Eric Pauwels

Determination of optical flow and its discontinuities using non-linear diffusion

A new method for optical flow computation by means of a coupled set of non-linear diffusion equations is presented. This approach integrates the classical differential approach with the correlation type of motion detectors. A measure of inconsistency within the optical flow field which indicates optical flow boundaries. This information is fed back to the optical flow equations in a non-linear way and allows the flow field to be reconstructed while preserving the discontinuities. The whole scheme is also applicable to stereo matching. The model is applied to a set of synthetic and real image sequences to illustrate the behaviour of the coupled diffusion equations.

Finding salient regions in images: nonparametric clustering for image segmentation and grouping

A major problem in content-based image retrieval (CBIR) is the unsupervised identification of perceptually salient regions in images. We contend that this problem can be tackled by mapping the pixels into various feature-spaces, whereupon they are subjected to a grouping algorithm. In this paper we develop a robust and versatile nonparametric clustering algorithm that is able to handle the unbalanced and highly irregular clusters encountered in such CBIR applications. The strength of our approach lies not so much in the clustering itself, but rather in the definition and use of two cluster-validity indices that are independent of the cluster topology. By combining them, an optimal clustering can be identified, and experiments confirm that the associated clusters do, indeed, correspond to perceptually salient image regions.

Foundations of semi-differential invariants

This paper elaborates the theoretical foundations of a semi-differential framework for invariance. Semi-differential invariants combine coordinates and their derivatives with respect to some contour parameter at several points of the image contour, thus allowing for an optimal trade-off between identification of points and the calculation of derivatives. A systematic way of generating complete and independent sets of such invariants is presented. It is also shown that invariance under reparametrisation can be cast in the same framework. The theory is illustrated by a complete analysis of 2D affine transformations. In a companion paper (Pauwels et al. 1995) these affine semi-differential invariants are implemented in the computer program FORM (Flat Object Recognition Method) for the recognition of planar contours under pseudo-perspective projection.

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. >

Affine reconstruction from perspective image pairs with a relative object-camera translation in between

A method is described to recover the three-dimensional affine structure of a scene consisting of at least five points identified in two perspective views with a relative object-camera translation in between. When compared to the results for arbitrary stereo views, a more detailed reconstruction is possible using less information. The method presented only assumes that the two images are obtained by identical cameras, but no knowledge about the intrinsic parameters of the camera(s) or about the performed translation is assumed. By the same method, affine 3D reconstruction from a single view can be achieved for parallel structures. In that case, four points suffice for affine reconstruction.

Recognition of planar shapes under affine distortion

Methods for the recognition ofplanar shapes from arbitrary viewpoints are described. The adopted model of projection is orthographic. The invariant descriptions derived for this group are one-dimensional shape signatures comparable to the well-known curvature as a function of arc length description of Euclidean geometry. Since the use of such differential invariants in the affine case would lead to unacceptably high orders of derivatives, affine invariant descriptions based onsemi-differential invariants are proposed as an alternative. A systematic discussion of different types of these invariants is given. The usefulness and viability of this methodology is demonstrated on a database containing more than 40 objects.

Invariance from the Euclidean Geometer's Perspective

It is remarkable how well the human visual system can cope with changing viewpoints when it comes to recognising shapes. The state of the art in machine vision is still quite remote from solving such tasks. Nevertheless, a surge in invariance-based research has led to the development of methods for solving recognition problems still considered hard until recently. A nonmathematical account explains the basic philosophy and trade-offs underlying this strand of research. The principles are explained for the relatively simple case of planar-object recognition under arbitrary viewpoints. Well-known Euclidean concepts form the basis of invariance in this case. Introducing constraints in addition to that of planarity may further simplify the invariants. On the other hand, there are problems for which no invariants exist.

Image Segmentation by Nonparametric Clustering Based on the Kolmogorov-Smirnov Distance

In this paper we introduce a non-parametric clustering algorithm for 1-dimensional data. The procedure looks for the simplest (i.e. smoothest) density that is still compatible with the data. Compatibility is given a precise meaning in terms of the Kolmogorov-Smirnov statistic. After discussing experimental results for colour segmentation, we outline how this proposed algorithm can be extended to higher dimensions.

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. >

Show Me What You Mean! Pariss: A CBIR-Interface that Learns by Example

We outline the architecture of a CBIR-interface that allows the user to interactively classify images by dragging and dropping them into different piles and instructing the interface to come up with features that can mimic this classification. Logistic regression and Sammon projection are used to support this search mode.