The notion of skeleton plays a major role in shape analysis. Some usually desirable characteristics of a skeleton are: sufficient for the reconstruction of the original object, centered, thin and homotopic. The Euclidean Medial Axis presents all these characteristics in a continuous framework. In the discrete case, the Exact Euclidean Medial Axis (MA) is also sufficient for reconstruction and c...

The identity of an object is not only specified by its parts but also by the relations among the parts. Rearranging parts can produce a completely different object, in the same manner as rearranging the phonemes in "fur" can yield "rough." How does the visual system represent the relative positions of parts? Between-part relations can be characterized by specifying the relations between the med...

We present a mathematical theory of the two-dimensional offset curves from the viewpoint of medial axis transform. We explore the local geometry of the offset curve in relation with the medial axis transform, culminating in the classification of points on the offset curve. We then study the domain decomposition from the viewpoint of offsets, and in particular introduce the concept of monotonic ...

BACKGROUND Preoperative periarticular bone quality is affected by joint loading. The purpose of this study was to determine the periarticular bone mineral density of the knee joint of patients undergoing total knee arthroplasty, and whether the location of the load-bearing axis correlates with the measured bone mineral density. MATERIALS AND METHODS The bone mineral densities of the medial an...

We examined the placement of the stem in relation to the medial tibial cortex when using total knee replacements (TKRs) with medially-offset tibial stems in Korean patients. Measurements were performed on the pre- and post-operative radiographs of 246 osteoarthritic knees replaced between January 2005 and May 2006 using the Genesis II or E-motion TKR with a medially-offset stem. Pre-operatively...

We denote by M R the test neighbourhood sufficient to extract the Euclidean Medial Axis of any n-dimensional discrete shape whose inner radius is no greater than R. In this paper, we study properties of discrete Euclidean disks overlappings so as to prove that in any given dimension n, M R tends to the set of visible vectors as R tends to infinity.

Probabilistic roadmap planners have been very successful in path planning for a wide variety of problems, especially applications involving robots with many degrees of freedom. These planners randomly sample the configuration space, building up a roadmap that connects the samples. A major problem is finding valid configurations in tight areas, and many methods have been proposed to more effecti...