A.A. Farag

MultiStencils Fast Marching Methods: A Highly Accurate Solution to the Eikonal Equation on Cartesian Domains

A wide range of computer vision applications require an accurate solution of a particular Hamilton-Jacobi (HJ) equation known as the Eikonal equation. In this paper, we propose an improved version of the fast marching method (FMM) that is highly accurate for both 2D and 3D Cartesian domains. The new method is called multistencils fast marching (MSFM), which computes the solution at each grid point by solving the Eikonal equation along several stencils and then picks the solution that satisfies the upwind condition. The stencils are centered at each grid point and cover its entire nearest neighbors. In 2D space, two stencils cover 8-neighbors of the point, whereas in 3D space, six stencils cover its 26-neighbors. For those stencils that are not aligned with the natural coordinate system, the Eikonal equation is derived using directional derivatives and then solved using higher order finite difference schemes. The accuracy of the proposed method over the state-of-the-art FMM-based techniques has been demonstrated through comprehensive numerical experiments.

Robust centerline extraction framework using level sets

In this paper, we present a novel framework for computing centerlines for both 2D and 3D shape analysis. The framework works as follows: an object centerline point is selected automatically as the point of global maximum Euclidean distance from the boundary, and is considered a point source (Ps) that transmits a wave front that evolves over time and traverses the object domain. The front propagates at each object point with a speed that is proportional to its Euclidean distance from the boundary. The motion of the front is governed by a nonlinear partial differential equation whose solution is computed efficiently using level set methods. Initially, the P/sub S/ transmits a moderate speed wave to explore the object domain and extract its topological information such as merging and extreme points. Then, it transmits a new front that is much faster at centerline points than non central ones. As a consequence, centerlines intersect the propagating fronts at those points of maximum positive curvature. Centerlines are computed by tracking them, starting from each topological point until the Ps is reached, by solving an ordinary differential equation using an efficient numerical scheme. The proposed method is computationally inexpensive, handles efficiently objects with complex topology, and computes centerlines that are centered, connected, one point thick, and less sensitive to boundary noise. In addition, the extracted paths form a tree graph without additional cost. We have extensively validated the robustness of the proposed method both quantitatively and qualitatively against several 2D and 3D shapes.

Modified fuzzy c-mean in medical image segmentation

This paper describes the application of fuzzy set theory in medical imaging, namely the segmentation of brain images. We propose a fully automatic technique to obtain image clusters. A modified fuzzy c-mean (FCM) classification algorithm is used to provide a fuzzy partition. Our new method, inspired from the Markov Random Field (MRF), is less sensitive to noise as it filters the image while clustering it, and the filter parameters are enhanced in each iteration by the clustering process. We applied the new method on a noisy CT scan and on a single channel MRI scan. We recommend using a methodology of over segmentation to the textured MRI scan and a user guided-interface to obtain the final clusters. One of the applications of this technique is TBI recovery prediction in which it is important to consider the partial volume. It is shown that the system stabilizes after a number of iterations with the membership value of the region contours reflecting the partial volume value. The final stage of the process is devoted to decision making or the defuzzification process.

On the Extraction of Curve Skeletons using Gradient Vector Flow

In this paper, we propose a new variational framework for computing continuous curve skeletons from discrete objects that are suitable for structural shape representation. We have derived a new energy function, which is proportional to some medialness function, such that the minimum cost path between any two medial voxels in the shape is a curve skeleton. We have employed two different medialness functions; the Euclidean distance field and a variant of the magnitude of the gradient vector flow (GVF), resulting in two different energy functions. The first energy controls the identification of the shape topological nodes from which curve skeletons start, while the second one controls the extraction of curve skeletons. The accuracy and robustness of the proposed framework are validated both quantitatively and qualitatively against competing techniques as well as several 3D shapes of different complexity.

A shape-based segmentation approach: an improved technique using level sets

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 (PDEs). 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

Curve/Surface Representation and Evolution Using Vector Level Sets with Application to the Shape-Based Segmentation Problem

In this paper, we revisit the implicit front representation and evolution using the vector level set function (VLSF) proposed in (H. E. Abd El Munim, et al., Oct. 2005). 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

A Novel Approach for Lung Nodules Segmentation in Chest CT Using Level Sets

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.

Shape Representation and Registration using Vector Distance Functions

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.

Evaluation of geometric feature descriptors for detection and classification of lung nodules in low dose CT scans of the chest

This paper examines the effectiveness of geometric feature descriptors, common in computer vision, for false positive reduction and for classification of lung nodules in low dose CT (LDCT) scans. A data-driven lung nodule modeling approach creates templates for common nodule types, using active appearance models (AAM); which are then used to detect candidate nodules based on optimum similarity measured by the normalized cross-correlation (NCC). Geometric feature descriptors (e.g., SIFT, LBP and SURF) are applied to the output of the detection step, in order to extract features from the nodule candidates, for further enhancement of output and possible reduction of false positives. Results on the clinical ELCAP database showed that the descriptors provide 2% enhancements in the specificity of the detected nodule above the NCC results when used in a k-NN classifier. Thus quantitative measures of enhancements of the performance of CAD models based on LDCT are now possible and are entirely model-based. Most importantly, our approach is applicable for classification of nodules into categories and pathologies.

Toward precise pulmonary nodule descriptors for nodule type classification

A framework for nodule feature-based extraction is presented to classify lung nodules in low-dose CT slices (LDCT) into four categories: juxta, well-circumscribed, vascularized and pleural-tail, based on the extracted information. The Scale Invariant Feature Transform (SIFT) and an adaptation to Daugmans Iris Recognition algorithm are used for analysis. The SIFT descriptor results are projected to lower-dimensional subspaces using PCA and LDA. Complex Gabor wavelet nodule response obtained from an adopted Daugman Iris Recognition algorithm revealed improvements from the original Daugman binary iris code. This showed that binarized nodule responses (codes) are inadequate for classification since nodules lack texture concentration as seen in the iris, while the SIFT algorithm projected using PCA showed robustness and precision in classification.