Implicit Surface Fitting Research Articles

A Coarse-to-Fine Strip Mosaicing Model for Airborne Bathymetric LiDAR Data

The airborne light detection and ranging (LiDAR) bathymetry (ALB) system is an extension of the ubiquitous topographic LiDAR mapping system and has been most simply characterized as adding a green laser to the infrared laser of topo systems. Due to the low point cloud density and monotonous objects in the scene, it is difficult to mosaicing the ALB strips. Therefore, the existing airborne laser scanning strip stitching algorithm has poor performance for ALB strips. In this article, a coarse-to-fine strip mosaicing model for ALB is proposed. The framework is fast and efficient and can handle large ALB data. An improved alpha shapes algorithm can fast and accurately determine the overlap region of strip is applied. Due to different data accuracy and spatial characteristics, the water area and land area are processed separately. A weight distribution-based coarse-to-fine registration model is designed for underwater areas. The topological constraint term is added to the nonrigid iterative closest point (ICP) cost function to prevent excessive deformation caused by outliers. The implicit B-spline surface fitting algorithm using the 3L algorithm and the least-squares trend surface fitting algorithm are applied separately to assign weights for overlapping strips to solve the limitation of no control or less control. Moreover, a random sample consensus (RANSAC)-ICP registration model characterized by the normal vector and curvature is constructed for land area. Finally, the comparisons with ICP highlight the superiority of the proposed approach in flexibility and accuracy. The root-mean-square error (RMSE) is 0.12 m and the maximum error is 0.36 m.

Volumetric lung nodule segmentation in thoracic CT scan using freehand sketch

The authors presented a novel computerised scheme to segment pulmonary nodules using freehand sketch. Here, freehand sketching is considered to identify the location of a nodule and it serves as a natural way and also it provides inferring adaptive information i.e. size, density, texture and mass centre etc. The proposed scheme includes two phases. In first phase using the freehand sketch analysis the multi seed points to select RoI. In the second phase nodule volumetric extraction is done using geometric modelling and implicit surface reconstruction for volumetric analysis. Spherical bins are used for ray triangle intersections and then local implicit surface fitting and blending method for surface reconstruction and depiction. The performance of the proposed scheme is assessed by accuracy and consistency using 112 CT examinations from LIDC. The IoU and ASD were used to assess the discrepancy between proposed method and inter observer agreement in the proposed approach. In estimating the reproducibility, the discrepancy in proposed scheme and the manual contouring by the expert is observed to be on an average of 0.13 ± 0.07 mm and 3.04 ± 1.7 mm respectively. The experiment shows that, the proposed scheme performs reasonably well and demonstrate merit of freehand sketch.

Quantifying Nanoscale Morphological Features of the Primary Cilium Membrane using Super-Resolution Fluorescence Microscopy

We present a method for capturing and quantifying the nanoscale morphological features of the primary cilium in mammalian cells. This finger-like organelle protrudes outside the plasma membrane on the order of 2-5 µm and is specialized to help facilitate Hedgehog signaling pathway activation. To study the primary cilium structure, we fix cells where individual transmembrane proteins, Smoothened, are tagged with single fluorescent labels. Using three-dimensional super-resolution fluorescence microscopy, we localize these proteins with 15-25 nm precision, providing us with a pointillistic reconstruction of the ciliary membrane. We then apply an implicit surface fitting algorithm on our point cloud to generate a triangulated surface mesh. This allows us to visualize and measure Mean Curvature (H)/Gaussian curvature (K) profiles along the shaft of the primary cilium. Not only do we measure the heterogeneity in shape from one cilium to another, but we also show a shift in curvature toward negative K values when retrograde ciliary cargo transport is severely impaired. Our method can be directly applied to studying membrane deformations present in various ciliopathies and cell features where curvature plays a role in determining the overall shape.

Computerized segmentation of pulmonary nodules depicted in CT examinations using freehand sketches

To aid a consistent segmentation of pulmonary nodules, the authors describe a novel computerized scheme that utilizes a freehand sketching technique and an improved break-and-repair strategy. This developed scheme consists of two primary parts. The first part is freehand sketch analysis, where the freehand sketching not only serves a natural way of specifying the location of a nodule, but also provides a mechanism for inferring adaptive information (e.g., the mass center, the density, and the size) in regard to the nodule. The second part is an improved break-and-repair strategy. The improvement avoids the time-consuming ray-triangle intersections using spherical bins and replaces the original global implicit surface reconstruction with a local implicit surface fitting and blending scheme. The performance of this scheme, including accuracy and consistence, was assessed using 50 CT examinations in the Lung Image Database Consortium (LIDC). For each of these examinations, a single nodule was selected under the aid of a publically available tool to assure these nodules were diverse in size, location, and density. Two radiologists were asked to use the developed tool to segment these nodules twice at different times (at least three months apart). A Hausdorff distance based method was used to assess the discrepancies (agreements) between the computerized results and the results by the four radiologists in the LIDC as well as the inter- and intrareader agreements in freehand sketching. The maximum and mean discrepancies in boundary outlines between the computerized scheme and the radiologists were 2.73 ± 1.32 mm and 1.01 ± 0.47 mm, respectively. When the nodules were classified (binned) into different size ranges, the maximum errors ranged from 1.91 to 4.13 mm; but smaller nodules had larger percentage discrepancies in term of size. Under the aid of the developed scheme, the inter- and intrareader variability in averaged maximum discrepancy across all types of pulmonary nodules were consistently smaller than 0.15 ± 0.07 mm. The computational cost in time of segmenting a pulmonary nodule ranged from 0.4 to 2.3 s with an average of 1.1 s for a typical desktop computer. The experiments showed that this scheme could achieve a reasonable performance in nodule segmentation and demonstrated the merits of incorporating freehand sketching into pulmonary nodule segmentation.

Parametric fitting of corneal height data to a biconic surface

As the average corneal shape can effectively be approximated by a conic section, a determination of the corneal shape by biconic parameters is desired. The purpose of the paper is to introduce a straightforward mathematical approach for extracting clinically relevant parameters of corneal surface, such as radii of curvature and conic constants for principle meridians and astigmatism.A general description for modeling the ocular surfaces in a biconic form is given, based on which an implicit parametric surface fitting algorithm is introduced. The solution of the biconic fitting is obtained by a two sequential least squares optimization approach with constrains. The data input can be raw information from any corneal topographer with not necessarily a uniform data distribution.Various simulated and clinical data are studied including surfaces with rotationally symmetric and non-symmetric geometries. The clinical data was obtained from the Pentacam (Oculus) for the patient having undergone a refractive surgery. A sub-micrometer fitting accuracy was obtained for all simulated surfaces: 0,08μm RMS fitting error at max for rotationally symmetric and 0,125μm for non-symmetric surfaces. The astigmatism was recovered in a sub-minutes resolution. The equality in rotational symmetric and the superiority in non-symmetric surfaces of the presented model over the widely used quadric fitting model is shown.The introduced biconic surface fitting algorithm is able to recover the apical radii of curvature and conic constants in principle meridians. This methodology could be a platform for advanced IOL calculations and enhanced contact lens fitting.

Automatic pulmonary fissure detection and lobe segmentation in CT chest images.

BackgroundMulti-detector Computed Tomography has become an invaluable tool for the diagnosis of chronic respiratory diseases. Based on CT images, the automatic algorithm to detect the fissures and divide the lung into five lobes will help regionally quantify, amongst others, the lung density, texture, airway and, blood vessel structures, ventilation and perfusion.MethodsSagittal adaptive fissure scanning based on the sparseness of the vessels and bronchi is employed to localize the potential fissure region. Following a Hessian matrix based line enhancement filter in the coronal slice, the shortest path is determined by means of Uniform Cost Search. Implicit surface fitting based on Radial Basis Functions is used to extract the fissure surface for lobe segmentation. By three implicit fissure surface functions, the lung is divided into five lobes. The proposed algorithm is tested by 14 datasets. The accuracy is evaluated by the mean (±S.D.), root mean square, and the maximum of the shortest Euclidian distance from the manually-defined fissure surface to that extracted by the algorithm.ResultsAveraged over all datasets, the mean (±S.D.), root mean square, and the maximum of the shortest Euclidian distance are 2.05 ± 1.80, 2.46 and 7.34 mm for the right oblique fissure. The measures are 2.77 ± 2.12, 3.13 and 7.75 mm for the right horizontal fissure, 2.31 ± 1.76, 3.25 and 6.83 mm for the left oblique fissure. The fissure detection works for the data with a small lung nodule nearby the fissure and a small lung subpleural nodule. The volume and emphysema index of each lobe can be calculated. The algorithm is very fast, e.g., to finish the fissure detection and fissure extension for the dataset with 320 slices only takes around 50 seconds.ConclusionsThe sagittal adaptive fissure scanning can localize the potential fissure regions quickly. After the potential region is enhanced by a Hessian based line enhancement filter, Uniform Cost Search can extract the fissures successfully in 2D. Surface fitting is able to obtain three implicit surface functions for each dataset. The current algorithm shows good accuracy, robustness and speed, may help locate the lesions into each lobe and analyze them regionally.

A rapid approach to convective aeroheating prediction of hypersonic vehicles

A rapid approach to hypersonic aeroheating predictions in the stagnation region and downstream is developed in the present paper. The engineering method is used to calculate inviscid hypersonic flowfields to reduce time cost, and a combination of the mass flow balance technique and the axisymmetric analog is proposed to account for the entropy swallowing effects. A three-dimensional linear method is derived to fit the vehicle surface flowfields. Then a new axisymmetric analog method based on linear flowfields and linear surface equations is developed, with the complexity and computational cost reduced dramatically. In the stagnation region, an implicit surface fitting is introduced to approximate the primary curvatures and a robust aeroheating prediction method is constructed. The proposed approach is verified on a variety of configurations including spherically blunted cone, double ellipsoid and aerospace vehicle. Numerical results indicate the followings: 1) The approach predicts aeroheating in about one second and the results agree well with CFD simulations and wind-tunnel measurements; 2) with the help of entropy correction, the precision is further improved in the streamline diverging regions on the vehicle surface, while little improvement is found after entropy correction in the regions where the streamlines do not diverge.

Shape “Break-and-Repair” Strategy and Its Application to Automated Medical Image Segmentation

In three-dimensional medical imaging, segmentation of specific anatomy structure is often a preprocessing step for computer-aided detection/diagnosis (CAD) purposes, and its performance has a significant impact on diagnosis of diseases as well as objective quantitative assessment of therapeutic efficacy. However, the existence of various diseases, image noise or artifacts, and individual anatomical variety generally impose a challenge for accurate segmentation of specific structures. To address these problems, a shape analysis strategy termed "break-and-repair" is presented in this study to facilitate automated medical image segmentation. Similar to surface approximation using a limited number of control points, the basic idea is to remove problematic regions and then estimate a smooth and complete surface shape by representing the remaining regions with high fidelity as an implicit function. The innovation of this shape analysis strategy is the capability of solving challenging medical image segmentation problems in a unified framework, regardless of the variability of anatomical structures in question. In our implementation, principal curvature analysis is used to identify and remove the problematic regions and radial basis function (RBF) based implicit surface fitting is used to achieve a closed (or complete) surface boundary. The feasibility and performance of this strategy are demonstrated by applying it to automated segmentation of two completely different anatomical structures depicted on CT examinations, namely human lungs and pulmonary nodules. Our quantitative experiments on a large number of clinical CT examinations collected from different sources demonstrate the accuracy, robustness, and generality of the shape "break-and-repair" strategy in medical image segmentation.

Orienting unorganized points for surface reconstruction

We address the problem of assigning consistently oriented normal vectors to unorganized point cloud with noises, non-uniformities, and thin-sharp features as a pre-processing step to surface reconstruction. The conventional orienting scheme using minimal spanning tree fails on points with the above defects. Different from the recently developed consolidation technique, our approach does not modify (i.e., down-sampling) the given point cloud so that we can reconstruct more surface details in the regions with very few points. The method consists of three major steps. We first propose a modified scheme of generating adaptive spherical cover for unorganized points by adding a sphere splitting step based on eigenvalue analysis. This modification can better preserve the connectivity of surface generated from the spheres in the highly sparse region. After generating the triangular mesh surface and cleaning its topology, a local search based algorithm is conducted to find the closest triangle to every input points and then specify their orientations. Lastly, an orientation-aware principle component analysis step gives correct and consistently oriented normal vectors to the unorganized input points. Conventional implicit surface fitting based approach can successfully reconstruct high quality surfaces from the unorganized point cloud with the help of consistently oriented normal vectors generated by our method.

Pulmonary Lobe Segmentation in CT Examinations Using Implicit Surface Fitting

Lobe identification in computed tomography (CT) examinations is often an important consideration during the diagnostic process as well as during treatment planning because of their relative independence of each other in terms of anatomy and function. In this paper, we present a new automated scheme for segmenting lung lobes depicted on 3-D CT examinations. The unique characteristic of this scheme is the representation of fissures in the form of implicit functions using Radial Basis Functions (RBFs), capable of seamlessly interpolating "holes" in the detected fissures and smoothly extrapolating the fissure surfaces to the lung boundaries resulting in a "natural" segmentation of lung lobes. A previously developed statistically based approach is used to detect pulmonary fissures and the constraint points for implicit surface fitting are selected from detected fissure surfaces in a greedy manner to improve fitting efficiency. In a preliminary assessment study, lobe segmentation results of 65 chest CT examinations, five of which were reconstructed with three section thicknesses of 0.625 mm, 1.25 mm, and 2.5 mm, were subjectively and independently evaluated by two experienced chest radiologists using a five category rating scale (i.e., excellent, good, fair, poor, and unacceptable). Thirty-three of 65 examinations (50.8%) with a section thickness of 0.625 mm were rated as either "excellent" or "good" by both radiologists and only one case (1.5%) was rated by both radiologists as "poor" or "unacceptable." Comparable performance was obtained with a slice thickness of 1.25 mm, but substantial performance deterioration occurred in examinations with a section thickness of 2.5 mm. The advantages of this scheme are its full automation, relative insensitivity to fissure completeness, and ease of implementation.

Weighted Least Squares for Visualization of Scanned Point Clouds

AbstractThis paper describes several improvements to implicit surface fitting over point clouds. Noisy stamped part point cloud data gathered by both a laser digitizer scanning system and a stereo vision sensor is processed using a method based on the weighted least squares algorithm. Two kernel functions are proposed: one using an enhanced sphere-of-influence graph (SIG) method to determine nearest neighbours; and a second using an improved Gaussian kernel. Automatic bandwidth adjustment is implemented for both methods. A method of incorporating a scalar attribute at each data point, which can represent any desired quantity and relate it to the surface at that point, is introduced. In this case surface strain data was gathered and processed by the scanning system, with a resulting thickness strain measurement calculated at each point. This strain data was used to introduce a temperature plot style colour map over the surface, allowing for fast and simple analysis of the strain of the formed part.

Sparse surface reconstruction with adaptive partition of unity and radial basis functions

A new implicit surface fitting method for surface reconstruction from scattered point data is proposed. The method combines an adaptive partition of unity approximation with least-squares RBF fitting and is capable of generating a high quality surface reconstruction. Given a set of points scattered over a smooth surface, first a sparse set of overlapped local approximations is constructed. The partition of unity generated from these local approximants already gives a faithful surface reconstruction. The final reconstruction is obtained by adding compactly supported RBFs. The main feature of the developed approach consists of using various regularization schemes which lead to economical, yet accurate surface reconstruction.

Finding ridges and valleys in a discrete surface using a modified MLS approximation

Implicit surface fitting is a promising approach to finding ridges and valleys in discrete surfaces, but existing techniques are time-consuming and rely on user-supplied tuning parameters. We use a modified MLS (moving-least-squares) approximation technique to estimate the local differential information near a vertex by means of an approximating surface. Ridge and valley vertices are easily detected as zero-crossings, and can then be connected along the direction of principal curvature. Our method, demonstrated on several large meshed models, produces a good fit which leads to improved visualization. It does not oscillate and is quick to compute.

Ridge-valley lines on meshes via implicit surface fitting

We propose a simple and effective method for detecting view-and scale-independent ridge-valley lines defined via first- and second-order curvature derivatives on shapes approximated by dense triangle meshes. A high-quality estimation of high-order surface derivatives is achieved by combining multi-level implicit surface fitting and finite difference approximations. We demonstrate that the ridges and valleys are geometrically and perceptually salient surface features, and, therefore, can be potentially used for shape recognition, coding, and quality evaluation purposes.

Implicit Fitting Using Radial Basis Functions with Ellipsoid Constraint

AbstractImplicit planar curve and surface fitting to a set of scattered points plays an important role in solving a wide variety of problems occurring in computer graphics modelling, computer graphics animation, and computer assisted surgery. The fitted implicit surfaces can be either algebraic or non‐algebraic. The main problem with most algebraic surface fitting algorithms is that the surface fitted to a given data set is often unbounded, multiple sheeted, and disconnected when a high degree polynomial is used, whereas a low degree polynomial is too simple to represent general shapes. Recently, there has been increasing interest in non‐algebraic implicit surface fitting. In these techniques, one popular way of representing an implicit surface has been the use of radial basis functions. This type of implicit surface can represent various shapes to a high level of accuracy. In this paper, we present an implicit surface fitting algorithm using radial basis functions with an ellipsoid constraint. This method does not need to build interior and exterior layers for the given data set or to use information on surface normal but still can fit the data accurately. Furthermore, the fitted shape can still capture the main features of the object when the data sets are extremely sparse. The algorithm involves solving a simple general eigen‐system and a computation of the inverse or psedo‐inverse of a matrix, which is straightforward to implement.