Analyzing cerebrovascular changes using Time-of-Flight Magnetic Resonance Angiography (ToF-MRA) images can detect the presence of serious diseases and track their progress, e.g., hypertension. Such analysis requires accurate segmentation of the vasculature from the surroundings, which motivated us to propose a fully automated cerebral vasculature segmentation approach based on extracting both prior and current appearance features that capture the appearance of macro and micro-vessels. The appearance prior is modeled with a novel translation and rotation invariant Markov-Gibbs Random Field (MGRF) of voxel intensities with pairwise interaction analytically identified from a set of training data sets, while the current appearance is represented with a marginal probability distribution of voxel intensities by using a Linear Combination of Discrete Gaussians (LCDG) whose parameters are estimated by a modified Expectation-Maximization (EM) algorithm. The proposed approach was validated on 190 data sets using three metrics, which revealed high accuracy compared to existing approaches.

A novel framework for the classification of lung nodules using computed tomography (CT) scans is proposed in this paper. To get an accurate diagnosis of the detected lung nodules, the proposed framework integrates the following two groups of features: (i) appearance features that is modeled using higher-order Markov Gibbs random field (MGRF)-model that has the ability to describe the spatial inhomogeneities inside the lung nodule; and (ii) geometric features that describe the shape geometry of the lung nodules. The novelty of this paper is to accurately model the appearance of the detected lung nodules using a new developed 7th-order MGRF model that has the ability to model the existing spatial inhomogeneities for both small and large detected lung nodules, in addition to the integration with the extracted geometric features. Finally, a deep autoencoder (AE) classifier is fed by the above two feature groups to distinguish between the malignant and benign nodules. To evaluate the proposed framework, we used the publicly available data from the Lung Image Database Consortium (LIDC). We used a total of 727 nodules that were collected from 467 patients. The proposed system demonstrates the promise to be a valuable tool for the detection of lung cancer evidenced by achieving a nodule classification accuracy of 92.20%.

To improve the accuracy of segmenting medical images from different modalities we propose to integrate three types of comprehensive quantitative image descriptors with a deep 3D convolutional neural network. The descriptors include: (i) a Gibbs energy for a prelearned 7th-order Markov-Gibbs random field (MGRF) model of visual appearance, (ii) a relearned adaptive shape prior model, and a first-order conditional random field model of visual appearance of regions at each current stage of segmentation. The neural network fuses the computed descriptors, together with the raw image data, for obtaining the final voxel-wise probabilities of the goal regions. Quantitative assessment of our framework in terms of Dice similarity coefficients, 95-percentile bidirectional Hausdorff distances, and percentage volume differences confirms the high accuracy of our model on 95 CT lung images (98.37±0.68%,2.79±1.32 mm,3.94±2.11%) and 95 diffusion weighted kidney MRI (96.65±2.15%,4.32±3.09 mm,5.61±3.37%), respectively.

This paper proposes a novel framework for the classification of lung nodules using computed tomography (CT) scans. The proposed framework is based on the integrating the following features to get accurate diagnosis of detected lung nodules: (i) Spherical Harmonics-based shape features that have the ability to describe the shape complexity of the lung nodules; (ii) Higher-Order Markov Gibbs Random Field (MGRF)-based appearance model that has the ability to describe the spatial inhomogeneities in the lung nodule; and (iii) volumetric features that describe the size of lung nodules. To accurately model the surface/shape of the detect lung nodules, we used spherical harmonics expansion due to its ability to approximate the surfaces of complicated shapes. We will use the reconstruction error curve as a new metric to describe the shape complexity of the detected lung nodules. Moreover, we developed a new higher 7th-order MGRF model that has the ability to model the existing the spatial inhomogeneities for both small and large detected lung nodules. Finally, a deep autoencoder (AE) classifier is fed by the above three features to distinguish between the malignant and benign nodules. To evaluate the proposed framework, we used the publicly available data from the Lung Image Database Consortium (LIDC). We used a total of 116 nodules that were collected from 60 patients. By achieving a classification accuracy of 96.00%, the proposed system demonstrates promise to be a valuable tool for the detection of lung cancer.

A novel framework for the detection of radiation-induced lung injury (RILI) from 4D computed tomography (CT) has been proposed. Our framework performs 4D-CT lung fields segmentation, deformable image registration (DIR), extraction of textural and functional features, and classification of lung voxels using deep 3D convolutional neural networks (CNN). The 4D-CT images segmentation extracts the lung fields inside the exhale phase using our multi-scale Gaussian adaptive shape prior technique followed by label propagation to other 4D-CT phases using a newly developed adaptive shape model. Then, the 4D-CT DIR locally aligns consecutive phases of the respiratory cycle using the 3D Laplace equation for finding voxel correspondences between the iso-surfaces for the fixed and moving lungs and generalized Gaussian Markov random field (GGMRF) as an anatomical consistency constraint. In addition to common lung functionality features, such as ventilation and elasticity, specific regional textural features are estimated by modeling the segmented images as samples of a novel 7th-order contrast-offset-invariant Markov-Gibbs random field (MGRF). Finally, a deep 3D CNN is applied to distinguish between the injured and normal lung tissues. 4D-CT datasets collected from 13 patients, who undergone the radiation therapy (RT), have been used in the evaluation of the proposed framework. The experimental results show the promise of our framework.

To accurately segment pathological and healthy lungs for reliable computer-aided disease diagnostics, a stack of chest CT scans is modeled as a sample of a spatially inhomogeneous joint 3D Markov-Gibbs random field (MGRF) of voxel-wise lung and chest CT image signals (intensities). The proposed learnable MGRF integrates two visual appearance sub-models with an adaptive lung shape submodel. The first-order appearance submodel accounts for both the original CT image and its Gaussian scale space (GSS) filtered version to specify local and global signal properties, respectively. Each empirical marginal probability distribution of signals is closely approximated with a linear combination of discrete Gaussians (LCDG), containing two positive dominant and multiple sign-alternate subordinate DGs. The approximation is separated into two LCDGs to describe individually the lungs and their background, i.e., all other chest tissues. The second-order appearance submodel quantifies conditional pairwise intensity dependencies in the nearest voxel 26-neighborhood in both the original and GSS-filtered images. The shape submodel is built for a set of training data and is adapted during segmentation using both the lung and chest appearances. The accuracy of the proposed segmentation framework is quantitatively assessed using two public databases (ISBI VESSEL12 challenge and MICCAI LOLA11 challenge) and our own database with, respectively, 20, 55, and 30 CT images of various lung pathologies acquired with different scanners and protocols. Quantitative assessment of our framework in terms of Dice similarity coefficients, 95-percentile bidirectional Hausdorff distances, and percentage volume differences confirms the high accuracy of our model on both our database (98.4±1.0%, 2.2±1.0mm, 0.42±0.10%) and the VESSEL12 database (99.0±0.5%, 2.1±1.6mm, 0.39±0.20%), respectively. Similarly, the accuracy of our approach is further verified via a blind evaluation by the organizers of the LOLA11 competition, where an average overlap of 98.0% with the expert’s segmentation is yielded on all 55 subjects with our framework being ranked first among all the state-of-the-art techniques compared.

A framework for 3D kidney segmentation from abdominal computed tomography (CT) images is proposed. Accurate kidney segmentation from CT images is a challenging task due to the large inhomogeneity of the kidney (e.g., cortex and medulla), inter-patient anatomical differences, etc. To account for these challenges, a novel framework utilizing random forest (RF) classification that has the ability to cluster complex data is proposed. To build a robust classification model, discriminative features are needed for better separation of data classes. In this work, regional features from the CT appearance, a kidney shape prior model, and higher-order spatial interactions are extracted and are used for tissue classification. The shape model is constructed using a set of training images and is updated during segmentation using an appearance-based method taking into account both voxels' locations and appearances. The spatial interactions between CT data voxels are modeled using a higher-order spatial model that adds to the pairwise cliques the families of the triple- and quad cliques. The proposed framework has been tested on CT data that has been collected from 20 subjects and consist of multiple 3D CT scans acquired at the pre-and post-contrast agent administration. Evaluation results, using both volumetric and distance-based metrics, between manually drawn and automatically segmented contours confirm the high accuracy of the proposed technique.

This paper proposes a novel framework for the identification of the radiation-induced lung injury (RILI) after radiation therapy (RT) using 4D computed tomography (CT) scans. The proposed methodology consists of four components: (i) elastic image registration; (ii) segmentation of the lung fields; (iii) extraction of functional and texture features; and (iv) classification of the lung tissues. The registration step locally aligns the consecutive phases of the respiratory cycle using an elastic image registration approach based on descent minimization of the sum of squared difference similarity metric. Secondly, lung fields are segmented using a hybrid framework that integrates an adaptive shape prior model, a first-order intensity model, and a second order homogeneity descriptor of the lung tissues. Next, regional features that describe both the texture features using the novel 7th-order Markov-Gibbs random field (MGRF) model in addition to the lung functionality features (e.g., ventilation and elasticity) are estimated from a segmented lungs. Finally, a random forest classifier (RF) is applied to distinguish between injured and normal lung tissues. To evaluate the proposed framework, we used data sets that have been collected from 13 patients who had underwent RT treatment. Experimental results demonstrate the promise of the proposed framework for the identification of the injured lung region, and thus hold the promise as a valuable tool for early detection of RILI.

This paper introduces a novel computer-aided diagnostic (CAD) system for the assessment of renal transplant status that integrates image-based biomarkers derived from 4D (3D + b -value) diffusion-weighted (DW) MRI, and clinical biomarkers. To analyze DW-MRI, our framework starts with kidney tissue segmentation using a level set approach after DW-MRI data alignment to handle the motion effects. Secondly, the cumulative empirical distributions (i.e., CDFs) of apparent diffusion coefficients (ADCs) of the segmented DW-MRIs are estimated at low and high gradient strengths and duration ( b -values) accounting for both blood perfusion and diffusion, respectively. Finally, these CDFs are fused with laboratory-based biomarkers (creatinine clearance and serum plasma creatinine) for the classification of transplant status using a deep learning-based classification approach utilizing a stacked non-negativity constrained auto-encoder. Using “leave-one-subject-out” experiments on a cohort of 58 subjects, the proposed CAD system distinguished non-rejection transplants from kidneys with abnormalities with a 95 % accuracy (sensitivity = 95 %, specificity = 94 %) and achieved a 95 % correct classification between early rejection and other kidney diseases. Our preliminary results demonstrate the promise of the proposed CAD system as a reliable non-invasive diagnostic tool for renal transplants assessment.

Stereo matching techniques aim at reconstructing disparity maps from a pair of images. The use of stereo matching techniques in embedded systems is very challenging due to the complexity of the state-of-the-art algorithms. Local stereo matching algorithms are efficiently implemented on GPU and DSP. This paper presents the optimization of the One Dimension Belief Propagation (BP-1D) algorithm. BP-1D is faster than previous algorithms on monocore DSP and its implementation onto multicore DSPs is straightforward. BP-1D implemented on multicore embedded platforms out-performs previous stereo matching implementations reaching real-time performances for resolutions up to 1080p with a 10 Watts power consumption.

This paper introduces a new framework for the segmentation of different brain structures from 3D infant MR brain images. The proposed segmentation framework is based on a shape prior built using a subset of co-aligned training images that is adapted during the segmentation process based on higher-order visual appearance characteristics of infant MRIs. These characteristics are described using voxel-wise image intensities and their spatial interaction features. In order to more accurately model the empirical grey level distribution of infant brain signals, a Linear Combination of Discrete Gaussians (LCDG) is used that has positive and negative components. Also to accurately account for the large inhomogeneity in infant MRIs, a higher-order Markov Gibbs Random Field (MGRF) spatial interaction model that integrates third- and fourth-order families with a traditional second-order model is proposed. The proposed approach was tested on 40 in-vivo infant 3D MR brain scans, having their ground truth created by an expert radiologist, using three metrics: the Dice coefficient, the 95-percentile modified Hausdorff distance, and the absolute brain volume difference. Experimental results promise an accurate segmentation of infant MR brain images compared to current open source segmentation tools.

A novel framework for assessing wall thickening from 4D cine cardiac magnetic resonance imaging (CMRI) is proposed. The proposed approach is primarily based on using geometrical features to track the left ventricle (LV) wall during the cardiac cycle. The 4D tracking approach consists of the following two main steps: (i) Initially, the surface points on the LV wall are tracked by solving a 3D Laplace equation between two successive LV surfaces; and (ii) Secondly, the locations of the tracked LV surface points are iteratively adjusted through an energy minimization cost function using a generalized Gauss-Markov random field (GGMRF) image model in order to remove inconsistencies and preserve the anatomy of the heart wall during the tracking process. Then the myocardial wall thickening is estimated by co-allocation of the corresponding points, or matches between the endocardium and epicardium surfaces of the LV wall using the solution of the 3D Laplace equation. Experimental results on in vivo data confirm the accuracy and robustness of our method. Moreover, the comparison results demonstrate that our approach outperforms 2D wall thickening estimation approaches.

We propose a novel approach to justify and guide regularisation of an ill-posed one-dimensional global optimisation with multiple solutions using a massively parallel (P system) model of the solution space. Classical optimisation assumes a well-posed problem with a stable unique solution. Most of important practical problems are ill posed due to an unstable or non-unique global optimum and are regularised to get a unique best-suited solution. Whilst regularisation theory exists largely for unstable unique solutions, its recommendations are often routinely applied to inverse optical problems with essentially non-unique solutions, e.g. computer stereo vision or image segmentation, typically formulated in terms of global energy minimisation. In these cases the recommended regularisation becomes purely heuristic and does not guarantee a unique solution. As a result, classical optimisation algorithms: dynamic programming (DP) and belief propagation (BP) – meet with difficulties. Our recent concurrent propagation (CP), leaning upon the P systems paradigm, extends DP and BP to always detect whether the problem is ill posed or not and store in the ill-posed case an entire space of solutions that yield the same global optimum. This suggests a radically new path to proper regularisation: select the best-suited unique solution by exploring statistical and structural features of this space. We propose a P systems based implementation of CP and set out as a case study an application of CP to the image matching problem in stereo vision.

The survey outlines and compares popular computational techniques for quantitative description of shapes of major structural parts of the human brain, including medial axis and skeletal analysis, geodesic distances, Procrustes analysis, deformable models, spherical harmonics, and deformation morphometry, as well as other less widely used techniques. Their advantages, drawbacks, and emerging trends, as well as results of applications, in particular, for computer-aided diagnostics, are discussed.

A novel framework for the classification of acute rejection versus nonrejection status of renal transplants from 2-D dynamic contrast-enhanced magnetic resonance imaging is proposed. The framework consists of four steps. First, kidney objects are segmented from adjacent structures with a level set deformable boundary guided by a stochastic speed function that accounts for a fourth-order Markov-Gibbs random field model of the kidney/background shape and appearance. Second, a Laplace-based nonrigid registration approach is used to account for local deformations caused by physiological effects. Namely, the target kidney object is deformed over closed, equispaced contours (iso-contours) to closely match the reference object. Next, the cortex is segmented as it is the functional kidney unit that is most affected by rejection. To characterize rejection, perfusion is estimated from contrast agent kinetics using empirical indexes, namely, the transient phase indexes (peak signal intensity, time-to-peak, and initial up-slope), and a steady-phase index defined as the average signal change during the slowly varying tissue phase of agent transit. We used a kn-nearest neighbor classifier to distinguish between acute rejection and nonrejection. Performance of our method was evaluated using the receiver operating characteristics (ROC). Experimental results in 50 subjects, using a combinatoric kn-classifier, correctly classified 92% of training subjects, 100% of the test subjects, and yielded an area under the ROC curve that approached the ideal value. Our proposed framework thus holds promise as a reliable noninvasive diagnostic tool.

A new framework for the precise segmentation of lung tissues from Computed Tomography (CT) is proposed. The CT images, Gaussian Scale Space (GSS) data generation using Gaussian Kernels (GKs), and desired maps of regions (lung and the other chest tissues) are described by a joint Markov-Gibbs Random Field Model (MGRF) of independent image signals and interdependent region labels. We focus on the most accurate model identification of the joint MGRF models. To better specify region borders, each empirical distribution of signals is rigorously approximated by a Linear Combination of Discrete Gaussians (LCDG) with positive and negative components. The classical Expectation-Maximization (EM) algorithm has been adapted for the LCDG model. The initial segmentations from the original and the generated GSS CT images are based on the LCDG-models; then they are iteratively refined using an MGRF model with analytically estimated potentials. Finally, these initial segmentations are fused together using a Bayesian fusion approach to get the final segmentation of the lung region. Experiments on eleven real data sets based on Dice Similarity Coefficient (DSC) metric confirms the high accuracy of the proposed approach.

A novel 2D approach for early assessment of malignant lung nodules based on analyzing the spatial distribution of Hounsfield values for the detected lung nodules is proposed. Spatial distribution of Hounsfield values comprising the malignant nodule appearance is accurately modeled with a new 2D rotationally invariant second-order Markov-Gibbs Random Field (MGRF). Preliminary experiments on 109 lung nodules (51 malignant and 58 benign) show that the proposed method is a promising supplement to current technologies (biopsy-based diagnostic systems) for the early diagnosis of lung cancer.

To estimate the number of unimodal components in a mixture model of a marginal probability distribution of signals while learning the model with a conventional Expectation-Maximization (EM) algorithm, a modification of the well-known Akaike information criterion (AIC) called the modified AIC (mAIC), is proposed. Embedding the mAIC into the EM algorithm allows us to exclude sequentially, one-by-one, the least informative components from their initially excessive, or over-fitting set. Experiments on modeling empirical marginal signal distributions with mixtures of continuous or discrete Gaussians in order to describe the visual appearance of synthetic phantoms and real medical 3D images (lung CT and brain MRI) demonstrate a marked and monotone increase of the mAIC towards its maximum at the proper number that is known for the synthetic phantom or practically justified for the real image. These results confirm the accuracy and robustness of the proposed automated mAIC-EM based learning.

A novel non-invasive approach for the early diagnosis of prostate cancer from diffusion-weighted MRI is proposed. The proposed diagnostic approach consists of three main steps. The first step is to isolate the prostate from the surrounding anatomical structures based on a Maximum a Posteriori (MAP) estimate of a new log-likelihood function that accounts for the shape priori, the spatial interaction, and the current appearance of prostate tissues and its background (surrounding anatomical structures). In the second step, a nonrigid registration algorithm is employed to account for any local deformation between the segmented prostates at different b-values that could occur during the scanning process due to patient breathing and local motion. In the final step, a kn-Nearest Neighbor-based classifier is used to classify the prostate into benign or malignant based on four appearance features extracted from registered images. Moreover, in this paper we introduce a new approach to generate color maps that illustrate the propagation of diffusion in prostate tissues based on the analysis of the 3D spatial interaction of the change of the gray level values of prostate voxel using a Generalized Gauss-Markov Random Field (GGMRF) image model. Finally, the tumor boundaries are determined using a level set deformable model controlled by the diffusion information and the spatial interactions between the prostate voxels. Experimental results on 28 clinical diffusion-weighted MRI data sets yield promising results.

Accurate registration of cardiac first-pass magnetic resonance imaging (FP-MRI) is fundamental for precise analysis of myocardial perfusion. In this paper, we introduce and validate a new framework for accurate registration of the segmented left ventricle (LV) wall on cardiac FP-MRI. Due to the continuous physiological motion of the heart that causes the LV wall to change shape significantly and to move within and through the image plane, we developed a new methodology for 2D FP-MRI nonrigid registration that includes: (i) global target-to-reference frame-to-frame alignment based on the maximization of the normalized mutual information (NMI); (ii) local alignment based on using a B-splines transformation model that maximizes a similarity function that accounts for 1st- and 2nd-order NMI between the globally aligned frames followed by (iii) a refinement step that is based on deforming each pixel of the target wall over evolving closed equi-spaced contours (iso-contours) to closely match the reference wall. Respective iso-contours in both reference and target frames are matched based on solving the Laplace equation. We have tested our framework on both synthetic phantoms and 20 in-vivo data sets that have been collected from patients with ischemic damage from heart attacks, who are undergoing a novel myoregeneration therapy.

To reduce noise within a tag line, unsharpen the tag edges in spatial domain, and amplify the tag-to-background contrast, a 3D energy minimization framework for the enhancement of tagged Cardiac Magnetic Resonance (CMR) image sequences, based on learning first- and second-order visual appearance models, is proposed. The first-order appearance modeling uses adaptive Linear Combinations of Discrete Gaussians (LCDG) to accurately approximate the empirical marginal probability distribution of CMR signals for a given sequence, and separates tag and background submodels. It is also used to classify the tag lines and the background. The second-order model considers image sequences as samples of a translation- and rotation-invariant 3D Markov-Gibbs Random Field (MGRF) with multiple pairwise voxel interactions. A 3D energy function for this model is built by using the analytical estimation of the spatio-temporal geometry and Gibbs potentials of interaction. To improve the strain estimation, by enhancing the tag and background homogeneity and contrast, the given sequence is adjusted using comparisons to the energy minimizer. Special 3D geometric phantoms, motivated by statistical analysis of the tagged CMR data, have been designed to validate the accuracy of our approach. Experiments with the phantoms and eight real data sets have confirmed the high accuracy of the functional parameters that are estimated for the enhanced tagged sequences when using popular spectral techniques, such as spectral Harmonic Phase (HARP).

Dyslexia severely impairs learning abilities; therefore, improved diagnostic methods are needed. Neuropathological studies have revealed an abnormal anatomy of the corpus callosum (CC) in dyslexic brains. We propose a new approach for the quantitative analysis of 3-D magnetic resonance images (MRI) of the brain that ensures a more accurate quantification of anatomical differences between the CC of dyslexic and control subjects. The proposed approach consists of three main processing steps: 1) segmenting the CC from a given 3-D MRI using the learned CC shape and visual appearance; 2) extracting the centerline of the CC; and 3) cylindrical mapping of the CC surface for its comparative analysis. Validation on 3-D simulated phantoms demonstrates the ability of the proposed approach to accurately detect the shape variability between two 3-D surfaces. Experimental results revealed significant differences (at the 95% confidence level) between 14 normal and 16 dyslexic subjects in all four anatomical divisions, i.e., splenium, rostrum, genu, and body of their CCs. Moreover, the initial classification results based on the centerline length and CC thickness suggest that the proposed shape analysis is a promising supplement to the current techniques for diagnosing dyslexia.

A novel automated framework for the segmentation of the left ventricle (LV) wall from contrast enhanced cardiac magnetic resonance images (CE-CMRI) is proposed. The framework consists of two main steps. First, the inner cavity of the LV is segmented from the surrounding tissues based on finding the Maximum A Posteriori (MAP) estimation of a new energy function using a graph-cuts-based optimization algorithm. The proposed energy function consists of three descriptors: 1st-order visual appearance descriptors of the CE-CMRI, a 2D spatially rotation-variant 2nd-order homogeneity descriptor, and a LV inner cavity shape descriptor. Second, the outer contour of the LV is segmented by generating an orthogonal wave, starting from the LV inner contour, by solving an Eikonal partial differential equation with a new speed function that combines the prior shape and current visual appearance models of the LV wall. The proposed framework was tested on in-vivo CE-CMR images and validated with manual expert delineations of left ventricle borders. Experiments and comparison results on real CE-CMR images confirm the robustness and accuracy of the proposed framework over the existing ones.

Prostate segmentation is an essential step in developing any non-invasive Computer-Assisted Diagnostic (CAD) system for the early diagnosis of prostate cancer using Magnetic Resonance Images (MRI). In this paper, a novel framework for 3D segmentation of the prostate region from Diffusion-Weighted Magnetic Resonance Imaging (DW-MRI) is proposed. The framework is based on a Maximum A Posteriori (MAP) estimate of a new log-likelihood function that accounts for Markov-Gibbs shape and appearance models of the object-of-interest and its background. The framework was evaluated on in vivo prostate DW-MRI with available manual expert segmentation. The performance evaluation of the proposed segmentation approach, based on voxel-based and distance-based metrics between manually drawn and automatically segmented contours, confirmed the robustness and accuracy of the proposed segmentation approach.

A new automatic approach for the estimation of global indexes from short-axis cine cardiac magnetic resonance (CMR) images is proposed. The inner contour of the left ventricle (LV) is segmented with a level set-based deformable model. Its evolution is controlled by a specially designed stochastic speed function that accounts for a learned spatially variant statistical shape prior, a 1st-order visual appearance descriptor of the contour interior and exterior (associated with the object and background, respectively), and a spatially invariant 2nd-order homogeneity descriptor. After the inner contour delineation, the total cavity volume (time varying LV volume) data is used to estimate the LV global functional indexes, i.e., ejection fraction, systolic and diastolic slopes. Experiments with in-vivo CMR data, obtained from subjects with chronic ischemic heart disease and damage that is documented by viability MRI, confirm a high robustness and accuracy of the proposed approach.

Kidney segmentation is an essential step in developing any non-invasive Computer-Assisted Diagnostic (CAD) system for the early detection of acute renal rejection. This paper describes a 3-D approach for kidney segmentation from abdominal Computed Tomography (CT) images using a level set-based deformable model. Its evolution is controlled by a specially designed stochastic speed function that accounts for a shape prior and features of image intensity and spatial interactions. The shape prior is learned from the co-aligned 3-D kidney data. The current visual appearances are described with marginal gray level distributions obtained by separating their mixture over the kidney data. The spatial interactions between the kidney voxels are modeled by a 3-D 2nd-order translation and rotation variant Markov-Gibbs Random Field (MGRF) of “object-background” labels with analytically estimated potentials. The proposed approach has been evaluated on the CT data sets of 29 patients, yielding an average volumetric overlap error of 3.71%. The presented results indicate that combing CT images' characteristics into level set evolution leads to more accurate segmentation results.

To discriminate more accurately between dyslexic and normal brains, we detect the brain cortex variability through a spherical harmonic analysis that represents a 3D surface supported by the unit sphere, having a linear combination of special basis functions, called spherical harmonics (SHs). The proposed 3D shape analysis is carried out in five steps: (i) 3D brain cortex segmentation, with a deformable 3D boundary, controlled by two probabilistic visual appearance models (the learned prior and the estimated current appearance one); (ii) 3D Delaunay triangulation to construct a 3D mesh model of the brain cortex surface; (iii) mapping this model to the unit sphere; (iv) computing the SHs for the surface, and (v) determining the number of the SHs to delineate the brain cortex. We describe the brain shape complexity with a new shape index, the estimated number of the SHs, and use it for the K-nearest classification into the normal and dyslexic brains. Initial experiments suggest that our shape index is a promising supplement to the current dyslexia diagnostic techniques.

Our long-term research goal is to develop a fully automated, image-based diagnostic system for early diagnosis of pulmonary nodules that may lead to lung cancer. This paper focuses on validating our approach for monitoring the development of lung nodules detected in successive chest low dose computed tomography (LDCT) scans of a patient. Our methodology for monitoring the detected lung nodules includes 3-D LDCT data registration, which is non-rigid and involves two steps: (i) global target-to-prototype alignment of one scan to another using the learned prior appearance model followed by (ii) local alignment in order to correct for intricate relative deformations. This approach has been validated on elastic lung phantoms constructed using state-of-the-art microfluidics technology. The elastic lung phantoms are fabricated from a flexible transparent polymer, i.e., polydimethylsiloxane (PDMS). These Phantoms mimic the contractions and expansions of the lung and nodules seen during normal breathing. Experiments confirm the high accuracy of the proposed approach for measuring the growth rate of the detected lung nodules.

The importance of accurate early diagnostics of autism that severely affects personal behavior and communication skills cannot be overstated. Neuropathological studies have revealed an abnormal anatomy of the Corpus Callosum (CC) in autistic brains. We propose a new approach to quantitative analysis of three-dimensional (3D) magnetic resonance images (MRI) of the brain that ensures a more accurate quantification of anatomical differences between the CC of autistic and normal subjects. It consists of three main processing steps: (i) segmenting the CC from a given 3D MRI using the learned CC shape and visual appearance; (ii) extracting a centerline of the CC; and (iii) cylindrical mapping of the CC surface for its comparative analysis. Our experiments revealed significant differences (at the 95% confidence level) between 17 normal and 17 autistic subjects in four anatomical divisions, i.e. splenium, rostrum, genu and body of their CC.

A new speed function to guide evolution of a level-set based active contour is proposed for segmenting an object from its background in a given image. The guidance accounts for a learned spatially variant statistical shape prior, 1st-order visual appearance descriptors of the contour interior and exterior (associated with the object and background, respectively), and a spatially invariant 2nd-order homogeneity descriptor. The shape prior is learned from a subset of co-aligned training images. The visual appearances are described with marginal gray level distributions obtained by separating their mixture over the image. The evolving contour interior is modeled by a 2nd-order translation and rotation invariant Markov-Gibbs random field of object / background labels with analytically estimated potentials. Experiments to segment the inner cavity of heart cine images confirm robustness and accuracy of the proposed approach.

A new speed function to guide evolution of a level-set based active contour is proposed for segmenting an object from its background in a given image. The guidance accounts for a learned spatially variant statistical shape prior, 1st-order visual appearance descriptors of the contour interior and exterior (associated with the object and background, respectively), and a spatially invariant 2nd-order homogeneity descriptor. The shape prior is learned from a subset of co-aligned training images. The visual appearances are described with marginal gray level distributions obtained by separating their mixture over the image. The evolving contour interior is modeled by a 2nd-order translation and rotation invariant Markov-Gibbs random field of object/background labels with analytically estimated potentials. Experiments with kidney CT images confirm robustness and accuracy of the proposed approach.

This paper presents a new stochastic marked point process for describing images in terms of a finite library of geometric objects. Image analysis based on conventional marked point processes has already produced convincing results but at the expense of parameter tuning, computing time, and model specificity. Our more general multimarked point process has simpler parametric setting, yields notably shorter computing times, and can be applied to a variety of applications. Both linear and areal primitives extracted from a library of geometric objects are matched to a given image using a probabilistic Gibbs model, and a Jump-Diffusion process is performed to search for the optimal object configuration. Experiments with remotely sensed images and natural textures show that the proposed approach has good potential. We conclude with a discussion about the insertion of more complex object interactions in the model by studying the compromise between model complexity and efficiency.

Even in state-of-the-art processors, real-time processing of stereo pairs to generate useful scene information is too computationally intensive to process high resolution images and the large disparity ranges necessary for precise depth information. We have implemented the Symmetric Dynamic Programming Stereo (SPDS) algorithm in reconfigurable hardware which is able to generate disparity and occlusion maps from one megapixel images in real-time (30fps). Here, we describe an algorithm for contour map generation which uses the occlusion and disparity maps to rapidly produce contour maps which outline objects in the image.

A novel parametric deformable model of a goal object controlled by shape and appearance priors learned from co-aligned training images is introduced. The shape prior is built in a linear space of vectors of distances to the training boundaries from their common centroid. The appearance prior is modeled with a spatially homogeneous 2nd-order Markov-Gibbs random field (MGRF) of gray levels within each training boundary. Geometric structure of the MGRF and Gibbs potentials are analytically estimated from the training data. To accurately separate goal objects from arbitrary background, the deformable model is evolved by solving an Eikonal partial differential equation with a speed function combining the shape and appearance priors and the current appearance model. The latter represents empirical gray level marginals inside and outside an evolving boundary with adaptive linear combinations of discrete Gaussians (LCDG). The analytical shape and appearance priors and a simple Expectation-Maximization procedure for getting the object and background LCDGs, make our segmentation considerably faster than most of the known counterparts. Experiments with various images confirm robustness, accuracy, and speed of our approach.

New techniques for more accurate unsupervised segmentation of lung tissues from Low Dose Computed Tomography (LDCT) are proposed. In this paper we describe LDCT images and desired maps of regions (lung and the other chest tissues) by a joint Markov-Gibbs random field model (MGRF) of independent image signals and interdependent region labels but focus on most accurate model identification. To better specify region borders, each empirical distribution of signals is precisely approximated by a Linear Combination of Discrete Gaussians (LCDG) with positive and negative components. We modify a conventional Expectation-Maximization (EM) algorithm to deal with the LCDG and develop a sequential EM-based technique to get an initial LCDG-approximation for the modified EM algorithm. The initial segmentation based on the LCDG-models is then iteratively refined using a MGRF model with analytically estimated potentials. Experiments on real data sets confirm high accuracy of the proposed approach. 1

Our goal is to represent images in terms of geometric objects acting as primitive elements of an image description. Similar representations obtained by stochastic marked point processes have already led to convincing image analysis results but suffer from serious drawbacks such as complex and unstable parameter tuning, large computing time, and lack of generality. We propose an alternative descriptive model based on a Jump-Diffusion process which can be performed in shorter computing times and applied to a variety of applications without changing the model or modifying the tuning parameters. In our approach, a probabilistic Gibbs model is adapted to a library of geometric objects and is sampled by a Jump-Diffusion process in order to closely match an underlying texture. Experiments with natural textures and remotely sensed images show good potentialities of the proposed approach 1 .

We propose a novel parametric deformable model controlled by shape and visual appearance priors learned from a training subset of co-aligned images of goal objects. The shape prior is derived from a linear combination of vectors of distances between the training boundaries and their common centroid. The appearance prior considers gray levels within each training boundary as a sample of a Markov-Gibbs random field with pairwise interaction. Spatially homogeneous interaction geometry and Gibbs potentials are analytically estimated from the training data. To accurately separate a goal object from an arbitrary background, empirical marginal gray level distributions inside and outside of the boundary are modeled with adaptive linear combinations of discrete Gaussians (LCDG). The evolution of the parametric deformable model is based on solving an Eikonal partial differential equation with a new speed function which combines the prior shape, prior appearance, and current appearance models. Due to the analytical shape and appearance priors and a simple Expectation-Maximization procedure for getting the object and background LCDG, our segmentation is considerably faster than most of the known geometric and parametric models. Experiments with various goal images confirm the robustness, accuracy, and speed of our approach.

A new approach to align an image of a textured object with a given prototype (learned reference object) is proposed. Visual appearance of the images, after equalizing their signals, is modeled with a Markov-Gibbs random field with pairwise interaction. Similarity to the prototype (learned reference object) is measured by a Gibbs energy of signal co-occurrences in a characteristic subset of pixel pairs derived automatically from the prototype. An object is aligned by an affine transformation maximizing the similarity by using an automatic initialization followed by gradient search. To get accurate appearance model, we developed a new approach to automatically select the most important cliques (neighborhood system) that describe the visual appearance of a texture object. Experiments confirm that our approach aligns complex objects better than popular conventional algorithms.

The importance of accurate early diagnosis of dyslexia, which severely affects the learning abilities of children, cannot be overstated. Neuropathological studies have revealed an abnormal anatomy of the cerebral white matter (CWM) in dyslexic brains. We explore a possibility of distinguishing between dyslexic and normal (control) brains by a quantitative shape analysis of CWM gyrifications on 3D magnetic resonance (MR) images. Our approach consists of (i) segmentation of the CWM on a 3D brain image using a deformable 3D boundary; (ii) extraction of gyrifications from the segmented CWM, and (iii) shape analysis to quantify thickness of the extracted gyrifications and classify dyslexic and normal subjects. The boundary evolution is controlled by two probabilistic models of visual appearance of 3D CWM: the learned prior and the current appearance model. Initial experimental results suggest that the proposed 3D texture analysis is a promising supplement to the current techniques for diagnosing dyslexia.

Acute renal rejection is the most common reason for graft (transplanted kidney) failure after kidney transplantation, and early detection is crucial to survival of function in the transplanted kidney. The current techniques for early detection of acute renal rejection are not accurate. For example, clearances of inulin and DTPA require multiple blood and urine tests, and they provide information on both kidneys together, but not unilateral information. Moreover, biopsy (the gold standard for diagnosis of acute renal rejection after renal transplantation) could cause bleeding and infection. Also, the relatively small needle biopsies may lead to over- or underestimation of the extent of inflammation in the entire graft. Hence, a noninvasive and repeatable technique would not only be useful but is needed to ensure survival of transplanted kidneys. For this reason, we introduced a new non-invasive framework for automatic classification of normal and acute renal rejection transplants using Dynamic Contrast Enhanced Magnetic Resonance Images (DCE-MRI). In this paper, we introduce a new approach for the automatic classification of normal and acute rejection transplants from Dynamic Contrast Enhanced Magnetic Resonance Imaging (DCE-MRI). The proposed algorithm consists of three main steps; the first step isolates the kidney from the surrounding anatomical structures. In the second step, new motion correction models are employed to account for both the global and local motion of the kidney due to patient moving and breathing. Finally, the perfusion curves that show the transportation of the contrast agent into the tissue are obtained from the kidney and used in the classification of normal and acute rejection transplants. In this paper, we will focus on the second and third steps and the first step is shown in detail in [1].

This paper proposes a new analytical method for estimating parameters of a homogeneous isotropic Potts model with an asymmetric Gibbs potential function. The model is generalized by including both pairwise and triple cliques. The maximum likelihood estimates of the cliques potentials are obtained by a further elaboration of the approximate analytical estimator proposed in. Experiments with synthetic textures have shown that our potential estimates are more accurate and practicable than their counterparts obtained with classical methods.

The importance of accurate early diagnostics of dyslexia that severely affects the learning abilities of children cannot be overstated. Neuropathological studies have revealed an abnormal anatomy of the cerebral white matter (CWM) in dyslexic brains. We explore a possibility of distinguishing between dyslexic and normal (control) brains by a quantitative shape analysis of CWM gyrifications on 3D Magnetic Resonance (MR) images. Our approach consists of (i) segmentation of the CWM on a 3D brain image using a deformable 3D boundary; (ii) extraction of gyrifications from the segmented CWM, and (iii) shape analysis to quantify thickness of the extracted gyrifications and classify dyslexic and normal subjects. The boundary evolution is controlled by two probabilistic models of visual appearance of 3D CWM: the learned prior and the current appearance model. Initial experimental results suggest that the proposed 3D texture analysis is a promising supplement to the current techniques for diagnosing dyslexia.

Acute renal rejection is the most common reason for graft (transplanted kidney) failure after kidney transplantation, and early detection is crucial to survival of function in the transplanted kidney. The current techniques for early detection of acute renal rejection are not accurate. For example, clearances of inulin and DTPA require multiple blood and urine tests, and they provide information on both kidneys together, but not unilateral information. Moreover, biopsy (the gold standard for diagnosis of acute renal rejection after renal transplantation) could cause bleeding and infection. Also, the relatively small needle biopsies may lead to over- or underestimation of the extent of inflammation in the entire graft. Hence, a noninvasive and repeatable technique would not only be useful but is needed to ensure survival of transplanted kidneys. For this reason, we introduced a new non-invasive framework for automatic classification of normal and acute renal rejection transplants using dynamic contrast enhanced magnetic resonance images (DCE-MRI). In this paper, we introduce a new approach for the automatic classification of normal and acute rejection transplants from Dynamic Contrast Enhanced Magnetic Resonance Imaging (DCE-MRI). The proposed algorithm consists of three main steps; the first step isolates the kidney from the surrounding anatomical structures. In the second step, new motion correction models are employed to account for both the global and local motion of the kidney due to patient moving and breathing. Finally, the perfusion curves that show the transportation of the contrast agent into the tissue are obtained from the kidney and used in the classification of normal and acute rejection transplants. In this paper, we will focus on the second and third steps and the first step is shown in detail by A. El-Baz et al (2005).

Our long term research goal is to develop a fully automated, image-based diagnostic system for early diagnosis of pulmonary nodules that may lead to lung cancer. This paper focuses on monitoring the development of lung nodules detected in successive chest low dose (LD) CT scans of a patient. We propose a new methodology for 3D LDCT data registration which is non-rigid and involves two steps: (i) global alignment of one scan (target) to another scan (reference or prototype) using the learned prior appearance model followed by (ii) local alignment in order to correct for intricate deformations. After equalizing signals for two subsequent chest scans, visual appearance of these chest images is modeled with a Markov-Gibbs random field with pairwise interaction. We estimate the affine transformation that globally register the target to the prototype by gradient descent maximization of a special Gibbs energy function. To handle local deformations, we deform each voxel of the target over evolving closed equi-spaced surfaces (iso-surfaces) to closely match the prototype. The evolution of the iso-surfaces is guided by an exponential speed function in the directions that minimize distances between the corresponding voxel pairs on the iso-surfaces in both the data sets. Preliminary results on the 135 LDCT data sets from 27 patients show that our proper registration could lead to precise diagnosis and identification of the development of the detected pulmonary nodules.

Abstract. A new approach to align an image of a textured object with a given prototype is proposed. Visual appearance of the images, after equalizing their signals, is modeled with a Markov-Gibbs random field with pairwise interaction. Similarity to the prototype is measured by a Gibbs energy of signal co-occurrences in a characteristic subset of pixel pairs derived automatically from the prototype. An object is aligned by an affine transformation maximizing the similarity by using an automatic initialization followed by gradient search. Experiments confirm that our approach aligns complex 2D/3D objects better than popular conventional algorithms. 1

We propose novel expectation maximization (EM) based algorithms for accurate approximation of an empirical probability distribution of discrete scalar data. The algorithms refine our previous ones in that they approximate the empirical distribution with a linear combination of discrete Gaussians (LCDG). The use of the DGs results in closer approximation and considerably better convergence to a local likelihood maximum compared to previously involved conventional continuous Gaussian densities. Experiments in segmenting multimodal medical images show the proposed algorithms produce more adequate region borders.

A pulmonary nodule is the most common manifestation of lung cancer. Lung nodules are approximately-spherical regions of relatively high density that are visible in X-ray images of the lung. Large (generally defined as greater than 1 cm in diameter) malignant nodules can be easily detected with traditional imaging equipment and can be diagnosed by needle biopsy or bronchoscopy techniques. However, the diagnostic options for small malignant nodules are limited due to problems associated with accessing small tumors, especially if they are located deep in the tissue or away from the large airways; therefore, additional diagnostic and imaging techniques are needed. One of the most promising techniques for detecting small cancerous nodules relies on characterizing the nodule based on its growth rate. The growth rate is estimated by measuring the volumetric change of the detected lung nodules over time, so it is important to accurately measure the volume of the nodules to quantify their growth rate over time. In this paper, we introduce a novel Computer Assisted Diagnosis (CAD) system for early diagnosis of lung cancer. The proposed CAD system consists of five main steps. These steps are: (i) segmentation of lung tissues from low dose computed tomography (LDCT) images, (ii) detection of lung nodules from segmented lung tissues, (iii) a non-rigid registration approach to align two successive LDCT scans and to correct the motion artifacts caused by breathing and patient motion, (iv) segmentation of the detected lung nodules, and (v) quantification of the volumetric changes. Our preliminary classification results based on the analysis of the growth rate of both benign and malignant nodules for 10 patients (6 patients diagnosed as malignant and 4 diagnosed as benign) were 100% for 95% confidence interval. The preliminary results of the proposed image analysis have yielded promising results that would supplement the use of current technologies for diagnosing lung cancer.

Our long term research goal is to develop an image-based approach for early diagnosis of lung nodules that may lead to lung cancer. This paper focuses on monitoring the progress of detected lung nodules in successive chest low dose CT (LDCT) scans of a patient using non-rigid registration. In this paper, we propose a new methodology for 3D LDCT data registration. The registration methodology is non-rigid and involves two steps: global alignment of one scan (target data) to another scan (reference data) using the learned prior appearance model followed by local alignments in order to correct for intricate deformations. From two subsequent chest scans, visual appearance of the chest images, after equalizing their signals, are modeled with a Markov-Gibbs random field with pairwise interaction. Our approach is based on finding the affine transformation to register one data set (target data) to another data set (reference data) by maximizing a special Gibbs energy function using a gradient descent algorithm. To get accurate appearance model, we developed a new approach to an automatically select the most important cliques that describe the visual appearance of LDCT data. To handle local deformations, we propose a new approach based on deforming each voxel over evolving closed and equi-spaced surfaces (iso-surfaces) to closely match the prototype. The evolution of the iso-surfaces is guided by an exponential speed function in the directions minimizing distances between corresponding pixel pairs on the iso-surfaces on both data sets. Our preliminary results on 10 patients show that the proper registration could lead to precise identification of the progress of the detected lung nodules.

A new approach to align an image of a textured object with a given prototype is proposed. Visual appearance of the images, after equalizing their signals, is modeled with a Markov-Gibbs random field with pairwise interaction. Similarity to the prototype is measured by a Gibbs energy of signal cooccurrences in a characteristic subset of pixel pairs derived automatically from the prototype. An object is aligned by an affine transformation maximizing the similarity by using an automatic initialization followed by gradient search. Experiments confirm that our approach aligns complex objects better than popular conventional algorithms.

A new physically justified adaptive probabilistic model of blood vessels on magnetic resonance angiography (MRA) images is proposed. The model accounts for both laminar (for normal subjects) and turbulent blood flow (in abnormal cases like anemia or stenosis) and results in a fast algorithm for extracting a 3D cerebrovascular system from the MRA data. Experiments with real data sets confirm the high accuracy of the proposed approach.

We compare three Computer Vision approaches to 3-D reconstruction, namely passive Binocular Stereo and active Structured Lighting and Photometric Stereo, in application to human face reconstruction for modelling virtual humans. An integrated lab environment was set up to simultaneously acquire images for 3-D reconstruction and corresponding data from a 3-D scanner. This allowed us to quantitatively compare reconstruction results to accurate ground truth. Our goal was to determine whether any current Computer Vision approach is accurate enough for practically useful 3-D facial surface reconstruction. Comparative experiments show the combination of Structured Lighting with Symmetric Dynamic Programming based Binocular Stereo has good prospects due to reasonable processing time and sufficient accuracy.

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.

Deformable or active contour, and surface models are powerful image segmentation techniques. We introduce a novel fast and robust bi-directional parametric deformable model which is able to segment regions of intricate shape in multi-modal greyscale images. The power of the algorithm in terms of computation time and robustness is owing to the use of joint probabilities of the signals and region labels in individual points as external forces guiding the model evolution. These joint probabilities are derived from a Markov– Gibbs random field (MGRF) image model considering an image as a sample of two interrelated spatial stochastic processes. The low level process with conditionally independent and arbitrarily distributed signals relates to the observed image whereas its hidden map of regions is represented with the high level MGRF of interdependent region labels. Marginal probability distributions of signals in each region are recovered from a mixed empirical signal distribution over the whole image. In so doing, each marginal is approximated with a linear combination of Gaussians (LCG) having both positive and negative components. The LCG parameters are estimated using our previously proposed modification of the EM algorithm, and the high-level Gibbs potentials are computed analytically. Comparative experiments show that the proposed model outlines complicated boundaries of different modal objects much more accurately than other known counterparts. 1

In this paper, we propose a novel algorithm for isolating lung abnormalities (nodules) from low dose spiral chest CT scans. The proposed algorithm consists of three main steps. The first step isolates the lung nodules, arteries, veins, bronchi, and bronchioles from the surrounding anatomical structures. The second step detects lung nodules using deformable 2D and 3D templates describing typical geometry and gray level distribution within the nodules of the same type. The detection combines the normalized cross-correlation template matching and genetic optimization algorithm. The final step eliminates the false positive nodules (FPNs) using three features that robustly define the true lung nodules. Accurate density estimation for these three features is obtained using logistic regression model and linear combination of Gaussians (LCG) with positive and negative components. This paper focuses on the second and third steps. Experiments with 200 patients' CT scans demonstrate the accuracy of our approach.

The reconstruction of 3D face models is mostly achieved by using 2D images. We compare the strengths and weaknesses of different image processing techniques for 3D face generation. It is anticipated that the optimal solution will be applied in the future for 3D face analysis and synthesis. As approaches to 3D face modelling, the paper presents: binocular stereo, using a stereo correspondence algorithm or manual triangulation; orthogonal views; photometric stereo. Photometric stereo and orthogonal views seem to provide the best rendering while keeping a reasonable time efficiency, implementation difficulty and cumbersomeness. However, 3D face acquisition techniques have not closed the gap between accuracy and cumbersomeness.

Empirical and analytical methods of selecting a characteristic structure of pairwise pixel interactions in Gibbs random field texture models are compared. Simple thresholding of partial interaction energies recovers a basic structure for modelling spatially homogeneous stochastic textures. Computationally intensive empirical sequential learning reduces the size of a basic structure and complements it by a fine structure describing characteristic minor details of regular textures. The empirical selection implicitly assumes that characteristic structures should include only statistically independent interactions. It can be approximated using analytical estimates of energies. Experiments show that a combined analytical-empirical sequential learning finds reduced basic and fine interaction structures much faster than the purely empirical one, but the sequential selection based on relative interaction energies may deteriorate basic structures of stochastic textures with strongly interdependent characteristic interactions.

Relative orientation of images obtained by cameras located around a 3D terrain can be considered as an estimation of relative geometric distortions of the images. In this paper a rough affine approximation of image distortions is found by combining an exhaustive and Hooke-Jeeves directed unconstrained search for affine parameters that ensure the best match between the selected areas in the images. Experiments with natural multiple-view images show a feasibility of this approach.

Gibbs random field image models with multiple translation invariant pairwise pixel interactions show promise for segmenting piecewise-homogeneous image textures because they allow learning of both the interaction structure and strengths from a given training sample. We discuss whether the learnt parameters fit our expectations with respect to discriminating the given textures. Experiments with natural textures show that the learning tends to adapt the model more to peculiarities of the training sample than to general discriminating features of the textures. Low segmentation errors for just the training image or the image containing big texture patches used for learning may mislead in predicting the errors for the test images. Texture inhomogeneities or different region statistics in the training and test images are outside the scope of the models. Thus, the textures have to meet specific constraints for using such a supervised segmentation in practice.

Two MLEs of Gibbs potentials in Gibbs random field image models with translation invariant pixel interactions are discussed. The unconditional MLE presents the potentials in an implicit form of a system of stochastic equations to be solved by analytic and stochastic approximation. The conditional MLE, provided a training sample holds the least upper bound (top rank) in the Gibbs energy within the parent population, results in the explicit, to scaling factors, potentials. Then only these factors have to be found using analytic and stochastic approximation. Both MLEs are consistent, in a statistical sense, but may need large training samples for determining the potentials with a tolerable accuracy. For typical in practice small samples the conditional MLE suggests how to interpolate the potentials using the available training data.

Novel joint and conditional non-Markov Gibbs random field models are proposed for simulating and segmenting piecewise-uniform grayscale image textures under arbitrary linear transformations of their gray ranges. Structure of interactions is recovered using analytical initial estimates of Gibbs potentials. These estimates are refined then by a stochastic approximation. The models embed both image simulation and segmentation into the same Bayesian processing framework. Experiments with simulated and natural textures confirm an efficacy of the models.

Novel non-Markov Gibbs model of spatially uniform gray-scale textures extends the original Markov/Gibbs one, allowing for gray range shifts to linear gray range transformations. The models possess similar procedures of estimating structures and strengths of pixel interactions based on an analytical initial approximation of Gibbs potentials for a great many interactions. These initial estimates allow one to search for most characteristic interactions. Maximum likelihood estimates of the potentials for the chosen interaction structure are found by a stochastic approximation. This model involves, basically, only minor modifications in a stochastic relaxation used to simulate images. Experiments with natural textures are presented.

Joint Gibbs random field model with multiple pairwise pixel interactions is introduced to describe piecewise-uniform grayscale textures and their region maps. The model allows to deduce Gibbs conditional models of the images under a given region map for simulating and of the region maps under a given grayscale image for segmenting these textures. All the models possess similar procedures of parameter estimation and integrate both image simulation and segmentation into the same Bayesian framework. Experiments with collages of natural textures are presented.

Automatic reconstruction of 3D terrain models by a digital photogrammetric station "Delta", which is now under development in the Ukraine, is discussed. It is based on a previously proposed symmetric intensity-based dynamic programming technique. Basic features of the DPS "Delta" are briefly outlined experiments with stereo images of the Earth's surface are presented.

A Markov random field model with a Gibbs probability distribution (GPD) is proposed for describing particular classes of grayscale images which can be called spatially uniform stochastic textures. The model takes into account only multiple short- and long-range pairwise interactions between the gray levels in the pixels. An effective learning scheme is introduced to recover structure and strength of the interactions using maximal likelihood estimates of the potentials in the GPD as desired parameters. The scheme is based on an analytic initial approximation of the estimates and their subsequent refinement by a stochastic approximation. Experiments in modeling natural textures show the utility of the proposed model.

Methods to amplify and regularize the symmetric approach proposed before solving the ill-posed problem of the computational stereo vision are discussed. Under this approach epipolar profiles of a continuous optical surface are reconstructed from stereo images by using the dynamic programming (DP) implementation of a simple Bayesian MAP-decision which takes into account the symmetry of images, interdependent allowable distortions of the images, possible occlusions of surface parts, etc. Here we show that for this problem compound decisions can also be implemented by the same DP techniques. The regularization of MAP-decision in the binocular case and a scheme of symmetric trinocular stereo is also proposed. Some experimental results with the real images are presented.