-transform parameters.
Source: §1 · p. 1, §2.1 · p. 5Results
The discrete approach produces more accurate and robust rigid-transform estimates than simplex, and simplex refinement yields still more accurate estimates.
Source: §4 · p. 11Takeaways & Limitations
Slice-to-volume registration is used for image-guided surgery and can alleviate motion problems in volumetric acquisitions.
Source: §1.1 · p. 2On similar images, approaches jointly estimating rigid and local deformable parameters produced considerably better results than this rigid-only approach, including its refined version.
Source: §1 · p. 1, §4 · p. 11
Abstract
from arXiv · showhide
Rigid slice-to-volume registration is a challenging task, which finds application in medical imaging problems like image fusion for image guided surgeries and motion correction for volume reconstruction. It is usually formulated as an optimization problem and solved using standard continuous methods. In this paper, we discuss how this task be formulated as a discrete labeling problem on a graph. Inspired by previous works on discrete estimation of linear transformations using Markov Random Fields (MRFs), we model it using a pairwise MRF, where the nodes are associated to the rigid parameters, and the edges encode the relation between the variables. We compare the performance of the proposed method to a continuous formulation optimized using simplex, and we discuss how it can be used to further improve the accuracy of our approach. Promising results are obtained using a monomodal dataset composed of magnetic resonance images (MRI) of a beating heart.
1 Introduction
Slice-to-volume registration matches a tomographic 2D slice to a slice extracted from a 3D volume, a distinct task from matching projective images. This paper proposes a discrete graph-based approach to rigid registration, addressing a gap in prior work that focused on continuous or heuristic methods.
1 Introduction
- Unlike projective 2D/3D registration, slice-to-volume registration matches a tomographic slice whose pixels each correspond to a single voxel in 3D.In a projective image, each pixel represents a projection of voxels from a viewpoint.Source: §1 · p. 1
- The paper formulates single-slice, single-volume rigid registration as a discrete graph problem and evaluates it on heart MRI against continuous simplex optimization.The authors identify this as a demonstration that discrete methods and graphical models can estimate rigid transformations mapping a slice to a volume.Source: §1 · pp. 1–2
1.1 Motivation
- Slice-to-volume registration can fuse pre-operative volumes with intra-operative slices for image-guided surgery and correct slice-wise motion in volumetric acquisitions.Motivating examples include cardiac procedures, fetal brain imaging, and fMRI.Source: §1.1 · p. 2
1.2 Previous Work
- Prior discrete graph-based work addressed deformable slice-to-volume or projective registration, but rigid-only slice-to-volume methods had used continuous or heuristic optimization.The proposed discrete MRF formulation is inspired by; the authors also discuss refining its estimates with continuous optimization, following.Source: §1.2 · p. 3
2 Rigid Slice-to-Volume Registration through Markov Random Fields
The paper formulates rigid slice-to-volume registration as a discrete labeling problem over six rigid parameters, using a pairwise MRF to approximate their dependencies. It solves the labeling problem with FastPD, then uses incremental and simplex-refinement steps to improve search and accuracy.
2.1 Rigid Slice-to-Volume Registration as a Discrete Labeling Problem
- The six rigid parameters become nodes in a fully connected pairwise graph, an approximation of their higher-order dependencies that makes estimation tractable.The parameters are three rotations and three translations.Source: §2.1 · p. 5
- Each variable takes discrete variations around its current estimate, and pairwise costs evaluate matching after changing only the corresponding parameter pair.The label set includes zero variation, allowing a parameter to retain its current estimate.Source: §2.1 · p. 5
2.2 Discrete Optimization
- FastPD solves the resulting discrete multi-labeling problem, although the formulation does not satisfy the conditions for metric labeling.FastPD is based on linear programming and primal-dual strategies and generalizes α-expansion.Source: §2.2 · p. 5
- The refined approach gives better visual results than simplex and discrete approaches in the two illustrated slice tests.The figure compares difference images for the initial, simplex, discrete, and refined results.Source: Figure 2 · p. 6
2.3 Incremental Approach
- The incremental approach repeatedly solves the labeling problem while shrinking variation ranges, and a Gaussian pyramid increases the method’s capture range.The number of labels stays fixed as the maximum variation sizes decrease.Source: §2.3 · p. 6
2.4 Simplex Refinement Step
- When initialization is sufficiently good, both discrete and simplex methods perform well; the authors refine discrete results by optimizing the matching objective with simplex.The discrete solution initializes the simplex refinement.Source: §2.4 · pp. 6–7
3 Experiments and Results
The experiments compare discrete, simplex, and simplex-refined rigid slice-to-volume registration on beating-heart MRI. Discrete and refined approaches outperform simplex on individual tests, and they maintain good estimation error across a temporal series where simplex does not.
3 Experiments and Results
- The experiments compare the approaches on beating-heart MRI using individual registration cases and a temporal series, evaluating transformation error and image-match error.The evaluation measures translation and rotation distance from ground truth and mean absolute differences (MAD).Source: §3 · p. 7, §3.2 · p. 8
3.1 Implementation Details and Parameters Setting
- The experiments use four Gaussian pyramid levels; the refined approach runs simplex initialized with the discrete solution.The 3D images are not downsampled in z because of their low resolution in that direction.Source: §3.1 · pp. 7–8
3.2 Experiments
- Discrete and refined methods outperform simplex in average rotation, translation, and MAD errors, with the refined method also improving on the discrete estimate.The comparison is reported for the three alternative approaches in Table 1.Source: Table 1 · p. 8
- For 300 individual tests, discrete and refined methods reduce mean error and dispersion, and perform better than simplex in MAD and rotation/translation error.The tests use 100 slices with three initializations spanning progressively larger perturbation ranges.Source: Figure 4 · p. 9, §3.2 · p. 9
- Across the temporal series, discrete and refined approaches maintain good estimation error, whereas simplex cannot.Each slice's estimate initializes registration of the next slice; the first slice is initialized with the same noise parameters used to generate the sequence.Source: §3.2 · p. 10, Figure 5 · p. 10
4 Discussion, Conclusions and Future Works
The discrete graph-labeling approach produces more accurate and robust rigid estimates than simplex on the beating-heart MRI dataset, and simplex refinement further improves accuracy. Its rigid model is limited when slices are locally deformed relative to the volume; the paper proposes extending the model and exploring other applications.
4 Discussion, Conclusions and Future Works
- On the beating-heart MRI dataset, the discrete approach is more accurate and robust than simplex, and simplex refinement yields still more accurate estimates.The conclusion also notes consistency with conclusions for optical-flow estimation.Source: §4 · p. 11
- Rigid transformations cannot represent local deformations, and the method performs best when the slice is not deformed relative to the volume.The authors propose extending the approach to linear transformations that include anisotropic scaling and shearing.Source: §4 · p. 11
- The authors identify motion correction for volume reconstruction as another application of slice-to-volume registration to explore.Source: §4 · p. 11