Publications by Year: 2006

2006
MacFall JR, Taylor WD, Rex DE, Pieper S, Payne ME, McQuoid DR, Steffens DC, Kikinis R, Toga AW, Krishnan RRK. Lobar distribution of lesion volumes in late-life depression: the Biomedical Informatics Research Network (BIRN). Neuropsychopharmacology. 2006;31 (7) :1500-7.Abstract
White matter hyperintense lesions on T2-weighted images are associated with late-life depression. Little work has been carried out examining differences in lesion location between elderly individuals with and without depression. In contrast to previous studies examining total brain white matter lesion volume, this study examined lobar differences in white matter lesion volumes derived from brain magnetic resonance imaging. This study examined 49 subjects with a DSM-IV diagnosis of major depression and 50 comparison subjects without depression. All participants were age 60 years or older. White matter lesion volumes were measured in each hemisphere using a semiautomated segmentation process and localized to lobar regions using a lobar atlas created for this sample using the imaging tools provided by the Biomedical Informatics Research Network (BIRN). The lobar lesion volumes were compared against depression status. After controlling for age and hypertension, subjects with depression exhibited significantly greater total white matter lesion volume in both hemispheres and in both frontal lobes than did control subjects. Although a similar trend was observed in the parietal lobes, the difference did not reach a level of statistical significance. Models of the temporal and occipital lobes were not statistically significant. Older individuals with depression have greater white matter disease than healthy controls, predominantly in the frontal lobes. These changes are thought to disrupt neural circuits involved in mood regulation, thus increasing the risk of developing depression.
Pohl KM, Fisher J, Grimson EWL, Kikinis R, Wells III WM. A Bayesian Model for Joint Segmentation and Registration. Neuroimage. 2006;31 (1) :228-39.Abstract

A statistical model is presented that combines the registration of an atlas with the segmentation of magnetic resonance images. We use an Expectation Maximization-based algorithm to find a solution within the model, which simultaneously estimates image artifacts, anatomical labelmaps, and a structure-dependent hierarchical mapping from the atlas to the image space. The algorithm produces segmentations for brain tissues as well as their substructures. We demonstrate the approach on a set of 22 magnetic resonance images. On this set of images, the new approach performs significantly better than similar methods which sequentially apply registration and segmentation.

Guttmann CRG, Meier DS, Holland CM. Can MRI reveal phenotypes of multiple sclerosis?. Magn Reson Imaging. 2006;24 (4) :475-81.Abstract
The multicontrast capability of magnetic resonance imaging (MRI) is discussed in its role in the search for phenotypes of multiple sclerosis (MS). Aspects of MRI specificity, putative markers for pathogenetic components of disease and issues of spatial and temporal distribution are discussed. While particular reference is made to MS, the concepts apply to common pathological features of many neurologic diseases and to neurodegenerative disease in general. The assessment and dissociation of disease activity and disease severity, as well as the combination of varied metrics for the purposes of inferential and predictive disease modeling, are explored with respect to biomarkers and clinical outcomes. By virtue of its noninvasive nature and multicontrast capabilities depicting multiple facets of MS pathology, MRI lends itself to the systematic search of pathogenetically distinct subtypes of MS in large populations of patients. In conjunction with clinical, immunological, serological and genetic information, clusters of MS patients with distinct clinical prognosis and diverse response profiles to available and future treatments may be identified.
Learned-Miller EG. Data driven image models through continuous joint alignment. IEEE Trans Pattern Anal Mach Intell. 2006;28 (2) :236-50.Abstract
This paper presents a family of techniques that we call congealing for modeling image classes from data. The idea is to start with a set of images and make them appear as similar as possible by removing variability along the known axes of variation. This technique can be used to eliminate "nuisance" variables such as affine deformations from handwritten digits or unwanted bias fields from magnetic resonance images. In addition to separating and modeling the latent images-i.e., the images without the nuisance variables-we can model the nuisance variables themselves, leading to factorized generative image models. When nuisance variable distributions are shared between classes, one can share the knowledge learned in one task with another task, leading to efficient learning. We demonstrate this process by building a handwritten digit classifier from just a single example of each class. In addition to applications in handwritten character recognition, we describe in detail the application of bias removal from magnetic resonance images. Unlike previous methods, we use a separate, nonparametric model for the intensity values at each pixel. This allows us to leverage the data from the MR images of different patients to remove bias from each other. Only very weak assumptions are made about the distributions of intensity values in the images. In addition to the digit and MR applications, we discuss a number of other uses of congealing and describe experiments about the robustness and consistency of the method.
Michailovich OV, Tannenbaum A. Despeckling of medical ultrasound images. IEEE Trans Ultrason Ferroelectr Freq Control. 2006;53 (1) :64-78.Abstract
Speckle noise is an inherent property of medical ultrasound imaging, and it generally tends to reduce the image resolution and contrast, thereby reducing the diagnostic value of this imaging modality. As a result, speckle noise reduction is an important prerequisite, whenever ultrasound imaging is used for tissue characterization. Among the many methods that have been proposed to perform this task, there exists a class of approaches that use a multiplicative model of speckled image formation and take advantage of the logarithmical transformation in order to convert multiplicative speckle noise into additive noise. The common assumption made in a dominant number of such studies is that the samples of the additive noise are mutually uncorrelated and obey a Gaussian distribution. The present study shows conceptually and experimentally that this assumption is oversimplified and unnatural. Moreover, it may lead to inadequate performance of the speckle reduction methods. The study introduces a simple preprocessing procedure, which modifies the acquired radio-frequency images (without affecting the anatomical information they contain), so that the noise in the log-transformation domain becomes very close in its behavior to a white Gaussian noise. As a result, the preprocessing allows filtering methods based on assuming the noise to be white and Gaussian, to perform in nearly optimal conditions. The study evaluates performances of three different, nonlinear filters--wavelet denoising, total variation filtering, and anisotropic diffusion--and demonstrates that, in all these cases, the proposed preprocessing significantly improves the quality of resultant images. Our numerical tests include a series of computer-simulated and in vivo experiments.
Talos I-F, Mian AZ, Zou KH, Hsu L, Goldberg-Zimring D, Haker S, Bhagwat JG, Mulkern RV. Magnetic resonance and the human brain: anatomy, function and metabolism. Cell Mol Life Sci. 2006;63 (10) :1106-24.Abstract
The introduction and development, over the last three decades, of magnetic resonance (MR) imaging and MR spectroscopy technology for in vivo studies of the human brain represents a truly remarkable achievement, with enormous scientific and clinical ramifications. These effectively non-invasive techniques allow for studies of the anatomy, the function and the metabolism of the living human brain. They have allowed for new understandings of how the healthy brain works and have provided insights into the mechanisms underlying multiple disease processes which affect the brain. Different MR techniques have been developed for studying anatomy, function and metabolism. The primary focus of this review is to describe these different methodologies and to briefly review how they are being employed to more fully appreciate the intricacies associated with the organ, which most distinctly differentiates the human species from the other animal forms on earth.
Angenent S, Pichon E, Tannenbaum A. MATHEMATICAL METHODS IN MEDICAL IMAGE PROCESSING. Bull New Ser Am Math Soc. 2006;43 :365-396.Abstract
In this paper, we describe some central mathematical problems in medical imaging. The subject has been undergoing rapid changes driven by better hardware and software. Much of the software is based on novel methods utilizing geometric partial differential equations in conjunction with standard signal/image processing techniques as well as computer graphics facilitating man/machine interactions. As part of this enterprise, researchers have been trying to base biomedical engineering principles on rigorous mathematical foundations for the development of software methods to be integrated into complete therapy delivery systems. These systems support the more effective delivery of many image-guided procedures such as radiation therapy, biopsy, and minimally invasive surgery. We will show how mathematics may impact some of the main problems in this area, including image enhancement, registration, and segmentation.
Magnotta VA, Friedman L. Measurement of Signal-to-Noise and Contrast-to-Noise in the fBIRN Multicenter Imaging Study. J Digit Imaging. 2006;19 (2) :140-7.Abstract
The ability to analyze and merge data across sites, vendors, and field strengths depends on one's ability to acquire images with the same image quality including image smoothness, signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR). SNR can be used to compare different magnetic resonance scanners as a measure of comparability between the systems. This study looks at the SNR and CNR ratios in structural fast spin-echo T2-weighted scans acquired in five individuals across ten sites that are part of Functional Imaging Research of Schizophrenia Testbed Biomedical Informatics Research Network (fBIRN). Different manufacturers, field strengths, gradient coils, and RF coils were used at these sites. The SNR of gray matter was fairly uniform (41.3-43.3) across scanners at 1.5 T. The higher field scanners produced images with significantly higher SNR values (44.5-108.7 at 3 T and 50.8 at 4 T). Similar results were obtained for CNR measurements between gray/white matter at 1.5 T (9.5-10.2), again increasing at higher fields (10.1-28.9 at 3 T and 10.9 at 4 T).
Dimaio SP, Kacher DF, Ellis RE, Fichtinger G, Hata N, Zientara GP, Panych LP, Kikinis R, Jolesz FA. Needle Artifact Localization in 3T MR Images. Stud Health Technol Inform. 2006;119 :120-5.Abstract

This work explores an image-based approach for localizing needles during MRI-guided interventions, for the purpose of tracking and navigation. Susceptibility artifacts for several needles of varying thickness were imaged, in phantoms, using a 3 tesla MRI system, under a variety of conditions. The relationship between the true needle positions and the locations of artifacts within the images, determined both by manual and automatic segmentation methods, have been quantified and are presented here.

Dambreville S, Rathi Y, Tannenbaum A. Shape-Based Approach to Robust Image Segmentation using Kernel PCA. Proc IEEE Comput Soc Conf Comput Vis Pattern Recognit. 2006 :977-984.Abstract
Segmentation involves separating an object from the background. In this work, we propose a novel segmentation method combining image information with prior shape knowledge, within the level-set framework. Following the work of Leventon et al., we revisit the use of principal component analysis (PCA) to introduce prior knowledge about shapes in a more robust manner. To this end, we utilize Kernel PCA and show that this method of learning shapes outperforms linear PCA, by allowing only shapes that are close enough to the training data. In the proposed segmentation algorithm, shape knowledge and image information are encoded into two energy functionals entirely described in terms of shapes. This consistent description allows to fully take advantage of the Kernel PCA methodology and leads to promising segmentation results. In particular, our shape-driven segmentation technique allows for the simultaneous encoding of multiple types of shapes, and offers a convincing level of robustness with respect to noise, clutter, partial occlusions, or smearing.
Talos I-F, Zou KH, Ohno-Machado L, Bhagwat JG, Kikinis R, Black PM, Jolesz FA. Supratentorial low-grade glioma resectability: statistical predictive analysis based on anatomic MR features and tumor characteristics. Radiology. 2006;239 (2) :506-13.Abstract
PURPOSE: To retrospectively assess the main variables that affect the complete magnetic resonance (MR) imaging-guided resection of supratentorial low-grade gliomas. MATERIALS AND METHODS: Institutional review board approval was obtained for this retrospective HIPAA-compliant study, with the requirement for informed consent waived. Data from 101 patients (61 men, 40 women; mean age, 39 years; age range, 18-72 years) who had nonenhancing supratentorial mass lesions that were histopathologically diagnosed as low-grade (World Health Organization grade II) gliomas and consecutively underwent surgery with intraoperative MR imaging guidance were analyzed. There were 21 low-grade astrocytomas, 64 oligodendrogliomas, and 16 mixed oligoastrocytomas. Initial and residual tumor volumes were measured on intraoperative T2-weighted MR images and three-dimensional spoiled gradient-echo MR images. The anatomic relationships between the tumor and eloquent cortical and/or subcortical regions and the influence of these relationships on the extent of resection were analyzed on the basis of preoperative MR imaging findings. Summary measures, univariate Fisher exact test and t test, and multivariate logistic regression analyses were performed. RESULTS: Tumor volume ranged from 2.7-231.0 mL. Univariate analyses revealed the following tumor characteristics to be significant predictive variables of incomplete tumor resection: diffuse tumor margin on T2-weighted MR images, oligodendroglioma or oligoastrocytoma histopathologic type, and large tumor volume (P < .05 for all). Tumor involvement of the following structures was associated with incomplete resection: corpus callosum, corticospinal tract, insular lobe, middle cerebral artery, motor cortex, optic radiation, visual cortex, and basal ganglia (P < .05 for all). Multivariate analyses revealed that incomplete tumor resection was due to tumor involvement of the corticospinal tract (P < .01), large tumor volume (P < .01), and oligodendroglioma histopathologic type (P = .02). CONCLUSION: The main variables associated with incomplete tumor resection in 101 patients were identified by using statistical predictive analyses.
Archip N, Rohling R, Dessenne V, Erard P-J, Nolte LP. Anatomical structure modeling from medical images. Comput Methods Programs Biomed. 2006;82 (3) :203-15.Abstract
Some clinical applications, such as surgical planning, require volumetric models of anatomical structures represented as a set of tetrahedra. A practical method of constructing anatomical models from medical images is presented. The method starts with a set of contours segmented from the medical images by a clinician and produces a model that has high fidelity with the contours. Unlike most modeling methods, the contours are not restricted to lie on parallel planes. The main steps are a 3D Delaunay tetrahedralization, culling of non-object tetrahedra, and refinement of the tetrahedral mesh. The result is a high-quality set of tetrahedra whose surface points are guaranteed to match the original contours. The key is to use the distance map and bit volume structures that were created along with the contours. The method is demonstrated on computed tomography, MRI and 3D ultrasound data. Models of 170,000 tetrahedra are constructed on a standard workstation in approximately 10s. A comparison with related methods is also provided.
Wu Y, Warfield SK, Tan LI, Wells WM, Meier DS, van Schijndel RA, Barkhof F, Guttmann CRG. Automated segmentation of multiple sclerosis lesion subtypes with multichannel MRI. Neuroimage. 2006;32 (3) :1205-15.Abstract
PURPOSE: To automatically segment multiple sclerosis (MS) lesions into three subtypes (i.e., enhancing lesions, T1 "black holes", T2 hyperintense lesions). MATERIALS AND METHODS: Proton density-, T2- and contrast-enhanced T1-weighted brain images of 12 MR scans were pre-processed through intracranial cavity (IC) extraction, inhomogeneity correction and intensity normalization. Intensity-based statistical k-nearest neighbor (k-NN) classification was combined with template-driven segmentation and partial volume artifact correction (TDS+) for segmentation of MS lesions subtypes and brain tissue compartments. Operator-supervised tissue sampling and parameter calibration were performed on 2 randomly selected scans and were applied automatically to the remaining 10 scans. Results from this three-channel TDS+ (3ch-TDS+) were compared to those from a previously validated two-channel TDS+ (2ch-TDS+) method. The results of both the 3ch-TDS+ and 2ch-TDS+ were also compared to manual segmentation performed by experts. RESULTS: Intra-class correlation coefficients (ICC) of 3ch-TDS+ for all three subtypes of lesions were higher (ICC between 0.95 and 0.96) than that of 2ch-TDS+ for T2 lesions (ICC = 0.82). The 3ch-TDS+ also identified the three lesion subtypes with high specificity (98.7-99.9%) and accuracy (98.5-99.9%). Sensitivity of 3ch-TDS+ for T2 lesions was 16% higher than with 2ch-TDS+. Enhancing lesions were segmented with the best sensitivity (81.9%). "Black holes" were segmented with the least sensitivity (62.3%). CONCLUSION: 3ch-TDS+ is a promising method for automated segmentation of MS lesion subtypes.
Friman O, Farnebäck G, Westin C-F. A Bayesian approach for stochastic white matter tractography. IEEE Trans Med Imaging. 2006;25 (8) :965-78.Abstract
White matter fiber bundles in the human brain can be located by tracing the local water diffusion in diffusion weighted magnetic resonance imaging (MRI) images. In this paper, a novel Bayesian modeling approach for white matter tractography is presented. The uncertainty associated with estimated white matter fiber paths is investigated, and a method for calculating the probability of a connection between two areas in the brain is introduced. The main merits of the presented methodology are its simple implementation and its ability to handle noise in a theoretically justified way. Theory for estimating global connectivity is also presented, as well as a theorem that facilitates the estimation of the parameters in a constrained tensor model of the local water diffusion profile.
Szymczak A, Stillman A, Tannenbaum A, Mischaikow K. Coronary vessel trees from 3D imagery: a topological approach. Med Image Anal. 2006;10 (4) :548-59.Abstract
We propose a simple method for reconstructing vascular trees from 3D images. Our algorithm extracts persistent maxima of the intensity on all axis-aligned 2D slices of the input image. The maxima concentrate along 1D intensity ridges, in particular along blood vessels. We build a forest connecting the persistent maxima with short edges. The forest tends to approximate the blood vessels present in the image, but also contains numerous spurious features and often fails to connect segments belonging to one vessel in low contrast areas. We improve the forest by applying simple geometric filters that trim short branches, fill gaps in blood vessels and remove spurious branches from the vascular tree to be extracted. Experiments show that our technique can be applied to extract coronary trees from heart CT scans.
O'Donnell LJ, Kubicki M, Shenton ME, Dreusicke MH, Grimson WEL, Westin C-F. A Method for Clustering White Matter Fiber Tracts. AJNR Am J Neuroradiol. 2006;27 (5) :1032-6.Abstract

BACKGROUND/PURPOSE: Despite its potential for visualizing white matter fiber tracts in vivo, diffusion tensor tractography has found only limited applications in clinical research in which specific anatomic connections between distant regions need to be evaluated. We introduce a robust method for fiber clustering that guides the separation of anatomically distinct fiber tracts and enables further estimation of anatomic connectivity between distant brain regions. METHODS: Line scanning diffusion tensor images (LSDTI) were acquired on a 1.5T magnet. Regions of interest for several anatomically distinct fiber tracts were manually drawn; then, white matter tractography was performed by using the Runge-Kutta method to interpolate paths (fiber traces) following the major directions of diffusion, in which traces were seeded only within the defined regions of interest. Next, a fully automatic procedure was applied to fiber traces, grouping them according to a pairwise similarity function that takes into account the shapes of the fibers and their spatial locations. RESULTS: We demonstrated the ability of the clustering algorithm to separate several fiber tracts which are otherwise difficult to define (left and right fornix, uncinate fasciculus and inferior occipitofrontal fasciculus, and corpus callosum fibers). CONCLUSION: This method successfully delineates fiber tracts that can be further analyzed for clinical research purposes. Hypotheses regarding specific fiber connections and their abnormalities in various neuropsychiatric disorders can now be tested.

Meier DS, Guttmann CRG. MRI time series modeling of MS lesion development. Neuroimage. 2006;32 (2) :531-7.Abstract
A mathematical model was applied to new lesion formation in multiple sclerosis, as apparent on frequent T2-weighted MRI. The pathophysiologically motivated two-process model comprises two opposing nonlinear self-limiting processes, intended to represent degenerative and reparatory processes, respectively, investigating T2 activity from a dynamic/temporal rather than a spatial/static perspective. Parametric maps were obtained from the model to characterize the MRI dynamics of lesion development, answering the questions of how long new T2 lesion activity persists, how much residual damage/hyperintensity remains and how the T2 dynamics compare to those of contrast-enhancing MRI indicating active inflammation. 997 MRI examinations were analyzed, acquired weekly to monthly from 45 patients over a 1-year period. The model was applied to all pixels within 332 new lesions, capturing the time profiles with excellent fidelity (r = 0.89 +/- 0.03 average correlation between model and image data). From this modeling perspective, the observed dynamics in new T2 lesions are in agreement with two opposing processes of longitudinal intensity change, such as inflammation and degeneration versus resorbtion and repair. On average, about one third of a new lesion consisted of transient signal change with little or no residual hyperintensity and activity of 10 weeks or less. Global lesion burden as MRI surrogate of disease activity may therefore be confounded by large amounts of transient hyperintensity. T2 activity also persisted significantly beyond the period of contrast enhancement, thereby defining MRI sensitivity toward a subacute phase of lesion development beyond blood-brain barrier patency. Concentric patterns of dynamic properties within a lesion were observed, consistent with concentric histological appearance of resulting MS plaques.
Shah DK, Guinane C, August P, Austin NC, Woodward LJ, Thompson DK, Warfield SK, Clemett R, Inder TE. Reduced occipital regional volumes at term predict impaired visual function in early childhood in very low birth weight infants. Invest Ophthalmol Vis Sci. 2006;47 (8) :3366-73.Abstract
PURPOSE: Premature infants are at increased risk of impaired visual performance related to both cortical and subcortical pathways for oculomotor control. The hypothesis for the current study was that preterm infants with impaired saccades, smooth pursuit, and binocular eye alignment at age 2 years would have smaller occipital brain volumes at term equivalent, as measured by volumetric magnetic resonance (MR) techniques, than would preterm infants without such abnormalities. METHODS: Study participants consisted of 68 infants from a representative regional cohort of 100 preterm infants born between 23 and 33 weeks' gestation. At term equivalent, all infants underwent MR imaging, and the images were coregistered, tissue segmented into five cerebral tissue subtypes, and further subdivided into eight regions for each hemisphere. At 2 years corrected, all infants completed a comprehensive orthoptic evaluation performed by a single examiner. RESULTS: Twenty-four (35%) of the 68 infants had abnormal oculomotor control at 2 years, including abnormalities in saccadic movements (n = 7), smooth pursuit (n = 14), or strabismus (n = 9, four with esotropia and five with exotropia). When compared with preterm infants without visuomotor impairment, these infants had significantly smaller inferior occipital region brain tissue volumes bilaterally (n = 24 vs. n = 44; total tissue, mean +/- SD, left, 37.9 +/- 7.4 cm(3) vs. 43.7 +/- 7.4 cm(3); mean difference [95% CI] -5.7 [-9.4 to -2.0] cm(3), P = 0.003; right, 36.8 +/- 7.1 cm(3) vs. 41.4 +/- 6.2 cm(3), mean difference -4.6 [-7.9 to -1.3] cm(3), P = 0.007). This difference remained significant after adjusting for intracranial volume (ICV; left, mean difference -3.5 [-6.7 to -0.2] cm(3), P = 0.04; right, mean difference -2.4 [-5.2 to -0.4] cm(3), P = 0.09). Within this region, the cortical gray matter volume was the most significantly reduced (left, 20.4 +/- 6.2 cm(3) vs. 25.4 +/- 5.6 cm(3), mean difference -3.1 [-5.7 to -0.5] cm(3), P = 0.02; right 21.0 +/- 5.4 cm(3) vs. 24.9 +/- 5.0 cm(3), mean difference -2.2 [-4.4 to 0.0] cm(3), P = 0.05, ICV adjusted). Abnormalities in saccadic eye movements accounted for the largest effect on inferior occipital regional brain volumes (left side, P = 0.02). CONCLUSIONS: Volumetric MR imaging techniques demonstrated an overall reduction in the inferior occipital regional brain volumes in preterm infants at term corrected who later exhibit impaired oculomotor function control. These findings assist in understanding the neuroanatomic correlates of later visual difficulties experienced by infants born prematurely.
Mewes AUJ, Hüppi PS, Als H, Rybicki FJ, Inder TE, McAnulty GB, Mulkern RV, Robertson RL, Rivkin MJ, Warfield SK. Regional brain development in serial magnetic resonance imaging of low-risk preterm infants. Pediatrics. 2006;118 (1) :23-33.Abstract
OBJECTIVE: MRI studies have shown that preterm infants with brain injury have altered brain tissue volumes. Investigation of preterm infants without brain injury offers the opportunity to define the influence of early birth on brain development and provide normative data to assess effects of adverse conditions on the preterm brain. In this study, we investigated serial MRI of low-risk preterm infants with the aim to identify regions of altered brain development. METHODS: Twenty-three preterm infants appropriate for gestational age without magnetic resonance-visible brain injury underwent MRI twice at 32 and at 42 weeks' postmenstrual age. Fifteen term infants were scanned 2 weeks after birth. Brain tissue classification and parcellation were conducted to allow comparison of regional brain tissue volumes. Longitudinal brain growth was assessed from preterm infants' serial scans. RESULTS: At 42 weeks' postmenstrual age, gray matter volumes were not different between preterm and term infants. Myelinated white matter was decreased, as were unmyelinated white matter volumes in the region including the central gyri. The gray matter proportion of the brain parenchyma constituted 30% and 37% at 32 and 42 weeks' postmenstrual age, respectively. CONCLUSIONS: This MRI study of preterm infants appropriate for gestational age and without brain injury establishes the influence of early birth on brain development. No decreased cortical gray matter volumes were found, which is in contrast to findings in preterm infants with brain injury. Moderately decreased white matter volumes suggest an adverse influence of early birth on white matter development. We identified a sharp increase in cortical gray matter volume in preterm infants' serial data, which may correspond to a critical period for cortical development.
Niethammer M, Kalies WD, Mischaikow K, Tannenbaum A. On the detection of simple points in higher dimensions using cubical homology. IEEE Trans Image Process. 2006;15 (8) :2462-9.Abstract
Simple point detection is an important task for several problems in discrete geometry, such as topology preserving thinning in image processing to compute discrete skeletons. In this paper, the approach to simple point detection is based on techniques from cubical homology, a framework ideally suited for problems in image processing. A (d-dimensional) unitary cube (for a d-dimensional digital image) is associated with every discrete picture element, instead of a point in epsilon(d) (the d-dimensional Euclidean space) as has been done previously. A simple point in this setting then refers to the removal of a unitary cube without changing the topology of the cubical complex induced by the digital image. The main result is a characterization of a simple point p (i.e., simple unitary cube) in terms of the homology groups of the (3d - 1) neighborhood of p for arbitrary, finite dimensions

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