A common task in the analysis of digitized histological sections is reconstructing a volumetric representation
of the original specimen. Image registration algorithms are used in this task to compensate for translational,
rotational, scale, shear, and local geometric differences between slices. Various systems have been developed
to perform volumetric reconstruction by registering pairs of successive slices according to rigid, similarity,
affine, and/or deformable transformations. To provide a coarse initial volumetric reconstruction, rigid
transformations may be too constrained, as they do not allow for scale or shear; but, affine transformations may
be too flexible, enabling larger scale or shear factors than physically reflected in the histological sections.
One difficulty with these systems is caused by the aperture problem; even if successive slices are registered
reasonably well, the composition of transformations over tens or hundreds of slices can yield global twisting and
scale and shear changes that yield a volumetric reconstruction that is significantly distorted from the shape of
the true specimen. The impact of the aperture problem can be reduced by considering more than two successive
images in the registration process. Systems that take this approach use global energy functions, elastic spring
models, post hoc filtering/smoothing, or solutions to shortest-path problems on graphs.
In this article, we propose a volume reconstruction algorithm that handles the aperture problem and yields
nearly rigid transformations (i.e., affine transformations with small scale and shear factors). Our algorithm is
based on robust geometric alignment of descriptive feature points (for example, using SIFT16) via constrained
optimization. We will illustrate our algorithm on the task of volumetric reconstruction from histological sections
of a chicken embryo with an embedded tumor spheroid.