OBJECTIVE To determine the associations between serum levels of vitamin D, sunlight exposure, and knee cartilage loss cross-sectionally and longitudinally in older adults. METHODS A total of 880 randomly selected subjects (mean age 61 years [range 51-79 years], 50% women) were studied at baseline, and 353 of these subjects were studied 2.9 years later. Serum levels of 25-hydroxyvitamin D (25[...

The cut locus C of a closed set A in the Euclidean space E is defined as the closure of the set containing all points p A which have at least two shortest paths to A. We present a theorem stating that the complement of the cut locus i.e. E\(C ∪A) is the maximal open set in (E\A) where the distance function with respect to the set A is continuously A differentiable. This theorem includes also th...

Medial representation of a three-dimensional (3-D) object or an ensemble of 3-D objects involves capturing the object interior as a locus of medial atoms, each atom being two vectors of equal length joined at the tail at the medial point. Medial representation has a variety of beneficial properties, among the most important of which are 1) its inherent geometry, provides an object-intrinsic coo...

one of the debates concerning concepts of “medial motion” and “traversal motion” is the question of which of these two concepts of motion corresponds to motion in the corporeal world. in the present article we intend to employ the language of mathematics to present a model for each of these two concepts to study the above mentioned problem. as a result, medial motion represents a covering funct...

A core brain network has been proposed to underlie a number of different processes, including remembering, prospection, navigation, and theory of mind [Buckner, R. L., & Carroll, D. C. Self-projection and the brain. Trends in Cognitive Sciences, 11, 49-57, 2007]. This purported network-medial prefrontal, medial-temporal, and medial and lateral parietal regions-is similar to that observed during...

We present a new, continuously defined three-dimensional medial shape representation based on subdivision surfaces. The shape is modeled via its medial axis, and the associated boundary is computed directly from this axis at every point. Our model is parameterized over a fixed domain, so comparison among different shapes is possible. It is the first such model to support branch curves, which al...

Regulation of ACTH secretion changes between early (40 d) and late (60 d) puberty in male rats. We tested whether this occurs because of activating effects of testosterone on the brain. We measured testosterone and ACTH responses to repeated restraint in adrenalectomized, corticosterone-replaced rats entering and leaving puberty with or without treatment with flutamide, a nonsteroidal androgen-...

The medial axis transform provides an alternative r epresentation of geometric models that has many use ful properties for analysis modelling. Applications include decomposition of ge neral solids into sub regions for mapped meshing, i dentification of slender regions for dimensional reduction and recognition o f small features for suppression. In order to serve these purposes effectively, it i...

In this article, we study the (d − 1)-volume and the covering numbers of the medial axis of a compact subset of R. In general, this volume is infinite; however, the (d− 1)-volume and covering numbers of a filtered medial axis (the μ-medial axis) that is at distance greater than ε from the compact set can be explicitely bounded. The behaviour of the bound we obtain with respect to μ, ε and the c...

1077-3142/$ see front matter 2011 Elsevier Inc. A doi:10.1016/j.cviu.2010.12.011 ⇑ Corresponding author. E-mail address: [email protected] (D. Macrini) The recognition of 3-D objects from their silhouettes demands a shape representation which is stable with respect to minor changes in viewpoint and articulation. This can be achieved by parsing a silhouette into parts and relationships that do...