You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Image registration between histology and magnetic resonance imaging (MRI) is a challenging task due to differences in structural content and contrast. Too thick and wide specimens cannot be processed all at once and must be cut into smaller pieces. This dramatically increases the complexity of the problem, since each piece should be individually and manually pre-aligned. To the best of our knowledge, no automatic method can reliably locate such piece of tissue within its respective whole in the MRI slice, and align it without any prior information. We propose here a novel automatic approach to the joint problem of multimodal registration between histology and MRI, when only a fraction of tissue is available from histology. The approach relies on the representation of images using their level lines so as to reach contrast invariance. Shape elements obtained via the extraction of bitangents are encoded in a projective-invariant manner, which permits the identification of common pieces of curves between two images. We evaluated the approach on human brain histology and compared resulting alignments against manually annotated ground truths. Considering the complexity of the brain folding patterns, preliminary results are promising and suggest the use of characteristic and meaningful shape elements for improved robustness and efficiency.

Cited Abstract(s):
[1]: We present a method for fast, approximate registration of whole-slide images (WSIs) of histopathology serial sections. Popular histopathology slide registration methods in the existing literature tend towards intensity-based approaches. 1, 2 Further input, in the form of an approximate initial transformation to be applied to one of the two WSIs, is then usually required, and this transformation needs to be optimised. Such a transformation is not readily available in this context and thus there is a need for fast approximation of these parameters. Fast registration is achieved by comparison of the external boundaries of adjacent tissue sections, using local curvature on multiple scales to assess similarity. Our representation of curvature is a modified version of the Curvature Scale Space (CSS) 3 image. We substitute zero crossings with signed local absolute maxima of curvature to improve the registration's robustness to the subtle morphological differences of adjacent sections. A pairwise matching is made between curvature maxima at scales increasing exponentially, the matching minimizes the distance between maxima pairs at each scale. The boundary points corresponding to the matched maxima pairs are used to estimate the desired transformation. Our method is highly robust to translation, rotation, and linear scaling, and shows good performance in cases of moderate non-linear scaling. On our set of test images the algorithm shows improved reliability and processing speed in comparison to existing CSS based registration methods.

[2]: A new two-stage approach for nonlinear brain image registration is proposed. In the first stage, an active contour algorithm is used to establish a homothetic one-to-one map between a set of region boundaries in two images to be registered. This mapping is used in the second step: a two-dimensional transformation which is based on an elastic body deformation. This method is tested by registering magnetic resonance images to atlas images.

[3]: A new approach is proposed for registering a set of histological coronal two-dimensional images of a rat brain sectional material with coronal sections of a three-dimensional brain atlas, an intrinsic step and a significant challenge to current efforts in brain mapping and multimodal fusion of experimental data. The alignment problem is based on matching external contours of the brain sections, and operates in the presence of tissue distortion and tears which are routinely encountered, and possible scale, rotation, and shear changes (the affine and weak perspective groups). It is based on a novel set of local absolute affine invariants derived from the set of ordered inflection points on the external contour represented by a cubic B-spline curve. The inflection points are local intrinsic geometric features, which are preserved under both the affine and the weak perspective transformations. The invariants are constructed from the sequence of area patches bounded by the contour and the line connecting two consecutive inflection points, and hence do make direct use of the area (volume) invariance property associated with the affine transformation. These local absolute invariants are very well suited to handle the tissue distortion and tears (occlusion problem).

[4]:
Regarding geometric approaches, one possible strategy to align histology and clinical imaging is to simplify the images into their contours, so as to come down to a monomodal registration problem and use the shape information provided by the external boundaries. In [3] , contours from both histology and slices from a rat brain atlas were extracted via thresholding and represented using B-splines. Then, they were described by means of sets of affine invariants constructed from the sequence of area patches bounded by the contour and the line connecting two consecutive inflections. In [1] , Curvature Scale Space [4] was used for the registration of whole-slide images of histological sections in order to represent shape (the tissue boundary) at various scales. In [2] , curvature maps at different scales were used to match boundaries of full brain MRI extracted via an active contour algorithm. The main weaknesses of active contours are the number of parameters and the sensitivity to initialisation.