Topology repair of solid models using skeletons

Topology preserving thinning of cell complexes

A topology preserving skeleton is a synthetic representation of an object that retains its topology and many of its significant morphological properties. The process of obtaining the skeleton, referred to as skeletonization or thinning, is a very active research area. It plays a central role in reducing the amount of information to be processed during image analysis and visualization, computer-aided diagnosis, or by pattern recognition algorithms. This paper introduces a novel topology preserving thinning algorithm, which removes simple cells-a generalization of simple points-of a given cell complex. The test for simple cells is based on acyclicity tables automatically produced in advance with homology computations. Using acyclicity tables render the implementation of thinning algorithms straightforward. Moreover, the fact that tables are automatically filled for all possible configurations allows to rigorously prove the generality of the algorithm and to obtain fool-proof implementations. The novel approach enables, for the first time, according to our knowledge, to thin a general unstructured simplicial complex. Acyclicity tables for cubical and simplicial complexes and an open source implementation of the thinning algorithm are provided as an additional material to allow their immediate use in the vast number of applications arising in medical imaging and beyond.

Colon flattening using heat diffusion Riemannian metric

We propose a new colon flattening algorithm that is efficient, shape-preserving, and robust to topological noise. Unlike previous approaches, which require a mandatory topological denoising to remove fake handles, our algorithm directly flattens the colon surface without any denoising. In our method, we replace the original Euclidean metric of the colon surface with a heat diffusion metric that is insensitive to topological noise. Using this heat diffusion metric, we then solve a Laplacian equation followed by an integration step to compute the final flattening. We demonstrate that our method is shape-preserving and the shape of the polyps are well preserved. The flattened colon also provides an efficient way to enhance the navigation and inspection in virtual colonoscopy. We further show how the existing colon registration pipeline is made more robust by using our colon flattening. We have tested our method on several colon wall surfaces and the experimental results demonstrate the robustness and the efficiency of our method.

In situ casting and imaging of the rat airway tree for accurate 3D reconstruction

The use of anatomically accurate, animal-specific airway geometries is important for understanding and modeling the physiology of the respiratory system. One approach for acquiring detailed airway architecture is to create a bronchial cast of the conducting airways. However, typical casting procedures either do not faithfully preserve the in vivo branching angles or produce rigid casts that when removed for imaging are fragile and thus easily damaged. We address these problems by creating an in situ bronchial cast of the conducting airways in rats that can be subsequently imaged in situ using three-dimensional micro-CT imaging. We also demonstrate that deformations in airway branch angles resulting from the casting procedure are small, and that these angle deformations can be reversed through an interactive adjustment of the segmented cast geometry. Animal work was approved by the Institutional Animal Care and Use Committee of Pacific Northwest National Laboratory.

Cortical surface mapping using topology correction, partial flattening and 3D shape context-based non-rigid registration for use in quantifying atrophy in Alzheimer's disease

Magnetic resonance (MR) provides a non-invasive way to investigate changes in the brain resulting from aging or neurodegenerative disorders such as Alzheimer's disease (AD). Performing accurate analysis for population studies is challenging because of the interindividual anatomical variability. A large set of tools is found to perform studies of brain anatomy and population analysis (FreeSurfer, SPM, FSL). In this paper we present a newly developed surface-based processing pipeline (MILXCTE) that allows accurate vertex-wise statistical comparisons of brain modifications, such as cortical thickness (CTE). The brain is first segmented into the three main tissues: white matter, gray matter and cerebrospinal fluid, after CTE is computed, a topology corrected mesh is generated. Partial inflation and non-rigid registration of cortical surfaces to a common space using shape context are then performed. Each of the steps was firstly validated using MR images from the OASIS database. We then applied the pipeline to a sample of individuals randomly selected from the AIBL study on AD and compared with FreeSurfer. For a population of 50 individuals we found correlation of cortical thickness in all the regions of the brain (average r=0.62 left and r=0.64 right hemispheres). We finally computed changes in atrophy in 32 AD patients and 81 healthy elderly individuals. Significant differences were found in regions known to be affected in AD. We demonstrated the validity of the method for use in clinical studies which provides an alternative to well established techniques to compare different imaging biomarkers for the study of neurodegenerative diseases.

Topological correction of brain surface meshes using spherical harmonics

Surface reconstruction methods allow advanced analysis of structural and functional brain data beyond what can be achieved using volumetric images alone. Automated generation of cortical surface meshes from 3D brain MRI often leads to topological defects and geometrical artifacts that must be corrected to permit subsequent analysis. Here, we propose a novel method to repair topological defects using a surface reconstruction that relies on spherical harmonics. First, during reparameterization of the surface using a tiled platonic solid, the original MRI intensity values are used as a basis to select either a "fill" or "cut" operation for each topological defect. We modify the spherical map of the uncorrected brain surface mesh, such that certain triangles are favored while searching for the bounding triangle during reparameterization. Then, a low-pass filtered alternative reconstruction based on spherical harmonics is patched into the reconstructed surface in areas that previously contained defects. Self-intersections are repaired using a local smoothing algorithm that limits the number of affected points to less than 0.1% of the total, and as a last step, all modified points are adjusted based on the T1 intensity. We found that the corrected reconstructions have reduced distance error metrics compared with a "gold standard" surface created by averaging 12 scans of the same brain. Ninety-three percent of the topological defects in a set of 10 scans of control subjects were accurately corrected. The entire process takes 6-8 min of computation time. Further improvements are discussed, especially regarding the use of the T1-weighted image to make corrections.

High resolution lung airway cast segmentation with proper topology suitable for computational fluid dynamic simulations

Developing detailed lung airway models is an important step towards understanding the respiratory system. While modern imaging and airway casting approaches have dramatically improved the potential detail of such models, challenges have arisen in image processing as the demand for greater detail pushes the image processing approaches to their limits. Airway segmentations with proper topology have neither loops nor invalid voxel-to-voxel connections. Here we describe a new technique for segmenting airways with proper topology and apply the approach to an image volume generated by magnetic resonance imaging of a silicone cast created from an excised monkey lung.

Topology-corrected segmentation and local intensity estimates for improved partial volume classification of brain cortex in MRI

In magnetic resonance imaging (MRI), accuracy and precision with which brain structures may be quantified are frequently affected by the partial volume (PV) effect. PV is due to the limited spatial resolution of MRI compared to the size of anatomical structures. Accurate classification of mixed voxels and correct estimation of the proportion of each pure tissue (fractional content) may help to increase the precision of cortical thickness estimation in regions where this measure is particularly difficult, such as deep sulci. The contribution of this work is twofold: on the one hand, we propose a new method to label voxels and compute tissue fractional content, integrating a mechanism for detecting sulci with topology preserving operators. On the other hand, we improve the computation of the fractional content of mixed voxels using local estimation of pure tissue intensity means. Accuracy and precision were assessed using simulated and real MR data and comparison with other existing approaches demonstrated the benefits of our method. Significant improvements in gray matter (GM) classification and cortical thickness estimation were brought by the topology correction. The fractional content root mean squared error diminished by 6.3% (p<0.01) on simulated data. The reproducibility error decreased by 8.8% (p<0.001) and the Jaccard similarity measure increased by 3.5% on real data. Furthermore, compared with manually guided expert segmentations, the similarity measure was improved by 12.0% (p<0.001). Thickness estimation with the proposed method showed a higher reproducibility compared with the measure performed after partial volume classification using other methods.

Mesh composition on models with arbitrary boundary topology

This paper presents a new approach for the mesh composition on models with arbitrary boundary topology. After cutting the needed parts from existing mesh models and putting them into the right pose, an implicit surface is adopted to smoothly interpolate the boundaries of models under composition. An interface is developed to control the shape of the implicit transient surface by using sketches to specify the expected silhouettes. After that, a localized Marching Cubes algorithm is investigated to tessellate the implicit transient surface so that the mesh surface of composed model is generated. Different from existing approaches in which the models under composition are required to have pairwise merging boundaries, the framework developed based on our techniques have the new function to fuse models with arbitrary boundary topology.