In the framework of a European technological research project 2], a general method is presented for shape measurement and defect detection of industrially produced objects using the characteristic 2D projections of the objects. The method is applied to the visual inspection and dimensional measurement of ferrite cores. An optical shape gauge system is described, based on rotation-invariant shap...

We propose two differential geometric representations of planar shapes using: (i) direction functions and (ii) curvature functions, of their boundaries. Under either representation, planar shapes are treated as elements of infinite-dimensional shape spaces. Pairwise differences between the shapes are quantified using the lengths of geodesics connecting them on the shape spaces. We specify the g...

The problem of immersing a simply connected surface with a prescribed shape operator is discussed. It is shown that, aside from some special degenerate cases, such as when the shape operator can be realized by a surface with one family of principal curves being geodesic, the space of such realizations is a convex set in an affine space of dimension at most 3. The cases where this maximum dimens...

Recently we developed a periodic surface model to assist the construction of nano structures parametrically for computer-aided nano-design. In this paper, we study the properties of periodic surfaces for degree elevation and reduction. Degree elevation approaches are developed to incrementally increase shape complexities, including native, variational, and boundary constrained elevations. A gen...

This paper describes the generation of shape primitive detecting masks and their application in measurements on shapes as well as in conditions for topology preservation as used in skeletonization. The formalism is expanded from twoto four-dimensional images and elaborates on the extension of 3D skeletonization to 4D skeletonization. 2002 Elsevier Science B.V. All rights reserved.

In this paper we introduce a new method for computing the orientation for compound shapes. If the method is applied to single component shapes the computed orientation is consistent with the shape orientation defined by the axis of the least second moment of inertia. If the new method is applied to compound shapes this is not the case, and consequently the presented method is both new and diffe...

Diabetic Retinopathy is a medical condition where the retina is damaged because fluid leaks from blood vessels into the retina. The presence of hemorrhages in the retina is the earliest symptom of diabetic retinopathy. The number and shape of hemorrhages is used to indicate the severity of the disease. Early automated hemorrhage detection can help reduce the incidence of blindness. This paper i...