Smoothness-guided 3-D reconstruction of 2-D histological images

This paper tackles two problems: (1) the reconstruction of 3-D volumes from 2-D post-mortem slices (e.g., histology, autoradiography, immunohistochemistry) in the absence of external reference, and (2) the quantitative evaluation of the 3-D reconstruction. We note that the quality of a reconstructed volume is usually assessed by considering the smoothness of some reconstructed structures of interest (e.g., the gray–white matter surfaces in brain images). Here we propose to use smoothness as a means to drive the reconstruction process itself. From a pair-wise rigid reconstruction of the 2-D slices, we first extract the boundaries of structures of interest. Those are then smoothed with a min–max curvature flow confined to the 2-D planes in which the slices lie. Finally, for each slice, we estimate a linear or flexible transformation from the sparse displacement field computed from the flow, which we apply to the original 2-D slices to obtain a smooth volume. In addition, we present a co-occurrence matrix-based technique to quantify the smoothness of reconstructed volumes. We discuss and validate the application of both our reconstruction approach and the smoothness measure on synthetic examples as well as real histological data.