In this study, a novel probabilistic, geometric and dynamic shape‐based level sets method is proposed. The shape prior is coupled with the intensity information to enhance the segmentation results. The two‐dimensional principal component analysis method is applied on the training shapes to represent the shape variation with enough number of shape projections in the training step. The shape model is constructed using the implicit representation of the projected shapes. A new energy functional is proposed (i) to embed the shape model into the image domain and (ii) to estimate the shape coefficients. The proposed method is validated on synthetic and clinical images with various challenges such as the noise, occlusion and missing information. The authors compare their method with some of related works. Experiments show that the proposed segmentation method is more accurate and robust than other alternatives under different challenges. ∗ Note: Colour figures are available in the online version of this paper.

In this paper, We propose a new approach for solving the Lambertian shape from shading (SFS) problem. The proposed technique employs image information as well as camera calibration parameters. We claim that the incorporation of camera parameters results in a better surface reconstruction. In this work, we slightly modify this more realistic model in order to take into account the attenuation of the illumination due to distance. We propose a new variational formulation that relates an evolving surface model with image information, taking into consideration that the image is taken by a perspective camera with known parameters. A new energy functional is formulated to incorporate brightness, smoothness, and integrability constraints. All of these terms assume a hyper surface that evolves in time to meet their criteria. Gradient descent optimization with Euler-Lagrange is used for optimization. We constructed a database of real surfaces as a ground-truth for the experiments. The proposed approach shows superior performance when compared with other approaches in the literature.

In this paper, a novel method to solve the shape registration problem covering both global and local deformations is proposed. The vector distance function (VDF) is used to represent source and target shapes. The problem is formulated as an energy optimization process by matching the VDFs of the source and target shapes. The minimization process results in estimating the transformation parameters for the global and local deformation cases. Gradient descent optimization handles the computation of scaling, rotation, and translation matrices used to minimize the global differences between source and target shapes. Nonrigid deformations require a large number of parameters which make the use of the gradient descent minimization a very time-consuming process. We propose to compute the local deformation parameters using a closed-form solution as a linear system of equations derived from approximating an objective function. Extensive experimental validations and comparisons performed on generalized 2D shape data demonstrate the robustness and effectiveness of the method.

A new variational level set approach is proposed for lung nodule segmentation in lung CT scans. A general lung nodule shape model is proposed using implicit spaces as a signed distance function. The shape model is fused with the image intensity statistical information in a variational segmentation framework. The nodule shape model is mapped to the image domain by a global transformation that includes inhomogeneous scales, rotation, and translation parameters. A matching criteria between the shape model and the image implicit representations is employed to handle the alignment process. Transformation parameters evolve through gradient descent optimization to handle the shape alignment process and hence mark the boundaries of the nodule “head.” The embedding process takes into consideration the image intensity as well as prior shape information. A nonparametric density estimation approach is employed to handle the statistical intensity representation of the nodule and background regions. The proposed technique does not depend on nodule type or location. Exhaustive experimental and validation results are demonstrated on 742 nodules obtained from four different CT lung databases, illustrating the robustness of the approach.

In this paper, we propose a novel approach for 3D surface reconstruction of the human jaw. Due to the difficulties of setting up a data acquisition system inside the mouth, we use an intra-oral camera to capture a sequence of calibrated images. These images are registered together to build a panoramic view of the jaw. We incorporate a shape from shading(SFS) algorithm that benefits from camera calibration parameters to build a 3D model from the panoramic image obtained from the previous stage. Our approach results in a 3D surface which has more fine details compared with those resulting from other literature techniques. We will demonstrate different artificial jaws surfaces reconstruction to show the efficiency of our system. 1

We propose a new system for building a 3D database for human teeth. Real extracted human teeth are scanned using a cone-beam CT scanner to build. The teeth models are segmented from the resulting images by means of level sets. The database includes 3D models of these teeth after minimizing global differences between the models. An affine transformation function is used to model the differences between the models. The transformation parameters are estimated by minimizing a least squares energy. A total of 280 teeth 3-D models have been created to build the real database and demonstrate the performance of the proposed framework.

Our paper handles the elastic shape registration by combining the incremental free form deformation (IFFD) with the point- based registration technique using the sum of least squares method. The iterative closest point (ICP) algorithm is used as criteria to establish point correspondences in each level of the IFFD framework. The IFFD control lattice resolution is in- creased step by step to achieve a satisfactory deformation of the source shape to exactly match the target boundaries. Our point-based registration is based on least squares that measure the Euclidean distance between source and target boundaries in addition to the shape constrains. The minimization gives a closed form solution of the lattice control points positions. Promising results will be demonstrated for closed and open shapes and structures. The approach can also work for structures that contain multiple parts without any problems.

In this paper, we propose a new shape based segmentation and registration of the vertebral bodies (VBs) in clinical computed tomography (CT) images. The VB and surrounding organs have very close gray level information and there are no strong edges in some CT images. To overcome these challenges, image appearance and shape information of VBs are used. There are three phases of our experiments: i) the detection of the VB region using the Matched filter, ii) initial segmentation using the graph cuts which integrates the intensity and spatial interaction models, iii) registration of the shape priors and initially segmented region to obtain the final segmentation. Preliminary results show that our proposed algorithm gives very encouraging results and can solve many segmentation and registration problems.

We propose a new shape-based segmentation approach using the statistical shape prior and level sets method. The segmentation depends on the image information and shape prior. Training shapes are grouped to form a probabilistic model. The shape model is embedded into the image domain taking in consideration the evolution of a contour represented by a level set function. The evolution of the front gathers information from the image intensities and shape prior. The segmentation approach is applied in segmenting the vertebral bodies in CT images. Our results shows that the technique is accurate and robust compared with the other alternative in the literature.

Lung nodules from low dose CT (LDCT) scans may be used for early detection of lung cancer. However, these nodules vary in size, shape, texture, location, and may suffer from occlusion within the tissue. This paper presents an approach for segmentation of lung nodules detected by a prior step. First, regions around the detected nodules are segmented; using automatic seed point placement levels sets. The outline of the nodule region is further improved using the curvature characteristics of the segmentation boundary. We illustrate the effectiveness of this method for automatic segmentation of the Juxta-pleural nodules.

This paper introduces a new method for shape registration by matching vector distance functions. The vector distance function representation is more flexible than the conventional signed distance map since it enables us to better control the shapes registration process by using more general transformations. Based on this model, a variational frame work is proposed for the global and local registration of shapes which does not need any point correspondences. The optimization criterion can handle efficiently the estimation of the global registration parameters. A closed form solution is provided to handle an incremental free form deformation model for covering the local deformations. This is an advantage over the gradient descent optimization which is biased towards the initialization and is more time consuming. Results of real shapes registration will be demonstrated to show the efficiency of the proposed approach with small and large global/local deformations.

Geometric analysis of postmortem normal and autistic human subjects reveal distinctions in deformations in the corpus callosum (CC) that may be used for image analysis-based studies of autism. Preliminary studies showed that the CC of autistic patients is quite distinct from normal controls. We use an implicit vector representation of CC to carry out the registration process which measures the differences between different CC's. This paper introduces a new method for the 2D shape registration problem by matching vector distance functions. A variational frame work is proposed for the global and local registration of CC's. A gradient descent optimization is used which can efficiently handle both the rigid and the non-rigid operations together. The registration of real CC extracted from postmortem data sets demonstrates the potential of the proposed approach.

In this paper, we revisit the implicit front representation and evolution using the vector level set function (VLSF) proposed in [1]. Unlike conventional scalar level sets, this function is designed to have a vector form. The distance from any point to the nearest point on the front has components (projections) in the coordinate directions included in the vector function. This kind of representation is used to evolve closed planar curves and 3D surfaces as well. Maintaining the VLSF property as the distance projections through evolution will be considered together with a detailed derivation of the vector partial differential equation (PDE) for such evolution. A shape-based segmentation framework will be demonstrated as an application of the given implicit representation. The proposed level set function system will be used to represent shapes to give a dissimilarity measure in a variational object registration process. This kind of formulation permits us to better control the process of shape registration, which is an important part in the shape-based segmentation framework. The method depends on a set of training shapes used to build a parametric shape model. The color is taken into consideration besides the shape prior information. The shape model is fitted to the image volume by registration through an energy minimization problem. The approach overcomes the conventional methods problems like point correspondences and weighing coefficients tuning of the evolution (PDEs). It is also suitable for multidimensional data and computationally efficient. Results in 2D and 3D of real and synthetic data will demonstrate the efficiency of the framework.

The main focus of this paper is the shape representation and registration using vector level set functions. This powerful representation is more flexible than conventional signed distance level sets since it enables us to control the shapes registration process by using more complicated transforms. Based on this model, a variational frame work is proposed for the rigid and non-rigid registration of shapes which can be extended to the higher dimensional case in a straightforward manner and also does not need any point correspondences. The optimization criterion presented can handle efficiently both the rigid and the non-rigid operations together. Experimental results in 2D for real shapes registration are discussed to show the efficiency of the approach with small and large global deformations of shapes.

We propose a novel approach for shape-based segmentation based on a specially designed level set function format. This format permits us to better control the process of object registration which is an important part in the shape-based segmentation framework. The method depends on a set of training shapes used to build a parametric shape model. The color is taken into consideration besides the shape prior information. The shape model is fitted to the image volume by registration through an energy minimization problem. The approach overcomes the conventional methods problems like point correspondences and weighing coefficients tuning of the partial differential equations (PDE's). Also it is suitable for multidimensional data and computationally efficient. Results of extracting the 2D star fish and the brain ventricles in 3D demonstrate the efficiency of the approach.