We propose a new method to automatically group edge-segments (extracted from an image) into a fully connected line-drawing. Unlike some other methods, this algorithm does not assume that the result is topologically simple (i.e. composed of simple closed curves) but is able to recover more complicated, and therefore salient, topological features such as T-junctions. The method is based on a region-growing algorithm which uses stochastically obtained geometric information to halt the region expansion.

In this paper we show how both geometry-driven diffusion and optimization of the Mumford-Shah functional can be used to develop a type of curve-evolution that is able to preserve salient features of closed curves (such as corners and straight line segments), while simultaneously suppressing noise and irrelevant details. The idea is to characterize the curve by means of its angle-function (i.e. the angle between the tangent and a fixed axis) and to apply the appropriate dynamics to this one-dimensional representation. We show how constrained evolution equations can be used to keep the corresponding curve closed at all times.>

We show how optimization of the Nordstrom and Mumford-Shah functionals can be used to develop a type of curve-evolution that is able to preserve salient features of closed curves while simultaneously suppressing noise and irrelevant details. The idea is to characterize a curve by means of its angle-function and apply the appropriate dynamics to this representation. Upon convergence, the resulting form of the contour is reconstructed from the representation.>

Explores how the functional form of scale space filters is determined by a number of a priori conditions. In particular, if one assumes scale space filters to be linear, isotropic convolution filters, then two conditions (viz. recursivity and scale-invariance) suffice to narrow down the collection of possible filters to a family that essentially depends on one parameter which determines the qualitative shape of the filter. Gaussian filters correspond to one particular value of this shape-parameter. For other values the filters exhibit a more complicated pattern of excitatory and inhibitory regions. This might well be relevant to the study of the neurophysiology of biological visual systems, for recent research shows the existence of extensive disinhibitory regions outside the periphery of the classical center-surround receptive field of LGN and retinal ganglion cells (in cats). Such regions cannot be accounted for by models based on the second order derivative of the Gaussian. Finally, the authors investigate how this work ties in with another axiomatic approach of scale space operators which focuses on the semigroup properties of the operator family. The authors show that only a discrete subset of filters gives rise to an evolution which can be characterized by means of a partial differential equation.>