Fig 1.
Diagram depicting the registration methods.
The flow diagram in (A) depicts the overall experimental process, with (B) and (C) giving exploded views of the intensity-based and nucleus-based registration steps. Both approaches were initialized with a rigid, low-resolution intensity-based registration. The intensity-based registrations (B) were done using a standard iterative optimization loop. The nucleus-based registration (C) was computed non-iteratively in closed form based on automatically segmented and corresponded nucleus landmarks. Both methods were executed pairwise on each adjacent section pair, and as a final step these pairwise registrations were composed to form the final 3D reconstructed volume.
Fig 2.
Comparison of the alignment of bisected nuclei when measuring the accumulated registration error.
(A) The ideal error-free reference reconstruction, with bisected nuclei aligned with minimum residual error (a pairwise target registration error between corresponding halves of bisected nuclei of zero is depicted). (B) A reconstruction aligning nuclei with spatially unbiased error; but vessel connectedness (topology) and angle (geometry) are mostly conserved. (C) A reconstruction optimizing pairwise alignment of salient structures (the vessel cross sections in this example) preserves vessel topology but not geometry. Note that the pairwise target registration errors in (B) and (C) are similar, despite the lack of geometry preservation in C. The accumulated target registration error does capture the difference between (B) and (C); the plots in the bottom row indicate increasing accumulated error through the stack of sections.
Fig 3.
Nucleus correspondence method.
An illustration depicting the approach to establishing correspondence of nucleus p in section I with its best matching nucleus in adjacent section J. In this example, the candidate nuclei on section J are p’, q1, and q2, lying within a dashed circle of radius T centred on p (only 3 of the 18 candidate nuclei within the circle are illustrated here for simplicity). The candidate nucleus with the most similar surrounding tissue appearance is selected to correspond to p. Surrounding tissue appearance similarity is measured using the MSE image similarity metric, comparing the local square region I(p) centered on p with the local square regions J(p’), J(q1), and J(q2) centered on the candidates p’, q1, and q2. In this example, since MSE(I(p), J(p’)) < MSE(I(p), J(q1)) and MSE(I(p), J(p’)) < MSE(I(p), J(q2)), p is corresponded with p’.
Fig 4.
3D and 2D histology comparisons.
2D histology sections (pixel size 0.25 μm × 0.25 μm) and corresponding 3D reconstruction (voxel size of 0.25 μm × 0.25 μm × 5 μm) of serial histology sections of a normal (A-D) and regenerated mouse (E-H) TA post-femoral artery excision, immunostained for smooth muscle alpha-actin. A and E are registered using affine intensity based registration. B and F are registered using affine nucleus based registration. Within each column, the dashed lines indicate correspondence (according to color) between parts of the 2D sections and their locations on the 3D views. Also within each column, the lower case letter labels indicate correspondence between vessel cross sections on the 2D sections and their homologous locations within the 3D views. Blue arrows indicate incorrect vessel wall discontinuities arising from reconstruction error. The insets in the red boxes show 2D and 3D diameter measurements of the same vessel; note that the 2D measurement overestimates the 3D measurement by a factor of >6. Scale bars 100 μm.
Table 1.
Pairwise affine registration errors (μm) of the reference nucleus landmarks.
Table 2.
Pairwise and accumulated target registration error (TRE) values (μm) of the rigid and affine intensity-based and nucleus-based landmark registration (best in boldface).
Table 3.
Mean and SD of maximum pairwise and accumulated target registration error (TRE,) observed on each section for the rigid and affine intensity-based and nucleus-based landmark registration (best results in boldface).
Fig 5.
Registration accuracy measurement values.
Box plots of the rigid and affine target registration error (TRE) computed for each adjacent pair of sections (pairwise) and propagated throughout the 3D reconstruction (accumulated).
Table 4.
The displacement of the optimal mean squared error transformation from the affine nucleus-based registration.