Aly A. Farag

A modified fuzzy c-means algorithm for bias field estimation and segmentation of MRI data

We present a novel algorithm for fuzzy segmentation of magnetic resonance imaging (MRI) data and estimation of intensity inhomogeneities using fuzzy logic. MRI intensity inhomogeneities can be attributed to imperfections in the radio-frequency coils or to problems associated with the acquisition sequences. The result is a slowly varying shading artifact over the image that can produce errors with conventional intensity-based classification. Our algorithm is formulated by modifying the objective function of the standard fuzzy c-means (FCM) algorithm to compensate for such inhomogeneities and to allow the labeling of a pixel (voxel) to be influenced by the labels in its immediate neighborhood. The neighborhood effect acts as a regularizer and biases the solution toward piecewise-homogeneous labelings. Such a regularization is useful in segmenting scans corrupted by salt and pepper noise. Experimental results on both synthetic images and MR data are given to demonstrate the effectiveness and efficiency of the proposed algorithm.

CSIFT: A SIFT Descriptor with Color Invariant Characteristics

SIFT has been proven to be the most robust local invariant feature descriptor. SIFT is designed mainly for gray images. However, color provides valuable information in object description and matching tasks. Many objects can be misclassified if their color contents are ignored. This paper addresses this problem and proposes a novel colored local invariant feature descriptor. Instead of using the gray space to represent the input image, the proposed approach builds the SIFT descriptors in a color invariant space. The built Colored SIFT (CSIFT) is more robust than the conventional SIFT with respect to color and photometrical variations. The evaluation results support the potential of the proposed approach.

Precise segmentation of multimodal images

We propose new techniques for unsupervised segmentation of multimodal grayscale images such that each region-of-interest relates to a single dominant mode of the empirical marginal probability distribution of grey levels. We follow the most conventional approaches in that initial images and desired maps of regions are described by a joint Markov-Gibbs random field (MGRF) model of independent image signals and interdependent region labels. However, our focus is on more accurate model identification. To better specify region borders, each empirical distribution of image signals is precisely approximated by a linear combination of Gaussians (LCG) with positive and negative components. We modify an expectation-maximization (EM) algorithm to deal with the LCGs and also propose a novel EM-based sequential technique to get a close initial LCG approximation with which the modified EM algorithm should start. The proposed technique identifies individual LCG models in a mixed empirical distribution, including the number of positive and negative Gaussians. Initial segmentation based on the LCG models is then iteratively refined by using the MGRF with analytically estimated potentials. The convergence of the overall segmentation algorithm at each stage is discussed. Experiments show that the developed techniques segment different types of complex multimodal medical images more accurately than other known algorithms.

Free-form surface registration using surface signatures

The paper introduces a new free-form surface representation scheme for the purpose of fast and accurate registration and matching. Accurate registration of surfaces is a common task in computer vision. The proposed representation scheme captures the surface curvature information seen from certain points and produces images called surface signatures at these points. Matching signatures of different surfaces enables the recovery of the transformation parameters between these surfaces. We propose to use template matching to compare the signature images. To enable partial matching, another criterion, the overlap ratio, is used. This representation scheme can be used as a global representation of the surface as well as a local one and performs near real time registration. We show that the signature representation can be used to match objects in 3D scenes in the presence of clutter and occlusion. Applications presented include free-form object matching, multimodal medical volume registration and dental teeth reconstruction from intra-oral images.

Nonmetric calibration of camera lens distortion: differential methods and robust estimation

This paper addresses the problem of calibrating camera lens distortion, which can be significant in medium to wide angle lenses. Our approach is based on the analysis of distorted images of straight lines. We derive new distortion measures that can be optimized using nonlinear search techniques to find the best distortion parameters that straighten these lines. Unlike the other existing approaches, we also provide fast, closed-form solutions to the distortion coefficients. We prove that including both the distortion center and the decentering coefficients in the nonlinear optimization step may lead to instability of the estimation algorithm. Our approach provides a way to get around this, and, at the same time, it reduces the search space of the calibration problem without sacrificing the accuracy and produces more stable and noise-robust results. In addition, while almost all existing nonmetric distortion calibration methods needs user involvement in one form or another, we present a robust approach to distortion calibration based on the least-median-of-squares estimator. Our approach is, thus, able to proceed in a fully automatic manner while being less sensitive to erroneous input data such as image curves that are mistakenly considered projections of three-dimensional linear segments. Experiments to evaluate the performance of this approach on synthetic and real data are reported.

A unified framework for MAP estimation in remote sensing image segmentation

A complete framework is proposed for applying the maximum a posteriori (MAP) estimation principle in remote sensing image segmentation. The MAP principle provides an estimate for the segmented image by maximizing the posterior probabilities of the classes defined in the image. The posterior probability can be represented as the product of the class conditional probability (CCP) and the class prior probability (CPP). In this paper, novel supervised algorithms for the CCP and the CPP estimations are proposed which are appropriate for remote sensing images where the estimation process might to be done in high-dimensional spaces. For the CCP, a supervised algorithm which uses the support vector machines (SVM) density estimation approach is proposed. This algorithm uses a novel learning procedure, derived from the main field theory, which avoids the (hard) quadratic optimization problem arising from the traditional formulation of the SVM density estimation. For the CPP estimation, Markov random field (MRF) is a common choice which incorporates contextual and geometrical information in the estimation process. Instead of using predefined values for the parameters of the MRF, an analytical algorithm is proposed which automatically identifies the values of the MRF parameters. The proposed framework is built in an iterative setup which refines the estimated image to get the optimum solution. Experiments using both synthetic and real remote sensing data (multispectral and hyperspectral) show the powerful performance of the proposed framework. The results show that the proposed density estimation algorithm outperforms other algorithms for remote sensing data over a wide range of spectral dimensions. The MRF modeling raises the segmentation accuracy by up to 10% in remote sensing images.

Variational Curve Skeletons Using Gradient Vector Flow

Representing a 3D shape by a set of 1D curves that are locally symmetric with respect to its boundary (i.e., curve skeletons) is of importance in several machine intelligence tasks. This paper presents a fast, automatic, and robust variational framework for computing continuous, subvoxel accurate curve skeletons from volumetric objects. A reference point inside the object is considered a point source that transmits two wave fronts of different energies. The first front (\beta-front) converts the object into a graph, from which the object salient topological nodes are determined. Curve skeletons are tracked from these nodes along the cost field constructed by the second front (\alpha-front) until the point source is reached. The accuracy and robustness of the proposed work are validated against competing techniques as well as a database of 3D objects. Unlike other state-of-the-art techniques, the proposed framework is highly robust because it avoids locating and classifying skeletal junction nodes, employs a new energy that does not form medial surfaces, and finally extracts curve skeletons that correspond to the most prominent parts of the shape and hence are less sensitive to noise.

A system for human jaw modeling using intra-oral images

A novel integrated system is developed to obtain a record of the patients occlusion using computer vision. Data acquisition is obtained using intra-oral video camera. A modified Shape from Shading (SFS) technique using perspective projection and camera calibration is then used to extract accurate 3D information from a sequence of 2D images of the jaw. A novel technique for 3D data registration using Grid Closest Point (GCP) transform and genetic algorithms (GA) is used to register the output of the SFS stage. Triangulization is then performed, and a solid 3D model is obtained via a rapid prototype machine. The overall purpose of this research is to develop a model-based vision system for orthodontics that will replace traditional approaches and can be used in diagnosis, treatment planning, surgical simulation and implant purposes.

Edge linking by sequential search

Edge detection is mainly a two-stage process: edge enhancement followed by edge linking. In this paper we develop a linking algorithm for the combination of edge elements enhanced by an optimal filter. The linking algorithm (LINK) is based on sequential search. From a starting node, transitions are made to the goal nodes based on a maximum likelihood metric. Results of our search algorithm are compared to the sequential edge linking algorithm (SEL) as well as to two common nonsequential algorithms based on tracing the zero-crossings loci in the convolution output of the ▿2G operators, and based on nonmaximal suppression and thresholding of the convolution output of the ▿G operator. It is shown that the LINK algorithm provides comparable results, require only local calculations, and can accommodate any a priori information in the path metric used to guide the search.

A new genetic-based technique for matching 3-D curves and surfaces☆

A novel approach has been developed for fast registration of two sets of 3-D curves or surfaces. The technique is an extension of Besl and Mackays iterative closest point (ICP) algorithm. This technique solves the computation complexity associated with the ICP algorithm by applying a novel grid closest point (GCP) transform and a genetic algorithm to minimize the cost function. A detailed description of the algorithm is presented along with a comparison of its performance versus several registration techniques. Two applications are presented in this paper. In the rst, the algorithm is used to register 2-D head contours extracted from CT/MRI data to correct for possible miss-alignment caused by motion artifact during scanning. In the second, the algorithm is used to register 3-D segments of the human jaw obtained using shape from shading technique. Registration using the GCP/GA technique is found to be signiicantly faster and of comparable accuracy than two popular techniques in the computer vision and medical imaging literature.