Layer-wise relevance propagation (LRP) heatmaps aim to provide graphical explanation for decisions of a classifier. This could be of great benefit to scientists for trusting complex black-box models and getting insights from their data. The LRP heatmaps tested on benchmark datasets are reported to correlate significantly with interpretable image features. In this work, we investigate these claims and propose to refine them.

In this article, we explore the topic of extending aggregate computation in distributed networks with self-stabilizing properties to withstand network dynamics. Existing research suggests that fast gossiping algorithms, based on the properties of order statistics applied to families of exponential random variables, are a viable solution for computing functions of the values stored in the network. We focus on the specific case in which network changes and failures occur in batches with a minimum frequency in the order of the diameter of the network. Our contribution consists in two self-stabilizing mechanisms, allowing fast gossiping algorithms to be applicable to dynamic networks with minor increase in resources usage. The resulting algorithms can be deployed in networks exhibiting churn, node stop-failures and resets, and random topological changes. The theoretical results are verified with simulations on synthetic data, showcasing desirable properties for large-scale network designers such as scalability, lack of single points of failure, and anonymity.

Due to rapid advances in networking and sensing technology we are witnessing a growing interest in sensor networks, in which a variety of sensors are connected to each other and to computational devices capable of multimodal signal processing and data analysis. Such networks are seen to play an increasingly important role as key enablers in emerging pervasive computing technologies. In the first part of this paper we give an overview of recent developments in the area of multimodal sensor networks, paying special attention to ambient intelligence applications. In the second part, we discuss how the time series generated by data streams emanating from the sensors can be mined for temporal patterns, indicating cross-sensor signal correlations.

A statistically principled approach to 1-dimensional clustering was introduced by Pauwels abd Frederix (2000). In this approach clustering is achieved by finding the smoothest density that is statistically compatible with the observed data. In the current contribution we propose two solutions for the optimisation problem that is at the heart of this algorithm. The first solution is based on spline-functions, while the second hinges on an expansion of the density in terms of Gaussians. The latter is reminiscent of mixture-models but fundamentally different in its interpretation. Finally, we argue that 1-dimensional histogram segmentation yields a powerful local nonparametric cluster-validity criterion that can be used to check the quality of proposed clusterings in higher dimensions.

We outline the architecture of a content-based image retrieval (CBIR)-interface that offers the user a graphical tool to create new features by showing (as opposed to telling!) the system what he means. It allows him 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. We show how logistic regression and Sammon projection can be used to supervise this search mode.

In cluster-based segmentation pixels are mapped into various feature spaces whereupon they are subjected to a grouping algorithm. In this paper we develop a robust and versatile non-parametric clustering algorithm that is able to handle the unbalanced and irregular clusters encountered in such segmentation applications. The strength of our approach lies in the definition and use of two cluster validity indices that are independent of the cluster topology. By combining them, an excellent clustering can be identified, and experiments confirm that the associated clusters do indeed correspond to perceptually salient image regions.

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.

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.

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.>

The potential of coupled nonlinear diffusion processes to provide an efficient and implementable mechanism capable of edge preserving smoothing and noise suppression is investigated. The basic idea is that several maps undergo coupled development towards an equilibrium state. These maps could contain intensity, local edge strength, range, or another quantity. All these maps, including the edge map, contain continuous rather than all-or-nothing information, following a strategy of least commitment. Each of the approaches is developed and tested on a parallel transputer network.>

This paper introduces a number of systems of coupled, non-linear diffusion equations and investigates their role in edge-preserving smoothing and noise suppression. The basic idea is that several maps describing the image undergo coupled development towards an equilibrium state representing the enhanced image. These maps could contain: e.g., intensity, local edge strength, range or another quantity. All these maps, including the edge map, contain continuous rather than all-or-nothing information, following a strategy of least commitment. Each of the approaches has been developed and tested on a parallel transputer network.

It is shown how object recognition and optical flow can be captured within a single framework. These examples have been selected because they illustrate two complementary problems which can be tackled using the same unified approach based on Lie theory. The object recognition work referred to is based on the extraction of shape invariants and has been reported elsewhere. The present study focuses on using the same framework for the calculation of the optical flow. Besides the introduction of some new methods, it is shown that several well-known schemes can be derived following the same principles.>