Smooth 3-D Reconstruction for 2-D Histological Images

We present an image driven approach to the reconstruction of 3-D volumes from stacks of 2-D post-mortem sections (histology, cryoimaging, autoradiography or immunohistochemistry) in the absence of any external information. We note that a desirable quality of the reconstructed volume is the smoothness of its notable structures (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 an initial rigid pair-wise reconstruction of the input 2-D sections, we extract the boundaries of structures of interest. Those are then evolved under a mean curvature flow modified to constrain the flow within 2-D planes. Sparse displacement fields are then computed, independently for each slice, from the resulting flow. A variety of transformations, from globally rigid to arbitrarily flexible ones, can then be estimated from those fields and applied to the individual input 2-D sections to form a smooth volume. We detail our method and discuss preliminary results on both real histological data and synthetic examples.