Computing Topology Preservation of RBF Transformations for Landmark-Based Image Registration

In image registration, a proper transformation should be topology preserving. Especially for landmark-based image registration, if the displacement of one landmark is larger enough than those of neighbourhood landmarks, topology violation will be occurred. This paper aim to analyse the topology preservation of some Radial Basis Functions (RBFs) which are used to model deformations in image registration. Mat\'{e}rn functions are quite common in the statistic literature (see, e.g. \cite{Matern86,Stein99}). In this paper, we use them to solve the landmark-based image registration problem. We present the topology preservation properties of RBFs in one landmark and four landmarks model respectively. Numerical results of three kinds of Mat\'{e}rn transformations are compared with results of Gaussian, Wendland's, and Wu's functions

Symmetry-guided nonrigid registration: the case for distortion correction in multidimensional photoemission spectroscopy

Image symmetrization is an effective strategy to correct symmetry distortion in experimental data for which symmetry is essential in the subsequent analysis. In the process, a coordinate transform, the symmetrization transform, is required to undo the distortion. The transform may be determined by image registration (i.e. alignment) with symmetry constraints imposed in the registration target and in the iterative parameter tuning, which we call symmetry-guided registration. An example use case of image symmetrization is found in electronic band structure mapping by multidimensional photoemission spectroscopy, which employs a 3D time-of-flight detector to measure electrons sorted into the momentum ($k_x$, $k_y$) and energy ($E$) coordinates. In reality, imperfect instrument design, sample geometry and experimental settings cause distortion of the photoelectron trajectories and, therefore, the symmetry in the measured band structure, which hinders the full understanding and use of the volumetric datasets. We demonstrate that symmetry-guided registration can correct the symmetry distortion in the momentum-resolved photoemission patterns. Using proposed symmetry metrics, we show quantitatively that the iterative approach to symmetrization outperforms its non-iterative counterpart in the restored symmetry of the outcome while preserving the average shape of the photoemission pattern. Our approach is generalizable to distortion corrections in different types of symmetries and should also find applications in other experimental methods that produce images with similar features

Local interpolation schemes for landmark-based image registration: a comparison

In this paper we focus, from a mathematical point of view, on properties and performances of some local interpolation schemes for landmark-based image registration. Precisely, we consider modified Shepard's interpolants, Wendland's functions, and Lobachevsky splines. They are quite unlike each other, but all of them are compactly supported and enjoy interesting theoretical and computational properties. In particular, we point out some unusual forms of the considered functions. Finally, detailed numerical comparisons are given, considering also Gaussians and thin plate splines, which are really globally supported but widely used in applications

Incorporating 3-dimensional models in online articles

Introduction The aims of this article are to introduce the capability to view and interact with 3-dimensional (3D) surface models in online publications, and to describe how to prepare surface models for such online 3D visualizations. Methods Three-dimensional image analysis methods include image acquisition, construction of surface models, registration in a common coordinate system, visualization of overlays, and quantification of changes. Cone-beam computed tomography scans were acquired as volumetric images that can be visualized as 3D projected images or used to construct polygonal meshes or surfaces of specific anatomic structures of interest. The anatomic structures of interest in the scans can be labeled with color (3D volumetric label maps), and then the scans are registered in a common coordinate system using a target region as the reference. The registered 3D volumetric label maps can be saved in.obj,.ply,.stl, or.vtk file formats and used for overlays, quantification of differences in each of the 3 planes of space, or color-coded graphic displays of 3D surface distances. Results All registered 3D surface models in this study were saved in.vtk file format and loaded in the Elsevier 3D viewer. In this study, we describe possible ways to visualize the surface models constructed from cone-beam computed tomography images using 2D and 3D figures. The 3D surface models are available in the article's online version for viewing and downloading using the reader's software of choice. These 3D graphic displays are represented in the print version as 2D snapshots. Overlays and color-coded distance maps can be displayed using the reader's software of choice, allowing graphic assessment of the location and direction of changes or morphologic differences relative to the structure of reference. The interpretation of 3D overlays and quantitative color-coded maps requires basic knowledge of 3D image analysis. Conclusions When submitting manuscripts, authors can now upload 3D models that will allow readers to interact with or download them. Such interaction with 3D models in online articles now will give readers and authors better understanding and visualization of the results

ВЫДЕЛЕНИЕ УГЛОВ НА ИЗОБРАЖЕНИЯХ НА ОСНОВЕ ОРИЕНТИРОВАННОГО ГРАДИЕНТА

Рассматриваются алгоритмы автоматического выделения углов на полутоновых и цветныхизображениях, основанные на использовании ориентированного градиента. В отличие от известных алгоритмов они позволяют не только надежно выделить на изображении вершины углов заданной величины, но и оценить ориентацию их сторон

Deep-MDS Framework for Recovering the 3D Shape of 2D Landmarks from a Single Image

In this paper, a low parameter deep learning framework utilizing the Non-metric Multi-Dimensional scaling (NMDS) method, is proposed to recover the 3D shape of 2D landmarks on a human face, in a single input image. Hence, NMDS approach is used for the first time to establish a mapping from a 2D landmark space to the corresponding 3D shape space. A deep neural network learns the pairwise dissimilarity among 2D landmarks, used by NMDS approach, whose objective is to learn the pairwise 3D Euclidean distance of the corresponding 2D landmarks on the input image. This scheme results in a symmetric dissimilarity matrix, with the rank larger than 2, leading the NMDS approach toward appropriately recovering the 3D shape of corresponding 2D landmarks. In the case of posed images and complex image formation processes like perspective projection which causes occlusion in the input image, we consider an autoencoder component in the proposed framework, as an occlusion removal part, which turns different input views of the human face into a profile view. The results of a performance evaluation using different synthetic and real-world human face datasets, including Besel Face Model (BFM), CelebA, CoMA - FLAME, and CASIA-3D, indicates the comparable performance of the proposed framework, despite its small number of training parameters, with the related state-of-the-art and powerful 3D reconstruction methods from the literature, in terms of efficiency and accuracy

Variation and signatures of selection on the human face

AbstractThere has been much debate about why humans throughout the world differ in facial form. Previous studies of human skull morphology found levels of among-population differentiation that were comparable to those of neutral genetic markers, suggesting that genetic drift (neutral processes) played an important role in influencing facial differentiation. However, variation in soft-tissue morphology has not been studied in detail. In this study, we analyzed high-resolution 3D images of soft-tissue facial form in four Eurasian populations: Han Chinese, Tibetans, Uyghur and Europeans. A novel method was used to establish a high-density alignment across all of the faces, allowing facial diversity to be examined at an unprecedented resolution. These data exhibit signatures of population structure and history. However, among-population differentiation was higher for soft-tissue facial form than for genome-wide genetic loci, and high-resolution analyses reveal that the nose, brow area and cheekbones exhibit particularly strong signals of differentiation (Qst estimates: 0.3–0.8) between Europeans and Han Chinese. Our results suggest that local adaptation and/or sexual selection have been important in shaping human soft-tissue facial morphology

Regularized Surface and Point Landmarks Based Efficient Non-Rigid Medical Image Registration

Medical image registration is one of the fundamental tasks in medical image processing. It has various applications in field of image guided surgery (IGS) and computer assisted diagnosis (CAD). A set of non-linear methods have been already developed for inter-subject and intra-subject 3D medical image registration. However, efficient registration in terms of accuracy and speed is one of the most demanded of today surgical navigation (SN) systems. This paper is a result of a series of experiments which utilizes Fast Radial Basis Function (RBF) technique to register one or more medical images non-rigidly. Initially, a set of curves are extracted using a combined watershed and active contours algorithm and then tiled and converted to a regular surface using a global parameterization algorithm. It is shown that the registration accuracy improves when higher number of salient features (i.e. anatomical point landmarks and surfaces) are used and it also has no impact on the speed of the algorithm. The results show that the target registration error is less than 2 mm and has sub-second performance on intra-subject registration of MR image real datasets. It is observed that the Fast RBF algorithm is relatively insensitive to the increasing number of point landmarks used as compared with the competing feature based algorithms

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