We present a novel 3-D deformable model-based approach for accurate, robust, and automated tissue segmentation of brain MRI data of single as well as multiple magnetic resonance sequences. The main contribution of this study is that we employ an edge-based geodesic active contour for the segmentation task by integrating both image edge geometry and voxel statistical homogeneity into a novel hybrid geometric–statistical feature to regularize contour convergence and extract complex anatomical structures. We validate the accuracy of the segmentation results on simulated brain MRI scans of both single T1-weighted and multiple T1/T2/PD-weighted sequences. We also demonstrate the robustness of the proposed method when applied to clinical brain MRI scans. When compared to a current state-of-the-art region-based level-set segmentation formulation, our white matter and gray matter segmentation resulted in significantly higher accuracy levels with a mean improvement in Dice similarity indexes of 8.55% (p < 0.0001) and 10.18% (p < 0.0001), respectively.
3-D image segmentation; brain segmentation; deformable models; geodesic active contour
Accurate and efficient segmentation of the hippocampus from brain images is a challenging issue. Although experienced anatomic tracers can be reliable, manual segmentation is a time consuming process and may not be feasible for large-scale neuroimaging studies. In this paper, we compare an automated method, FreeSurfer (V4), with a published manual protocol on the determination of hippocampal boundaries from MRI scans, using data from an existing MCI/AD cohort. To perform the comparison, we develop an enhanced spherical harmonic processing framework to model and register these hippocampal traces. The framework treats the two hippocampi as a single geometric configuration and extracts the positional, orientation and shape variables in a multi-object setting. We apply this framework to register manual tracing and FreeSurfer results together and the two methods show stronger agreement on position and orientation than shape measures. Work is in progress to examine a refined FreeSurfer segmentation strategy and an improved agreement on shape features is expected.
Shape analysis; segmentation; registration; hippocampus
Clinical diagnosis and therapy for the lumbar disc herniation requires accurate vertebra segmentation. The complex anatomical structure and the degenerative deformations of the vertebrae makes its segmentation challenging.
An improved level set method, namely edge- and region-based level set method (ERBLS), is proposed for vertebra CT images segmentation. By considering the gradient information and local region characteristics of images, the proposed model can efficiently segment images with intensity inhomogeneity and blurry or discontinuous boundaries. To reduce the dependency on manual initialization in many active contour models and for an automatic segmentation, a simple initialization method for the level set function is built, which utilizes the Otsu threshold. In addition, the need of the costly re-initialization procedure is completely eliminated.
Experimental results on both synthetic and real images demonstrated that the proposed ERBLS model is very robust and efficient. Compared with the well-known local binary fitting (LBF) model, our method is much more computationally efficient and much less sensitive to the initial contour. The proposed method has also applied to 56 patient data sets and produced very promising results.
An improved level set method suitable for vertebra CT images segmentation is proposed. It has the flexibility of segmenting the vertebra CT images with blurry or discontinuous edges, internal inhomogeneity and no need of re-initialization.
Level set method; Image segmentation; Vertebra CT images
This paper presents an algorithm for segmenting left ventricular endocardial boundaries from RF ultrasound. Our method incorporates a computationally efficient linear predictor that exploits short-term spatio-temporal coherence in the RF data. Segmentation is achieved jointly using an independent identically distributed (i.i.d.) spatial model for RF intensity and a multiframe conditional model that relates neighboring frames in the image sequence. Segmentation using the RF data overcomes challenges due to image inhomogeneities often amplified in B-mode segmentation and provides geometric constraints for RF phase-based speckle tracking. The incorporation of multiple frames in the conditional model significantly increases the robustness and accuracy of the algorithm. Results are generated using between 2 and 5 frames of RF data for each segmentation and are validated by comparison with manual tracings and automated B-mode boundary detection using standard (Chan and Vese-based) level sets on echocardiographic images from 27 3D sequences acquired from 6 canine studies.
Ultrasound; Cardiac imaging; Segmentation; Radiofrequency signal
Accurate segmentation of neonatal brain MR images remains challenging mainly due to their poor spatial resolution, inverted contrast between white matter and gray matter, and high intensity inhomogeneity. Most existing methods for neonatal brain segmentation are atlas-based and voxel-wise. Although active contour/surface models with geometric information constraint have been successfully applied to adult brain segmentation, they are not fully explored in the neonatal image segmentation. In this paper, we propose a novel neonatal image segmentation method by combining local intensity information, atlas spatial prior, and cortical thickness constraint in a single level-set framework. Besides, we also provide a robust and reliable tissue surface initialization for the proposed method by using a convex optimization technique. Thus, tissue segmentation, as well as inner and outer cortical surface reconstruction, can be obtained simultaneously. The proposed method has been tested on a large neonatal dataset, and the validation on 10 neonatal brain images (with manual segmentations) shows very promising results.
Neonatal tissue segmentation; atlas-based segmentation; convex optimization; coupled level sets
Intensity inhomogeneities often occur in real-world images and may cause considerable difficulties in image segmentation. In order to overcome the difficulties caused by intensity inhomogeneities, we propose a region-based active contour model that draws upon intensity information in local regions at a controllable scale. A data fitting energy is defined in terms of a contour and two fitting functions that locally approximate the image intensities on the two sides of the contour. This energy is then incorporated into a variational level set formulation with a level set regularization term, from which a curve evolution equation is derived for energy minimization. Due to a kernel function in the data fitting term, intensity information in local regions is extracted to guide the motion of the contour, which thereby enables our model to cope with intensity inhomogeneity. In addition, the regularity of the level set function is intrinsically preserved by the level set regularization term to ensure accurate computation and avoids expensive reinitialization of the evolving level set function. Experimental results for synthetic and real images show desirable performances of our method.
Image segmentation; intensity inhomogeneity; level set method; region-scalable fitting energy; variational method
This paper describes an algorithm to extract adaptive and quality 3D meshes directly from volumetric imaging data. The extracted tetrahedral and hexahedral meshes are extensively used in the Finite Element Method (FEM). A top-down octree subdivision coupled with the dual contouring method is used to rapidly extract adaptive 3D finite element meshes with correct topology from volumetric imaging data. The edge contraction and smoothing methods are used to improve the mesh quality. The main contribution is extending the dual contouring method to crack-free interval volume 3D meshing with feature sensitive adaptation. Compared to other tetrahedral extraction methods from imaging data, our method generates adaptive and quality 3D meshes without introducing any hanging nodes. The algorithm has been successfully applied to constructing the geometric model of a biomolecule in finite element calculations.
adaptive and quality mesh; correct topology; feature sensitive adaptation; hanging node
Segmenting cell nuclei in microscopic images has become one of the most important routines in modern biological applications. With the vast amount of data, automatic localization, i.e. detection and segmentation, of cell nuclei is highly desirable compared to time-consuming manual processes. However, automated segmentation is challenging due to large intensity inhomogeneities in the cell nuclei and the background.
We present a new method for automated progressive localization of cell nuclei using data-adaptive models that can better handle the inhomogeneity problem. We perform localization in a three-stage approach: first identify all interest regions with contrast-enhanced salient region detection, then process the clusters to identify true cell nuclei with probability estimation via feature-distance profiles of reference regions, and finally refine the contours of detected regions with regional contrast-based graphical model. The proposed region-based progressive localization (RPL) method is evaluated on three different datasets, with the first two containing grayscale images, and the third one comprising of color images with cytoplasm in addition to cell nuclei. We demonstrate performance improvement over the state-of-the-art. For example, compared to the second best approach, on the first dataset, our method achieves 2.8 and 3.7 reduction in Hausdorff distance and false negatives; on the second dataset that has larger intensity inhomogeneity, our method achieves 5% increase in Dice coefficient and Rand index; on the third dataset, our method achieves 4% increase in object-level accuracy.
To tackle the intensity inhomogeneities in cell nuclei and background, a region-based progressive localization method is proposed for cell nuclei localization in fluorescence microscopy images. The RPL method is demonstrated highly effective on three different public datasets, with on average 3.5% and 7% improvement of region- and contour-based segmentation performance over the state-of-the-art.
A pleural effusion is a condition where there is a buildup of abnormal fluid within the pleural space. This paper presents an automated method to evaluate the severity of pleural effusion using regular chest CT images. First the lungs are segmented using region growing, mathematical morphology and anatomical knowledge. Then the visceral and parietal layers of the pleura are extracted based on anatomical landmarks, curve fitting and active contour models. Finally, the pleural space is segmented and the pleural effusion is quantified. Our method was tested on 15 chest CT studies. The automated segmentation is validated against manual tracing and radiologist’s qualitative grading. The Pearson correlation between computer evaluation and radiologist’s grading is 0.956 (P=10−7). The Dice coefficient between the automated and manual segmentation is 0.74±0.07, which is comparable to the variation between two different manual tracings.
Pleural Effusion; CAD; Segmentation
Extraction of the brain — i.e. cerebrum, cerebellum, and brain stem — from T1-weighted structural magnetic resonance images is an important initial step in neuroimage analysis. Although automatic algorithms are available, their inconsistent handling of the cortical mantle often requires manual interaction, thereby reducing their effectiveness. This paper presents a fully automated brain extraction algorithm that incorporates elastic registration, tissue segmentation, and morphological techniques which are combined by a watershed principle, while paying special attention to the preservation of the boundary between the gray matter and the cerebrospinal fluid. The approach was evaluated by comparison to a manual rater, and compared to several other leading algorithms on a publically available data set of brain images using the Dice coefficient and containment index as performance metrics. The qualitative and quantitative impact of this initial step on subsequent cortical surface generation is also presented. Our experiments demonstrate that our approach is quantitatively better than six other leading algorithms (with statistical significance on modern T1-weighted MR data). We also validated the robustness of the algorithm on a very large data set of over one thousand subjects, and showed that it can replace an experienced manual rater as preprocessing for a cortical surface extraction algorithm with statistically insignificant differences in cortical surface position.
Brain extraction; skull stripping; watershed principle; segmentation; medical image processing
Delineation of radiofrequency-ablation-induced coagulation (thermal lesion) boundaries is an important clinical problem that is not well addressed by conventional imaging modalities. Elastography, which produces images of the local strain after small, externally applied compressions, can be used for visualization of thermal coagulations. This paper presents an automated segmentation approach for thermal coagulations on 3-D elastographic data to obtain both area and volume information rapidly. The approach consists of a coarse-to-fine method for active contour initialization and a gradient vector flow, active contour model for deformable contour optimization with the help of prior knowledge of the geometry of general thermal coagulations. The performance of the algorithm has been shown to be comparable to manual delineation of coagulations on elastograms by medical physicists (r = 0.99 for volumes of 36 radiofrequency-induced coagulations). Furthermore, the automatic algorithm applied to elastograms yielded results that agreed with manual delineation of coagulations on pathology images (r = 0.96 for the same 36 lesions). This algorithm has also been successfully applied on in vivo elastograms.
Ablation; Active contour models; Breast tumor; Elasticity imaging; Elastography; Gradient vector flow; Image segmentation; Multiresolution; Snakes; Strain; 3-D ultrasound
This paper proposes a novel semiautomatic method to extract the pancreas from abdominal CT images. Traditional level set and region growing methods that request locating initial contour near the final boundary of object have problem of leakage to nearby tissues of pancreas region. The proposed method consists of a customized fast-marching level set method which generates an optimal initial pancreas region to solve the problem that the level set method is sensitive to the initial contour location and a modified distance regularized level set method which extracts accurate pancreas. The novelty in our method is the proper selection and combination of level set methods, furthermore an energy-decrement algorithm and an energy-tune algorithm are proposed to reduce the negative impact of bonding force caused by connected tissue whose intensity is similar with pancreas. As a result, our method overcomes the shortages of oversegmentation at weak boundary and can accurately extract pancreas from CT images. The proposed method is compared to other five state-of-the-art medical image segmentation methods based on a CT image dataset which contains abdominal images from 10 patients. The evaluated results demonstrate that our method outperforms other methods by achieving higher accuracy and making less false segmentation in pancreas extraction.
Performance of automated methods to isolate brain from nonbrain tissues in magnetic resonance (MR) structural images may be influenced by MR signal inhomogeneities, type of MR image set, regional anatomy, and age and diagnosis of subjects studied. The present study compared the performance of four methods: Brain Extraction Tool (BET; Smith : Hum Brain Mapp 17:143–155); 3dIntracranial (Ward  Milwaukee: Biophysics Research Institute, Medical College of Wisconsin; in AFNI); a Hybrid Watershed algorithm (HWA, Segonne et al.  Neuroimage 22:1060–1075; in FreeSurfer); and Brain Surface Extractor (BSE, Sandor and Leahy  IEEE Trans Med Imag 16:41–54; Shattuck et al.  Neuroimage 13:856 – 876) to manually stripped images. The methods were applied to uncorrected and bias-corrected datasets; Legacy and Contemporary T1-weighted image sets; and four diagnostic groups (depressed, Alzheimer’s, young and elderly control). To provide a criterion for outcome assessment, two experts manually stripped six sagittal sections for each dataset in locations where brain and nonbrain tissue are difficult to distinguish. Methods were compared on Jaccard similarity coefficients, Hausdorff distances, and an Expectation-Maximization algorithm. Methods tended to perform better on contemporary datasets; bias correction did not significantly improve method performance. Mesial sections were most difficult for all methods. Although AD image sets were most difficult to strip, HWA and BSE were more robust across diagnostic groups compared with 3dIntracranial and BET. With respect to specificity, BSE tended to perform best across all groups, whereas HWA was more sensitive than other methods. The results of this study may direct users towards a method appropriate to their T1-weighted datasets and improve the efficiency of processing for large, multisite neuroimaging studies.
brain; MRI; Alzheimer’s disease; aging; image processing; statistics
We present a method for semiautomatic segmentation of brain
structures such as thalamus from MRI images based on the concept
of geometric surface flow. Given an MRI image, the user can
interactively initialize a seed model within region of interest.
The model will then start to evolve by incorporating both boundary
and region information following the principle of variational
analysis. The deformation will stop when an equilibrium state is
achieved. To overcome the low contrast of the original image data,
a nonparametric kernel-based method is applied to simultaneously
update the interior probability distribution during the model
evolution. Our experiments on both 2D and 3D image data
demonstrate that the new method is robust to image noise and
inhomogeneity and will not leak from spurious edge gaps.
To provide a tool for quantifying the effects of retinitis pigmentosa (RP) seen on spectral domain optical coherence tomography images, an automated layer segmentation algorithm was developed. This algorithm, based on dual-gradient information and a shortest path search strategy, delineates the inner limiting membrane and three outer retinal boundaries in optical coherence tomography images from RP patients. In addition, an automated inner segment (IS)/outer segment (OS) contour detection method based on the segmentation results is proposed to quantify the locus of points at which the OS thickness goes to zero in a 3D volume scan. The segmentation algorithm and the IS/OS contour were validated with manual segmentation data. The segmentation and IS/OS contour results on repeated measures showed good within-day repeatability, while the results on data acquired on average 22.5 months afterward demonstrated a possible means to follow disease progression. In particular, the automatically generated IS/OS contour provided a possible objective structural marker for RP progression.
(100.0100) Image processing; (170.4470) Ophthalmology; (170.4500) Optical coherence tomography
This paper presents the boundary detection of atrium and ventricle in echocardiographic images. In case of mitral regurgitation, atrium and ventricle may get dilated. To examine this, doctors draw the boundary manually. Here the aim of this paper is to evolve the automatic boundary detection for carrying out segmentation of echocardiography images. Active contour method is selected for this purpose. There is an enhancement of Chan–Vese paper on active contours without edges. Our algorithm is based on Chan–Vese paper active contours without edges, but it is much faster than Chan–Vese model. Here we have developed a method by which it is possible to detect much faster the echocardiographic boundaries. The method is based on the region information of an image. The region-based force provides a global segmentation with variational flow robust to noise. Implementation is based on level set theory so it easy to deal with topological changes. In this paper, Newton–Raphson method is used which makes possible the fast boundary detection.
Echocardiographic images; Mitral regurgitation; Atrium; Ventricle; Active contours; Level set theory; Topological
Whole brain extraction is an important pre-processing step in neuro-image analysis. Manual or semi-automated brain delineations are labour-intensive and thus not desirable in large studies, meaning that automated techniques are preferable. The accuracy and robustness of automated methods are crucial because human expertise may be required to correct any sub-optimal results, which can be very time consuming. We compared the accuracy of four automated brain extraction methods: Brain Extraction Tool (BET), Brain Surface Extractor (BSE), Hybrid Watershed Algorithm (HWA) and a Multi-Atlas Propagation and Segmentation (MAPS) technique we have previously developed for hippocampal segmentation. The four methods were applied to extract whole brains from 682 1.5T and 157 3T T1-weighted MR baseline images from the Alzheimer’s Disease Neuroimaging Initiative database. Semi-automated brain segmentations with manual editing and checking were used as the gold-standard to compare with the results. The median Jaccard index of MAPS was higher than HWA, BET and BSE in 1.5T and 3T scans (p < 0.05, all tests), and the 1st-99th centile range of the Jaccard index of MAPS was smaller than HWA, BET and BSE in 1.5T and 3T scans (p < 0.05, all tests). HWA and MAPS were found to be best at including all brain tissues (median false negative rate ≤ 0.010% for 1.5T scans and ≤ 0.019% for 3T scans, both methods). The median Jaccard index of MAPS were similar in both 1.5T and 3T scans, whereas those of BET, BSE and HWA were higher in 1.5T scans than 3T scans (p < 0.05, all tests). We found that the diagnostic group had a small effect on the median Jaccard index of all four methods. In conclusion, MAPS had relatively high accuracy and low variability compared to HWA, BET and BSE in MR scans with and without atrophy.
Automated brain extraction; skull-stripping; segmentation; MAPS; BET; BSE; HWA
Snake or active contours are extensively used in computer vision and medical image processing applications, and particularly to locate object boundaries. Yet problems associated with initialization and the poor convergence to boundary concavities have limited their utility. The new method of external force for active contours, which is called gradient vector flow (GVF), was recently introduced to address the problems.
This paper presents an automatic initialization value of the snake algorithm for the segmentation of the chest wall. Snake algorithms are required to have manually drawn initial contours, so this needs automatic initialization. In this paper, our proposed algorithm is the mean shape for automatic initialization in the GVF.
The GVF is calculated as a diffusion of the gradient vectors of a gray-level or binary edge map derived from the medical images. Finally, the mean shape coordinates are used to automatic initialize thepoint of the snake. The proposed algorithm is composed of three phases: the landmark phase, the procrustes shape distance metric phase and aligning a set of shapes phase. The experiments showed the good performance of our algorithm in segmenting the chest wall by chest computed tomography.
An error analysis for the active contours results on simulated test medical images is also presented. We showed that GVF has a large capture range and it is able to move a snake into boundary concavities. Therefore, the suggested algorithm is better than the traditional potential forces of image segmentation.
Active Contour Model; Automatic Initialization; Mean Shape; Gradient Vector Flow; Computed Tomography
Purpose. To develop a technique to automate landmark selection for point-based interpolating transformations for nonlinear medical image registration. Materials and Methods. Interpolating transformations were calculated from homologous point landmarks on the source (image to be transformed) and target (reference image). Point landmarks are placed at regular intervals on contours of anatomical features, and their positions are optimized along the contour surface by a function composed of curvature similarity and displacements of the homologous landmarks. The method was evaluated in two cases (n = 5 each). In one, MRI was registered to histological sections; in the second, geometric distortions in EPI MRI were corrected. Normalized mutual information and target registration error were calculated to compare the registration accuracy of the automatically and manually generated landmarks. Results. Statistical analyses demonstrated significant improvement (P < 0.05) in registration accuracy by landmark optimization in most data sets and trends towards improvement (P < 0.1) in others as compared to manual landmark selection.
We presented and evaluated two deformable model-based approaches, region plus contour deformation (RPCD), and level sets to extract metastatic cervical nodal lesions from pretreatment T2-weighted magnetic resonance images. The RPCD method first uses a region deformation to achieve a rough boundary of the target node from a manually drawn initial contour, based on signal statistics. After that, an active contour deformation is employed to drive the rough boundary to the real node–normal tissue interface. Differently, the level sets move a manually drawn initial contour toward the desired nodal boundary under the control of the evolvement speed function, which is influenced by image gradient force. The two methods were tested by extracting 33 metastatic cervical nodes from 18 nasopharyngeal carcinoma patients. Experiments on a basis of pixel matching to reference standard showed that RPCD and level sets achieved averaged percentage matching at 82–84% and 87–88%, respectively. In addition, both methods had significantly lower interoperator variances than the manual tracing method. It was suggested these two methods could be useful tools for the evaluation of metastatic nodal volume as an indicator of classification and treatment response, or be alternatives for the delineation of metastatic nodal lesions in radiation treatment planning.
Object extraction; magnetic resonance imaging; deformable model; level sets; nasopharyngeal carcinoma; metastatic cervical nodes
Rationale and Objectives
Segmentation of anatomic structures from magnetic resonance brain scans can be a daunting task because of large inhomogeneities in image intensities across an image and possible lack of precisely defined shape boundaries for certain anatomical structures. One approach that has been quite popular in the recent past for these situations is the atlas-based segmentation. The atlas, once constructed, can be used as a template and can be registered nonrigidly to the image being segmented thereby achieving the desired segmentation. The goal of our study is to segment these structures with a registration assisted image segmentation technique.
Materials and Methods
We present a novel variational formulation of the registration assisted image segmentation problem which leads to solving a coupled set of nonlinear Partial Differential Equations (PDEs) that are solved using efficient numeric schemes. Our work is a departure from earlier methods in that we can simultaneously register and segment in three dimensions and easily cope with situations where the source (atlas) and target images have very distinct intensity distributions.
We present several examples (20) on synthetic and (3) real data sets along with quantitative accuracy estimates of the registration in the synthetic data case.
The proposed atlas-based segmentation technique is capable of simultaneously achieve the nonrigid registration and the segmentation; unlike previous methods of solution for this problem, our algorithm can accommodate for image pairs having very distinct intensity distributions.
Image segmentation; image registration; cumulative residual entropy
The segmentation and detection of various types of nodules in a Computer-aided detection
(CAD) system present various challenges, especially when (1) the nodule is connected to a vessel
and they have very similar intensities; (2) the nodule with ground-glass opacity (GGO)
characteristic possesses typical weak edges and intensity inhomogeneity, and hence it is difficult
to define the boundaries. Traditional segmentation methods may cause problems of boundary
leakage and “weak” local minima. This paper deals with the above mentioned problems. An
improved detection method which combines a fuzzy integrated active contour model
(FIACM)-based segmentation method, a segmentation refinement method based on Parametric
Mixture Model (PMM) of juxta-vascular nodules, and a knowledge-based C-SVM
(Cost-sensitive Support Vector Machines) classifier, is proposed for detecting various types of
pulmonary nodules in computerized tomography (CT) images. Our approach has several novel
aspects: (1) In the proposed FIACM model, edge and local region information is incorporated.
The fuzzy energy is used as the motivation power for the evolution of the active contour. (2) A
hybrid PMM Model of juxta-vascular nodules combining appearance and geometric
information is constructed for segmentation refinement of juxta-vascular nodules. Experimental
results of detection for pulmonary nodules show desirable performances of the proposed
We present a new segmentation approach that combines the strengths of label fusion and spectral clustering. The result is an atlas-based segmentation method guided by contour and texture cues in the test image. This offers advantages for datasets with high variability, making the segmentation less prone to registration errors. We achieve the integration by letting the weights of the graph Laplacian depend on image data, as well as atlas-based label priors. The extracted contours are converted to regions, arranged in a hierarchy depending on the strength of the separating boundary. Finally, we construct the segmentation by a region-wise, instead of voxel-wise, voting, increasing the robustness. Our experiments on cardiac MRI show a clear improvement over majority voting and intensity-weighted label fusion.
Segmentation of the left ventricle is important in the assessment of cardiac functional parameters. Manual segmentation of cardiac cine MR images for acquiring these parameters is time-consuming. Accuracy and automation are the two important criteria in improving cardiac image segmentation methods. In this paper, we present a comprehensive approach to segment the left ventricle from short axis cine cardiac MR images automatically. Our method incorporates a number of image processing and analysis techniques including thresholding, edge detection, mathematical morphology, and image filtering to build an efficient process flow. This process flow makes use of various features in cardiac MR images to achieve high accurate segmentation results. Our method was tested on 45 clinical short axis cine cardiac images and the results are compared with manual delineated ground truth (average perpendicular distance of contours near 2 mm and mean myocardium mass overlapping over 90%). This approach provides cardiac radiologists a practical method for an accurate segmentation of the left ventricle.
Image segmentation; cardiac imaging; image analysis; left ventricle
Active contours are very popular tools for video tracking and image segmentation. Parameterized contours are used due to their fast evolution and have become the method of choice in the Sobolev context. Unfortunately, these contours are not easily adaptable to topological changes, and they may sometimes develop undesirable loops, resulting in erroneous results. To solve such topological problems, one needs an algorithm for contour self-crossing detection. We propose a simple methodology via simple techniques from differential topology. The detection is accomplished by inspecting the total net change of a given contour’s angle, without point sorting and plane sweeping. We discuss the efficient implementation of the algorithm. We also provide algorithms for locating crossings by angle considerations and by plotting the four-connected lines between the discrete contour points. The proposed algorithms can be added to any parametric active-contour model. We show examples of successful tracking in real-world video sequences by Sobolev active contours and the proposed algorithms and provide ideas for further research.
Active contours; image segmentation; self-crossing; snakes; tracking