P. Fiddelaers

An extended class of scale-invariant and recursive scale space filters

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. >

Enhancement of planar shape through optimization of functionals for curves

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. >

Shape-extraction for curves using geometry-driven diffusion and functional optimization

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.<<ETX>>

Fully Unsupervised Clustering Using Center-Surround Receptive Fields with Applications to Color-Segmentation

In this paper we argue that the emphasis on similarity-matching within the context of Content-based Image Retrieval (CBIR) highlights the need for improved and reliable clustering-algorithms. We propose a fully unsupervised clustering algorithm that is obtained by changing the non-parametric density estimation problem in two ways. Firstly, we use cross-validation to select the appropriate width of the convolution-kernel. Secondly, using kernels with a positive centre and a negative surround (DOGS) allows for a better discrimination between clusters and frees us from having to choose an arbitrary cut-off thresh- old. No assumption about the underlying data-distribution is necessary and the algorithm can be applied in spaces of arbitrary dimension. As an illustration we have applied the algorithm to colour-segmentation problems.

Autonomous grouping of contour-segments using an adaptive region-growing algorithm

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.

Geometry-driven curve evolution

In this paper we show how geometry-driven diffusion can be used to develop a system 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 characterise the curve by means of its angle function (i.e. the angle between the tangent and a fixed axis) and to apply geometry-driven diffusion to this one-dimensional representation.

Autonomous extraction of shape and topology of contours using geometry-driven diffusion and optimization of functionals

We show how geometry-driven diffusion based on the Nordstrom-functional can be used to crystallize the geometric content of a closed contour by simultaneously suppressing noise while enhancing the salient features. Furthermore, we propose a robust and highly parallelizable method that will automatically group edge-segments to produce a set of fully connected contours. The result could be used e.g., as input for recognition programs based on aspect graphs, or as a good initial guess for snakes and active contours.