Geometry Processing of Conventionally Produced Mouse Brain Slice Images

Brain mapping research in most neuroanatomical laboratories relies on conventional processing techniques, which often introduce histological artifacts such as tissue tears and tissue loss. In this paper we present techniques and algorithms for automatic registration and 3D reconstruction of conventionally produced mouse brain slices in a standardized atlas space. This is achieved first by constructing a virtual 3D mouse brain model from annotated slices of Allen Reference Atlas (ARA). Virtual re-slicing of the reconstructed model generates ARA-based slice images corresponding to the microscopic images of histological brain sections. These image pairs are aligned using a geometric approach through contour images. Histological artifacts in the microscopic images are detected and removed using Constrained Delaunay Triangulation before performing global alignment. Finally, non-linear registration is performed by solving Laplace's equation with Dirichlet boundary conditions. Our methods provide significant improvements over previously reported registration techniques for the tested slices in 3D space, especially on slices with significant histological artifacts. Further, as an application we count the number of neurons in various anatomical regions using a dataset of 51 microscopic slices from a single mouse brain. This work represents a significant contribution to this subfield of neuroscience as it provides tools to neuroanatomist for analyzing and processing histological data.Comment: 14 pages, 11 figure

Guided Medical Data Segmentation Using Structure-Aligned Planar Contours

Segmentation of 3D/4D biological images is a critical step for a wide range of applications such as treatment planning, quantitative analysis, virtual simulations, and rendering visualizations. Automatic segmentation methods are becoming more reliable, but many experts still rely on manual intervention which makes segmentation a time and resource intensive bottleneck. Marking boundary contours in 3D images can be difficult when images are often noisy or the delineation of biological tissue is unclear. Non-parallel contours can be more accurate and reduce the amount of marking necessary, but require extra effort to ensure boundary consistency and maintain spatial orientation. This dissertation focuses three problems that pertain to drawing non-parallel contour networks and generating a segmentation surface from those networks. First a guided structure-aligned segmentation system is detailed that utilizes prior structure knowledge from past segmentations of similar data. It employs a contouring protocol to aid in navigating the volume data and support using arbitrarily-oriented contouring planes placed to capture or follow the global structure shape. A user study is provided to test how well novices perform segmentation using this system. The following two problems then aim to improve different aspects of this system. A new deformation approach to reconstruction is discussed which deforms previous segmentation meshes to fit protocol drawn contours from new data instances in order to obtain accurate segmentations that have the correct topology and general shape and preserves fine details. The focus is on the problem of finding a correspondence between a mesh and a set of contours describing a similar shape. And finally, a new robust algorithm that resolves inconsistencies in contour networks is detailed. Inconsistent contours are faster and less demanding to draw, and they allow the segmenter to focus on drawing boundaries and not maintaining consistency. However, inconsistency is detrimental to most reconstruction algorithms, so the network must be fixed as a post process after drawing

Composite Generalized Elliptic Curve-Based Surface Reconstruction

Cross-section curves play an important role in many fields. Analytically representing cross-section curves can greatly reduce design variables and related storage costs and facilitate other applications. In this paper, we propose composite generalized elliptic curves to approximate open and closed cross-section curves, present their mathematical expressions, and derive the mathematical equations of surface reconstruction from composite generalized elliptic curves. The examples given in this paper demonstrate the effectiveness and high accuracy of the proposed method. Due to the analytical nature of composite generalized elliptic curves and the surfaces reconstructed from them, the proposed method can reduce design variables and storage requirements and facilitate other applications such as level of detail

Construction of Smooth Branching Surfaces using T-splines

The request for designing or reconstructing objects from planar cross sections arises in various applications, ranging from CAD to GIS and Medical Imaging. The present work focuses on the " one-to-many " branching problem, where one of the planes can be populated with many, possibly tortuous and densely packed, contours. The proposed method combines the proximity information offered by the Euclidean Voronoi diagram with the concept of surrounding curve, introduced in [1], and T-splines technology [2] for securing a flexible and portable representation. Our algorithm delivers a single T-spline that deviates from the given contours less than a user-specified tolerance, measured via the so-called discrete Fréchet distance [3] and is C 2 everywhere except from a finite set of point-neighborhoods. Subject to minor enrichment, the algorithm is also capable to handle the " many-to-many " configuration as well as the global reconstruction problem involving contours on several planes

Toward Controllable and Robust Surface Reconstruction from Spatial Curves

Reconstructing surface from a set of spatial curves is a fundamental problem in computer graphics and computational geometry. It often arises in many applications across various disciplines, such as industrial prototyping, artistic design and biomedical imaging. While the problem has been widely studied for years, challenges remain for handling different type of curve inputs while satisfying various constraints. We study studied three related computational tasks in this thesis. First, we propose an algorithm for reconstructing multi-labeled material interfaces from cross-sectional curves that allows for explicit topology control. Second, we addressed the consistency restoration, a critical but overlooked problem in applying algorithms of surface reconstruction to real-world cross-sections data. Lastly, we propose the Variational Implicit Point Set Surface which allows us to robustly handle noisy, sparse and non-uniform inputs, such as samples from spatial curves