The aim of this paper is to adapt the Viability Theorem from differential inclusions (governing the evolution of vectors in a finite dimensional space) to so-called morphological inclusions (governing the evolution of nonempty compact subsets of the Euclidean space). In this morphological framework, the evolution of compact subsets of RN is described by means of flows along bounded Lipschitz ve...

In this paper, we take a predefined geometry shape as a constraint for accurate shape alignment. A shape model is divided in two parts: fixed shape and active shape. The fixed shape is a user-predefined simple shape with only a few landmarks which can be easily and accurately located by machine or human. The active one is composed of many landmarks with complex shape contour. When searching an ...

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...

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...

A method of shape generation using shape grammars which take shape as primitive and have shape-specific rules is presented. A formalism for the complete, generative specification of a class of non-representational, geometric paintings or sculptures is defined which has shape grammars as its structural component. Paintings are material representations of two-dimensional shapes gen~rated by shape...

In deformable model segmentation, the geometric training process plays a crucial role in providing shape statistical priors and appearance statistics that are used as likelihoods. Also, the geometric training process plays a crucial role in providing shape probability distributions in methods finding significant differences between classes. The quality of the training seriously affects the fina...

Shape recognition is a challenging task when images contain overlapping, noisy, occluded, partial shapes. This paper addresses the task of matching input shapes with model shapes described in terms of features such as line segments and angles. The quality of matching is gauged using a measure derived from attributed shape grammars. We apply genetic algorithms to the partial shape-matching task....

Level set based approaches are widely used for image segmentation and object tracking. As these methods are usually driven by low level cues such as intensity, colour, texture, and motion they are not sufficient for many problems. To improve the segmentation and tracking results, shape priors were introduced into level set based approaches. Shape priors are generated by presenting many views a ...

This paper pursues the idea of understanding shapes of unknown objects through establishing correspondence with points from the surface of known objects. A lot of geometryrelated knowledge, such as functionally correct grasps or object constellations, could thus be transferred from known shapes to novel shapes of the same or a similar category. As one critical module in such a system, this pape...

Shape grammars are, in general, intractable. Even amongst tractable shape grammars, their characteristics vary significantly. This paper describes a paradigm for practical general shape grammar interpreters, which aim to address computational difficulties posed by parameterization. The paradigm is expressed in terms of frameworks each comprising an underlying data structure, manipulation algori...