Piecewise Affine Registration of Biological Images for Volume Reconstruction

This manuscript tackles the reconstruction of 3D volumes via mono-modal registration of series of 2D biological images (histological sections, autoradiographs, cryosections, etc.). The process of acquiring these images typically induces composite transformations that we model as a number of rigid or affine local transformations embedded in an elastic one. We propose a registration approach closely derived from this model. Given a pair of input images, we first compute a dense similarity field between them with a block matching algorithm. We use as a similarity measure an extension of the classical correlation coefficient that improves the consistency of the field. A hierarchical clustering algorithm then automatically partitions the field into a number of classes from which we extract independent pairs of sub-images. Our clustering algorithm relies on the Earth mover’s distribution metric and is additionally guided by robust least-square estimation of the transformations associated with each cluster. Finally, the pairs of sub-images are, independently, affinely registered and a hybrid affine/non-linear interpolation scheme is used to compose the output registered image. We investigate the behavior of our approach on several batches of histological data and discuss its sensitivity to parameters and noise

Automated Piecewise Affine Registration of Biological Images

This report tackles the registration of 2D biological images (histological sections or autoradiographs) to 2D images from the same or different modalities (e.g., histology or MRI). The process of acquiring these images typically induces composite transformations that we model as a number of rigid or affine local transformations embedded in an elastic one. We propose a registration approach closely derived from this model. Given a pair of input images, we first compute a dense similarity field between them with a block matching algorithm. A hierarchical clustering algorithm then automatically partitions this field into a number of classes from which we extract independent pairs of sub-images. Our clustering algorithm relies on the Earth mover's distribution metric and is additionally guided by robust least-square estimation of the transformations associated with each cluster. Finally, the pairs of sub-images are, independently, affinely registered and a hybrid affine/non-linear interpolation scheme is used to compose the output registered image. We investigate the behavior of our approach under a variety of conditions, and discuss examples using simulated and real medical images, including MRI, autoradiography, histology and cryosection data. We also detail the reconstruction of a 3-D volume from a series of 2-D histological sections and compare it against a reconstruction obtained with a global rigid approach

M\"obius Invariants of Shapes and Images

Identifying when different images are of the same object despite changes caused by imaging technologies, or processes such as growth, has many applications in fields such as computer vision and biological image analysis. One approach to this problem is to identify the group of possible transformations of the object and to find invariants to the action of that group, meaning that the object has the same values of the invariants despite the action of the group. In this paper we study the invariants of planar shapes and images under the M\"obius group $\mathrm{PSL}(2,\mathbb{C})$, which arises in the conformal camera model of vision and may also correspond to neurological aspects of vision, such as grouping of lines and circles. We survey properties of invariants that are important in applications, and the known M\"obius invariants, and then develop an algorithm by which shapes can be recognised that is M\"obius- and reparametrization-invariant, numerically stable, and robust to noise. We demonstrate the efficacy of this new invariant approach on sets of curves, and then develop a M\"obius-invariant signature of grey-scale images

Class-Based Feature Matching Across Unrestricted Transformations

We develop a novel method for class-based feature matching across large changes in viewing conditions. The method is based on the property that when objects share a similar part, the similarity is preserved across viewing conditions. Given a feature and a training set of object images, we first identify the subset of objects that share this feature. The transformation of the feature's appearance across viewing conditions is determined mainly by properties of the feature, rather than of the object in which it is embedded. Therefore, the transformed feature will be shared by approximately the same set of objects. Based on this consistency requirement, corresponding features can be reliably identified from a set of candidate matches. Unlike previous approaches, the proposed scheme compares feature appearances only in similar viewing conditions, rather than across different viewing conditions. As a result, the scheme is not restricted to locally planar objects or affine transformations. The approach also does not require examples of correct matches. We show that by using the proposed method, a dense set of accurate correspondences can be obtained. Experimental comparisons demonstrate that matching accuracy is significantly improved over previous schemes. Finally, we show that the scheme can be successfully used for invariant object recognition

Large Deformation Diffeomorphic Metric Mapping Registration of Reconstructed 3D Histological Section Images and in vivo MR Images

Our current understanding of neuroanatomical abnormalities in neuropsychiatric diseases is based largely on magnetic resonance imaging (MRI) and post mortem histological analyses of the brain. Further advances in elucidating altered brain structure in these human conditions might emerge from combining MRI and histological methods. We propose a multistage method for registering 3D volumes reconstructed from histological sections to corresponding in vivo MRI volumes from the same subjects: (1) manual segmentation of white matter (WM), gray matter (GM) and cerebrospinal fluid (CSF) compartments in histological sections, (2) alignment of consecutive histological sections using 2D rigid transformation to construct a 3D histological image volume from the aligned sections, (3) registration of reconstructed 3D histological volumes to the corresponding 3D MRI volumes using 3D affine transformation, (4) intensity normalization of images via histogram matching, and (5) registration of the volumes via intensity based large deformation diffeomorphic metric (LDDMM) image matching algorithm. Here we demonstrate the utility of our method in the transfer of cytoarchitectonic information from histological sections to identify regions of interest in MRI scans of nine adult macaque brains for morphometric analyses. LDDMM improved the accuracy of the registration via decreased distances between GM/CSF surfaces after LDDMM (0.39 ± 0.13 mm) compared to distances after affine registration (0.76 ± 0.41 mm). Similarly, WM/GM distances decreased to 0.28 ± 0.16 mm after LDDMM compared to 0.54 ± 0.39 mm after affine registration. The multistage registration method may find broad application for mapping histologically based information, for example, receptor distributions, gene expression, onto MRI volumes

Image registration and visualization of in situ gene expression images.

In the age of high-throughput molecular biology techniques, scientists have incorporated the methodology of in-situ hybridization to map spatial patterns of gene expression. In order to compare expression patterns within a common tissue structure, these images need to be registered or organized into a common coordinate system for alignment to a reference or atlas images. We use three different image registration methodologies (manual; correlation based; mutual information based) to determine the common coordinate system for the reference and in-situ hybridization images. All three methodologies are incorporated into a Matlab tool to visualize the results in a user friendly way and save them for future work. Our results suggest that the user-defined landmark method is best when considering images from different modalities; automated landmark detection is best when the images are expected to have a high degree of consistency; and the mutual information methodology is useful when the images are from the same modality

Subset Warping: Rubber Sheeting with Cuts

Image warping, often referred to as "rubber sheeting" represents the deformation of a domain image space into a range image space. In this paper, a technique is described which extends the definition of a rubber-sheet transformation to allow a polygonal region to be warped into one or more subsets of itself, where the subsets may be multiply connected. To do this, it constructs a set of "slits" in the domain image, which correspond to discontinuities in the range image, using a technique based on generalized Voronoi diagrams. The concept of medial axis is extended to describe inner and outer medial contours of a polygon. Polygonal regions are decomposed into annular subregions, and path homotopies are introduced to describe the annular subregions. These constructions motivate the definition of a ladder, which guides the construction of grid point pairs necessary to effect the warp itself