Crest lines for surface segmentation and flattening

A Hierarchical Curve-Based Approach to the Analysis of Manifold Data

One of the data structures generated by medical imaging technology is high resolution point clouds representing anatomical surfaces. Stereophotogrammetry and laser scanning are two widely available sources of this kind of data. A standardised surface representation is required to provide a meaningful correspondence across different images as a basis for statistical analysis. Point locations with anatomical definitions, referred to as landmarks, have been the traditional approach. Landmarks can also be taken as the starting point for more general surface representations, often using templates which are warped on to an observed surface by matching landmark positions and subsequent local adjustment of the surface. The aim of the present paper is to provide a new approach which places anatomical curves at the heart of the surface representation and its analysis. Curves provide intermediate structures which capture the principal features of the manifold (surface) of interest through its ridges and valleys. As landmarks are often available these are used as anchoring points, but surface curvature information is the principal guide in estimating the curve locations. The surface patches between these curves are relatively flat and can be represented in a standardised manner by appropriate surface transects to give a complete surface model. This new approach does not require the use of a template, reference sample or any external information to guide the method and, when compared with a surface based approach, the estimation of curves is shown to have improved performance. In addition, examples involving applications to mussel shells and human faces show that the analysis of curve information can deliver more targeted and effective insight than the use of full surface information.

Accurate extraction of outermost biological characteristic curves in tooth preparations with fuzzy regions

BACKGROUND

The accuracy of extraction of biological characteristic curves in tooth preparations directly determines whether the tooth restorations and preparations are closely matched to allow appropriate adhesion. Ultimately, these will affect the success of the dental restoration surgery. In the process to obtain the tooth preparation, the dentist is required to grind the tooth manually and fuzzy regions may thus exist. Multiple feature curves with locally increased curvatures exist in these fuzzy regions, but only the outermost is preferred. The characteristic curve consists of points, some with and some without extreme curvature values. This study aims to extract an accurate biological characteristic curve.

METHOD

This challenging problem is mapped to the search of the minimum cost path for a graph, and is solved using the well-known A* algorithm. To identify the mapped graph, the outward direction coefficient is first introduced followed by the extremality coefficient node. Both of these coefficients ensure that the biological characteristic curve can be accurately extracted.

RESULTS

The conducted experiment demonstrated that the proposed algorithm can rapidly, accurately, and automatically obtain the outermost feature curve which passes through the fuzzy region of the tooth preparation. Additionally, the part of the biological characteristic curve related to the non-fuzzy region can also be accurately extracted.

CONCLUSIONS

The proposed algorithm significantly improves the accuracy of the extraction curve and the quality of the restoration design.

Anatomical curve identification

Methods for capturing images in three dimensions are now widely available, with stereo-photogrammetry and laser scanning being two common approaches. In anatomical studies, a number of landmarks are usually identified manually from each of these images and these form the basis of subsequent statistical analysis. However, landmarks express only a very small proportion of the information available from the images. Anatomically defined curves have the advantage of providing a much richer expression of shape. This is explored in the context of identifying the boundary of breasts from an image of the female torso and the boundary of the lips from a facial image. The curves of interest are characterised by ridges or valleys. Key issues in estimation are the ability to navigate across the anatomical surface in three-dimensions, the ability to recognise the relevant boundary and the need to assess the evidence for the presence of the surface feature of interest. The first issue is addressed by the use of principal curves, as an extension of principal components, the second by suitable assessment of curvature and the third by change-point detection. P-spline smoothing is used as an integral part of the methods but adaptations are made to the specific anatomical features of interest. After estimation of the boundary curves, the intermediate surfaces of the anatomical feature of interest can be characterised by surface interpolation. This allows shape variation to be explored using standard methods such as principal components. These tools are applied to a collection of images of women where one breast has been reconstructed after mastectomy and where interest lies in shape differences between the reconstructed and unreconstructed breasts. They are also applied to a collection of lip images where possible differences in shape between males and females are of interest.

Anisotropic elliptic PDEs for feature classification

The extraction and classification of multitype (point, curve, patch) features on manifolds are extremely challenging, due to the lack of rigorous definition for diverse feature forms. This paper seeks a novel solution of multitype features in a mathematically rigorous way and proposes an efficient method for feature classification on manifolds. We tackle this challenge by exploring a quasi-harmonic field (QHF) generated by elliptic PDEs, which is the stable state of heat diffusion governed by anisotropic diffusion tensor. Diffusion tensor locally encodes shape geometry and controls velocity and direction of the diffusion process. The global QHF weaves points into smooth regions separated by ridges and has superior performance in combating noise/holes. Our method's originality is highlighted by the integration of locally defined diffusion tensor and globally defined elliptic PDEs in an anisotropic manner. At the computational front, the heat diffusion PDE becomes a linear system with Dirichlet condition at heat sources (called seeds). Our new algorithms afford automatic seed selection, enhanced by a fast update procedure in a high-dimensional space. By employing diffusion probability, our method can handle both manufactured parts and organic objects. Various experiments demonstrate the flexibility and high performance of our method.

Consistent sulcal parcellation of longitudinal cortical surfaces

Automated accurate and consistent sulcal parcellation of longitudinal cortical surfaces is of great importance in studying longitudinal morphological and functional changes of human brains, since longitudinal cortical changes are normally very subtle, especially in aging brains. However, applying the existing methods (which were typically developed for cortical sulcal parcellation of a single cortical surface) independently to longitudinal cortical surfaces might generate longitudinally-inconsistent results. To overcome this limitation, this paper presents a novel energy function based method for accurate and consistent sulcal parcellation of longitudinal cortical surfaces. Specifically, both spatial and temporal smoothness are imposed in the energy function to obtain consistent longitudinal sulcal parcellation results. The energy function is efficiently minimized by a graph cut method. The proposed method has been successfully applied to sulcal parcellation of both real and simulated longitudinal inner cortical surfaces of human brain MR images. Both qualitative and quantitative evaluation results demonstrate the validity of the proposed method.

Automatic detection of anatomical features on 3D ear impressions for canonical representation

We propose a shape descriptor for 3D ear impressions, derived from a comprehensive set of anatomical features. Motivated by hearing aid (HA) manufacturing, the selection of the anatomical features is carried out according to their uniqueness and importance in HA design. This leads to a canonical ear signature that is highly distinctive and potentially well suited for classification. First, the anatomical features are characterized into generic topological and geometric features, namely concavities, elbows, ridges, peaks, and bumps on the surface of the ear. Fast and robust algorithms are then developed for their detection. This indirect approach ensures the generality of the algorithms with potential applications in biomedicine, biometrics, and reverse engineering.

Computer aided evaluation of ankylosing spondylitis using high-resolution CT

Ankylosing Spondylitis is a disease characterized by abnormal bone structures (syndesmophytes) growing at intervertebral disk spaces. Because this growth is so slow as to be undetectable on plain radiographs taken over years, it is desirable to resort to computerized techniques to complement qualitative human judgment with precise quantitative measures. We developed an algorithm with minimal user intervention that provides such measures using high-resolution computed tomography (CT) images. To the best of our knowledge it is the first time that determination of the disease's status is attempted by direct measurement of the syndesmophytes. The first part of our algorithm segments the whole vertebral body using a 3-D multiscale cascade of successive level sets. The second part extracts the continuous ridgeline of the vertebral body where syndesmophytes are located. For that we designed a novel level set implementation capable of evolving on the isosurface of an object represented by a triangular mesh using curvature features. The third part of the algorithm segments the syndesmophytes from the vertebral body using local cutting planes and quantitates them. We present experimental work done with 10 patients from each of which we processed five vertebrae. The results of our algorithm were validated by comparison with a semi-quantitative evaluation made by a medical expert who visually inspected the CT scans. Correlation between the two evaluations was found to be 0.936 ( p < 10(-18)) .

Computing length-preserved free boundary for quasi-developable mesh segmentation

Stretch-free surface flattening has been requested by a variety of applications. At present, the most difficult problem is how to segment a given model into nearly developable atlases so that a nearly stretch-free flattening can be computed. The criterion for segmentation is needed to evaluate the possibility of flattening a given surface patch, which should be fast computed. In this paper, we present a method to compute the length-preserved free boundary (LPFB) of a mesh patch which speeds up the mesh parameterization. The distortion on parameterization can then be employed as the criterion in a trial-and-error algorithm for segmenting a given model into nearly developable atlases. The computation of LPFB is formulated as a numerical optimization problem in the angle space, where we are trying to optimize the angle excesses on the boundary while preserving the constraints derived from the closed-path theorem and the length preservation.

An effective illustrative visualization framework based on photic extremum lines (PELs)

Conveying shape using feature lines is an important visualization tool in visual computing. The existing feature lines (e.g., ridges, valleys, silhouettes, suggestive contours, etc.) are solely determined by local geometry properties (e.g., normals and curvatures) as well as the view position. This paper is strongly inspired by the observation in human vision and perception that a sudden change in the luminance plays a critical role to faithfully represent and recover the 3D information. In particular, we adopt the edge detection techniques in image processing for 3D shape visualization and present Photic Extremum Lines (PELs) which emphasize significant variations of illumination over 3D surfaces. Comparing with the existing feature lines, PELs are more flexible and offer users more freedom to achieve desirable visualization effects. In addition, the user can easily control the shape visualization by changing the light position, the number of light sources, and choosing various light models. We compare PELs with the existing approaches and demonstrate that PEL is a flexible and effective tool to illustrate 3D surface and volume for visual computing.

Multiresolution imaging of MEG cortical sources using an explicit piecewise model

Imaging neural generators from MEG magnetic fields is often considered as a compromise between computationally-reasonable methodology that usually yields poor spatial resolution on the one hand, and more sophisticated approaches on the other hand, potentially leading to intractable computational costs. We approach the problem of obtaining well-resolved source images with unexcessive computation load with a multiresolution image model selection (MiMS) technique. The building blocks of the MiMS source model are parcels of the cortical surface which can be designed at multiple spatial resolutions with the combination of anatomical and functional priors. Computation charge is reduced owing to 1) compact parametric models of the activation of extended brain parcels using current multipole expansions and 2) the optimization of the generalized cross-validation error on image models, which is closed-form for the broad class of linear estimators of neural currents. Model selection can be complemented by any conventional imaging approach of neural currents restricted to the optimal image support obtained from MiMS. The estimation of the location and spatial extent of brain activations is discussed and evaluated using extensive Monte-Carlo simulations. An experimental evaluation was conducted with MEG data from a somatotopic paradigm. Results show that MiMS is an efficient image model selection technique with robust performances at realistic noise levels.

Robust feature classification and editing

Sharp edges, ridges, valleys, and prongs are critical for the appearance and an accurate representation of a 3D model. In this paper, we propose a novel approach that deals with the global shape of features in a robust way. Based on a remeshing algorithm which delivers an isotropic mesh in a feature-sensitive metric, features are recognized on multiple scales via integral invariants of local neighborhoods. Morphological and smoothing operations are then used for feature region extraction and classification into basic types such as ridges, valleys, and prongs. The resulting representation of feature regions is further used for feature-specific editing operations.

Thin structure segmentation and visualization in three-dimensional biomedical images: a shape-based approach

This paper presents a shape-based approach in extracting thin structures, such as lines and sheets, from three-dimensional (3D) biomedical images. Of particular interest is the capability to recover cellular structures, such as microtubule spindle fibers and plasma membranes, from laser scanning confocal microscopic (LSCM) data. Hessian-based shape methods are reviewed. A synthesized linear structure is used to evaluate the sensitivity of the multiscale filtering approach in extracting closely positioned fibers. We find that the multiscale approach tends to fuse lines together, which makes it unsuitable for visualizing mouse egg spindle fibers. Single-scale Gaussian filters, balanced between sensitivity and noise resistance, are adopted instead. In addition, through an ellipsoidal Gaussian model, the eigenvalues of the Hessian matrix are quantitatively associated with the standard deviations of the Gaussian model. Existing shape filters are simplified and applied to LSCM data. A significant improvement in extracting closely positioned thin lines is demonstrated by the resultant images. Further, the direct association of shape models and eigenvalues makes the processed images more understandable qualitatively and quantitatively.