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

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.

MR diffusion tensor imaging (DTI) of the brain and spine provides a unique tool for both visualizing directionality and assessing intactness of white matter fiber tracts in vivo. At the spatial resolution of clinical MRI, much of primate white matter is composed of interdigitating fibers. Analyses based on an assumed single diffusion tensor per voxel yield important information about the average diffusion in the voxel but fail to reveal structure in the presence of crossing tracts. Until today, all clinical scans assume only one tensor, causing potential serious errors in tractography. Since high angular resolution imaging remains, so far, untenable for routine clinical use, a method is proposed whereby the single-tensor field is augmented with additional information gleaned from standard clinical DTI. The method effectively resolves two distinct tract directions within voxels, in which only two tracts are assumed to exist. The underlying constrained two-tensor model is fitted in two stages, utilizing the information present in the single-tensor fit. As a result, the necessary MRI time can be drastically reduced when compared with other approaches, enabling widespread clinical use. Upon evaluation in simulations and application to in vivo human brain DTI data, the method appears to be robust and practical and, if correctly applied, could elucidate tract directions at critical points of uncertainty.

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.