Lu Liu

Surface Reconstruction From Non‐parallel Curve Networks

Building surfaces from cross‐section curves has wide applications including bio‐medical modeling. Previous work in this area has mostly focused on connecting simple closed curves on parallel cross‐sections. Here we consider the more general problem where input data may lie on non‐parallel cross‐sections and consist of curve networks that represent the segmentation of the underlying object by different material or tissue types (e.g., skin, muscle, bone, etc.) on each cross‐section. The desired output is a surface network that models both the exterior surface and the internal partitioning of the object. We introduce an algorithm that is capable of handling curve networks of arbitrary shape and topology on cross‐section planes with arbitrary orientations. Our algorithm is simple to implement and is guaranteed to produce a closed surface network that interpolates the curve network on each cross‐section. Our method is demonstrated on both synthetic and bio‐medical examples.

A simple and robust thinning algorithm on cell complexes

Thinning is a commonly used approach for computing skeleton descriptors. Traditional thinning algorithms often have a simple, iterative structure, yet producing skeletons that are overly sensitive to boundary perturbations. We present a novel thinning algorithm, operating on objects represented as cell complexes, that preserves the simplicity of typical thinning algorithms but generates skeletons that more robustly capture global shape features. Our key insight is formulating a skeleton significance measure, called medial persistence, which identify skeleton geometry at various dimensions (e.g., curves or surfaces) that represent object parts with different anisotropic elongations (e.g., tubes or plates). The measure is generally defined in any dimensions, and can be easily computed using a single thinning pass. Guided by medial persistence, our algorithm produces a family of topology and shape preserving skeletons whose shape and composition can be flexible controlled by desired level of medial persistence.

Interactive Separation of Segmented Bones in CT Volumes Using Graph Cut

We present a fast, interactive method for separating bones that have been collectively segmented from a CT volume. Given user-provided seed points, the method computes the separation as a multi-way cut on a weighted graph constructed from the binary, segmented volume. By properly designing and weighting the graph, we show that the resulting cut can accurately be placed at bone-interfaces using only a small number of seed points even when the data is noisy. The method has been implemented with an interactive graphical interface, and used to separate the 12 human foot bones in 10 CT volumes. The interactive tool produced compatible result with a ground-truth separation, generated by a completely manual labelling procedure, while reducing the human interaction time from a mean of 2.4 hours per volume in manual labelling down to approximately 18 minutes.

Tarsal and Metatarsal Bone Mineral Density Measurement Using Volumetric Quantitative Computed Tomography

A new method for measuring bone mineral density (BMD) of the tarsal and metatarsals is described using volumetric quantitative computed tomography (VQCT) in subjects with diabetes mellitus and peripheral neuropathy. VQCT images of a single foot were acquired twice from eight subjects (mean age 51 [11 SD], seven males, one female). The cortical shells of the seven tarsal and five metatarsal bones were identified and semiautomatically segmented from adjacent bones. Volume and BMD of each bone were measured separately from the two acquired scans for each subject. Whole-bone semiautomatic segmentation measurement errors were determined as the root mean square coefficient of variation for the volume and BMD of 0.8% and 0.9%, respectively. In addition to the whole-bone segmentation methods, we performed atlas-based partitioning of subregions within the second metatarsal for all subjects, from which the volumes and BMDs were obtained for each subregion. The subregion measurement BMD errors (root mean square coefficient of variation) within the shaft, proximal end, and distal end were shown to vary by approximately 1% between the two scans of each subject. The new methods demonstrated large variations in BMDs between the 12 bones of the foot within a subject and between subjects, and between subregions within the second metatarsal. These methods can provide an important outcome measure for clinical research trials investigating the effects of interventions, aging, or disease progression on bone loss, or gain, in individual foot bones.

Reliability of clinically relevant 3D foot bone angles from quantitative computed tomography

BackgroundSurgical treatment and clinical management of foot pathology requires accurate, reliable assessment of foot deformities. Foot and ankle deformities are multi-planar and therefore difficult to quantify by standard radiographs. Three-dimensional (3D) imaging modalities have been used to define bone orientations using inertial axes based on bone shape, but these inertial axes can fail to mimic established bone angles used in orthopaedics and clinical biomechanics. To provide improved clinical relevance of 3D bone angles, we developed techniques to define bone axes using landmarks on quantitative computed tomography (QCT) bone surface meshes. We aimed to assess measurement precision of landmark-based, 3D bone-to-bone orientations of hind foot and lesser tarsal bones for expert raters and a template-based automated method.MethodsTwo raters completed two repetitions each for twenty feet (10 right, 10 left), placing anatomic landmarks on the surfaces of calcaneus, talus, cuboid, and navicular. Landmarks were also recorded using the automated, template-based method. For each method, 3D bone axes were computed from landmark positions, and Cardan sequences produced sagittal, frontal, and transverse plane angles of bone-to-bone orientations. Angular reliability was assessed using intraclass correlation coefficients (ICCs) and the root mean square standard deviation (RMS-SD) for intra-rater and inter-rater precision, and rater versus automated agreement.ResultsIntra- and inter-rater ICCs were generally high (≥ 0.80), and the ICCs for each rater compared to the automated method were similarly high. RMS-SD intra-rater precision ranged from 1.4 to 3.6° and 2.4 to 6.1°, respectively, for the two raters, which compares favorably to uni-planar radiographic precision. Greatest variability was in Navicular: Talus sagittal plane angle and Cuboid: Calcaneus frontal plane angle. Precision of the automated, atlas-based template method versus the raters was comparable to each rater’s internal precision.ConclusionsIntra- and inter-rater precision suggest that the landmark-based methods have adequate test-retest reliability for 3D assessment of foot deformities. Agreement of the automated, atlas-based method with the expert raters suggests that the automated method is a valid, time-saving technique for foot deformity assessment. These methods have the potential to improve diagnosis of foot and ankle pathologies by allowing multi-planar quantification of deformities.

Volumetric Quantitative Computed Tomography Measurement Precision for Volumes and Densities of Tarsal and Metatarsal Bones

Diabetic foot diseases, such as ulcerations, infections, and neuropathic (Charcots) arthropathy, are major complications of diabetes mellitus (DM) and peripheral neuropathy (PN) and may cause osteolysis (bone loss) in foot bones. The purposes of our study were to make computed tomography (CT) measurements of foot-bone volumes and densities and to determine measurement precision (percent coefficients of variation for root-mean-square standard deviations) and least significant changes (LSCs) in these percentages that could be considered biologically real with 95% confidence. Volumetric quantitative CT scans were performed and repeated on 10 young healthy subjects and 13 subjects with DM and PN. Two raters used the original- and repeat-scan data sets to make measurements of volumes and bone mineral densities (BMDs) of the tarsal and metatarsal bones of the 2 feet (24 bones). Precisions for the bones ranged from 0.1% to 0.9% for volume measurements and from 0.6% to 1.9% for BMD measurements. The LSCs ranged from 0.4% to 2.5% for volume measurements and from 1.5% to 5.4% for BMD measurements. Volumetric quantitative CT provides precise measurements of volume and BMD for metatarsal and tarsal bones, where diabetic foot diseases commonly occur.

Subdivision meshes for organizing spatial biomedical data

As biomedical images and volumes are being collected at an increasing speed, there is a growing demand for efficient means to organize spatial information for comparative analysis. In many scenarios, such as determining gene expression patterns by in situ hybridization, the images are collected from multiple subjects over a common anatomical region, such as the brain. A fundamental challenge in comparing spatial data from different images is how to account for the shape variations among subjects, which make direct image-to-image comparisons meaningless. In this paper, we describe subdivision meshes as a geometric means to efficiently organize 2D images and 3D volumes collected from different subjects for comparison. The key advantages of a subdivision mesh for this purpose are its light-weight geometric structure and its explicit modeling of anatomical boundaries, which enable efficient and accurate registration. The multi-resolution structure of a subdivision mesh also allows development of fast comparison algorithms among registered images and volumes.

Polygonizing extremal surfaces with manifold guarantees

Extremal surfaces are a class of implicit surfaces that have been found useful in a variety of geometry reconstruction applications. Compared to iso-surfaces, extremal surfaces are particularly challenging to construct in part due to the presence of boundaries and the lack of a consistent orientation. We present a novel, grid-based algorithm for constructing polygonal approximations of extremal surfaces that may be open or unorientable. The algorithm is simple to implement and applicable to both uniform and adaptive grid structures. More importantly, the resulting discrete surface preserves the structural property of the extremal surface in a grid-independent manner. The algorithm is applied to extract ridge surfaces from intensity volumes and reconstruct surfaces from point sets with unoriented normals.

Automated, Foot-Bone Registration Using Subdivision-Embedded Atlases for Spatial Mapping of Bone Mineral Density

We present an atlas-based registration method for bones segmented from quantitative computed tomography (QCT) scans, with the goal of mapping their interior bone mineral densities (BMDs) volumetrically. We introduce a new type of deformable atlas, called subdivision-embedded atlas, which consists of a control grid represented as a tetrahedral subdivision mesh and a template bone surface embedded within the grid. Compared to a typical lattice-based deformation grid, the subdivision control grid possesses a relatively small degree of freedom tailored to the shape of the bone, which allows efficient fitting onto subjects. Compared with previous subdivision atlases, the novelty of our atlas lies in the addition of the embedded template surface, which further increases the accuracy of the fitting. Using this new atlas representation, we developed an efficient and fully automated pipeline for registering atlases of 12 tarsal and metatarsal bones to a segmented QCT scan of a human foot. Our evaluation shows that the mapping of BMD enabled by the registration is consistent for bones in repeated scans, and the regional BMD automatically computed from the mapping is not significantly different from expert annotations. The results suggest that our improved subdivision-based registration method is a reliable, efficient way to replace manual labor for measuring regional BMD in foot bones in QCT scans.

VolumeViewer: An Interactive Tool for Fitting Surfaces to Volume Data

Recent advances in surface reconstruction algorithms [BM07, LBD 08] allow surfaces to be built from contours lying on non-parallel planes. Such algorithms allow users to construct surfaces of similar quality more efficiently by using a small set of oblique contours, rather than many parallel contours. However, current medical imaging systems do not provide tools for sketching contours on oblique planes. In this paper, we take the first steps towards bridging the gap between the new surface reconstruction technologies and putting those methods to use in practice. We develop a novel interface for modeling surfaces from volume data by allowing the user to sketch contours on arbitrarily oriented cross-sections of the volume, and we examine the users’ ability to contour the same structures using oblique cross-sections with similar consistency as they can using parallel cross-sections. We measure the inter-observer and intra-observer variability of trained physicians contouring on oblique cross-sections of real patient data as compared to the traditional parallel cross-sections, and show that the variation is much higher for oblique contouring. We then show that this variability can be greatly reduced by integrating a collection of training images into the interface.