Alfons H. Salden

Context sensitive access control

We investigate the practical feasibility of using context information for controlling access to services. Based solely on situational context, we show that users can be transparently provided anonymous access to services and that service providers can still impose various security levels. Thereto, we propose context-sensitive verification methods that allow checking the users claimed authenticity in various ways and to various degrees. More precisely, conventional information management approaches are used to compare historic contextual (service usage) data of an individual user or group. The result is a relatively strong, less intrusive and more flexible access control process that mimics our natural way of authentication and authorization in the physical world.

Higher order differential structure of images

This paper is meant as a tutorial on the basic concepts for vision in the ‘Koenderink’ school. The concept of scale-space is a necessity, if the extraction of structure from measured physical signals (i.e. images) is at stage. The Gaussian derivative kernels for physical signals are then the natural analogues of the mathematical differential operators. This paper discusses some interesting properties of the Gaussian derivative kernels, like their orthogonality and behaviour with noisy input data. Geometrical structure to extract is expressed in terms of differential invariants, in this paper limited to invariants under orthogonal transformations. Three representations are summarized: Cartesian, gauge and manifest invariant notation. Many explicit examples are given. A section is included about the computer implementation of the calculation of higher order invariant structure.

Topological Numbers and Singularities in Scalar Images: Scale-Space Evolution Properties

Singular points of scalar images in any dimensions are classified by a topological number. This number takes integer values and can efficiently be computed as a surface integral on any closed hypersurface surrounding a given point. A nonzero value of the topological number indicates that in the corresponding point the gradient field vanishes, so the point is singular. The value of the topological number classifies the singularity and extends the notion of local minima and maxima in one-dimensional signals to the higher dimensional scalar images. Topological numbers are preserved along the drift of nondegenerate singular points induced by any smooth image deformation. When interactions such as annihilations, creations or scatter of singular points occurs upon a smooth image deformation, the total topological number remains the same.Our analysis based on an integral method and thus is a nonperturbative extension of the order-by-order approach using sets of differential invariants for studying singular points.Examples of typical singularities in one- and two-dimensional images are presented and their evolution induced by isotropic linear diffusion of the image is studied.

Linear Scale-Space Theory from Physical Principles

In the past decades linear scale-space theory was derived on the basis of various axiomatics. In this paper we revisit these axioms and show that they merely coincide with the following physical principles, namely that the image domain is a Galilean space, that the total energy exchange between a region and its surrounding is preserved under linear filtering and that the physical observables should be invariant under the group of similarity transformations. These observables are elements of the similarity jet spanned by natural coordinates and differential energies read out by a vision system.Furthermore, linear scale-space theory is extended to spatio-temporal images on bounded and curved domains. Our theory permits a delay-operation at the present moment which is in agreement with the motion detection model of Reichardt. In this respect our theory deviates from that of Koenderink which requires additional syntactical operators to realise such a delay-operation.Finally, the semi-discrete and discrete linear scale-space theories are derived by discretising the continuous theories following the theory of stochastic processes. The relation and difference between our stochastic approach and that of Lindeberg is pointed out. The connection between continuous and (semi-)discrete sale-space theory for infinitely high scales observed by Lindeberg is refined by applying appropriate scaling limits. It is shown that Lindebergs requirement of normalisation for one-dimensional discrete Greens functions can be incorporated into our theory for arbitrary dimensional discrete Greens functions, parameter determination can be avoided, and the requirement of operation at even and odd coordinates sum can be guaranteed simultaneously by taking a normalised linear combination of the identity operator and the first step discrete Greens functions. The new discrete Greens functions are still intimately related to the continuous Greens functions and appear to coincide with pyramidal discrete Greens functions.

Ubiquitous Attentiveness – Enabling Context-Aware Mobile Applications and Services

We present a concept called ‘ubiquitous attentiveness’: Context information concerning the user and his environment is aggregated, exchanged and constitutes triggers that allow mobile applications and services to react on them and adapt accordingly. Ubiquitous attentiveness is particularly relevant for mobile applications due to the use of positional user context information, such as location and movement. Key aspects foreseen in the realization of ubiquitously attentive (wearable) systems are acquiring, interpreting, managing, retaining and exchanging contextual information. Because various players own this contextual information, we claim in this paper that a federated service control architecture is needed to facilitate ubiquitous attentive services. Such a control architecture must support the necessary intelligent sharing of resources and information, and ensure trust.

A complete and irreducible set of local orthogonally invariant features of 2-dimensional images

Presents a method of multi-resolution image analysis that gives the most concise set of local orthogonally invariant features of 2-dimensional input images. Solving the equivalence problem corresponding to a local jet and the group of orthogonal transformations of the cartesian coordinate frame the authors find a complete and irreducible set of local algebraic invariants that may describe any local orthogonally invariant feature of the jet.<<ETX>>

A system for context-dependent user modeling

We present a system for learning and utilizing context-dependent user models The user models attempt to capture the interests of a user and link the interests to the situation of the user The models are used for making recommendations to applications and services on what might interest the user in her current situation In the design process we have analyzed several mock-ups of new mobile, context-aware services and applications The mock-ups spanned rather diverse domains, which helped us to ensure that the system is applicable to a wide range of tasks, such as modality recommendations (e.g., switching to speech output when driving a car), service category recommendations (e.g., journey planners at a bus stop), and recommendations of group members (e.g., people with whom to share a car) The structure of the presented system is highly modular First of all, this ensures that the algorithms that are used to build the user models can be easily replaced Secondly, the modularity makes it easier to evaluate how well different algorithms perform in different domains The current implementation of the system supports rule based reasoning and tree augmented naive Bayesian classifiers (TAN) The system consists of three components, each of which has been implemented as a web service The entire system has been deployed and is in use in the EU IST project MobiLife In this paper, we detail the components that are part of the system and introduce the interactions between the components In addition, we briefly discuss the quality of the recommendations that our system produces.

Differential and Integral Geometry of Linear Scale-Spaces

Linear scale-space theory provides a useful framework to quantify the differential and integral geometry of spatio-temporal input images. In this paper that geometry comes about by constructing connections on the basis of the similarity jets of the linear scale-spaces and by deriving related systems of Cartan structure equations. A linear scale-space is generated by convolving an input image with Greens functions that are consistent with an appropriate Cauchy problem. The similarity jet consists of those geometric objects of the linear scale-space that are invariant under the similarity group. The constructed connection is assumed to be invariant under the group of Euclidean movements as well as under the similarity group. This connection subsequently determines a system of Cartan structure equations specifying a torsion two-form, a curvature two-form and Bianchi identities. The connection and the covariant derivatives of the curvature and torsion tensor then completely describe a particular local differential geometry of a similarity jet. The integral geometry obtained on the basis of the chosen connection is quantified by the affine translation vector and the affine rotation vectors, which are intimately related to the torsion two-form and the curvature two-form, respectively. Furthermore, conservation laws for these vectors form integral versions of the Bianchi identities. Close relations between these differential geometric identities and integral geometric conservation laws encountered in defect theory and gauge field theories are pointed out. Examples of differential and integral geometries of similarity jets of spatio-temporal input images are treated extensively.

A Dynamic Scale–Space Paradigm

We present a novel mathematical, physical and logical framework for describing an input image of the dynamics of physical fields, in particular the optic field dynamics. Our framework is required to be invariant under a particular gauge group, i.e., a group or set of transformations consistent with the symmetries of that physical field dynamics enveloping renormalisation groups. It has to yield a most concise field description in terms of a complete and irreducible set of equivalences or invariants. Furthermore, it should be robust to noise, i.e., unresolvable perturbations (morphisms) of the physical field dynamics present below a specific dynamic scale, possibly not covered by the gauge group, do not affect Lyapunov or structural stability measures expressed in equivalences above that dynamic scale. The related dynamic scale symmetry encompasses then a gauge invariant similarity operator with which similarly prepared ensembles of physical field dynamics are probed and searched for partial equivalences coming about at higher scales.The framework of our dynamic scale-space paradigm is partly based on the initialisation of joint (non)local equivalences for the physical field dynamics external to, induced on and stored in a vision system and represented by an image, possibly at various scales. These equivalences are consistent with the scale-space paradigm considered and permit a faithful segmentation and interpretation of the dynamic scale-space at initial scale. Among the equivalences are differential invariants, integral invariants and topological invariants not affected by the considered gauge group. These equivalences form a quantisation of the external, induced and stored physical field dynamics, and are associated to a frame field, co-frame field, metric and/or connection invariant under the gauge group. Examples of these equivalences are the curvature and torsion two-forms of general relativity, the Burgers and Frank vector density fields of crystal theory (in both disciplines these equivalences measure the inhomogeneity of translational and (affine) rotation groups over space-time), and the winding numbers and other topological charges popping up in electromagnetism and chromodynamics.Besides based on a gauge invariant initialisation of equivalences the framework of our dynamic scale-space paradigm assumes that a robust, i.e. stable and reproducible, partially equivalent representation of the physical field dynamics is acquired by a multi-scale filtering technique adapted to those initial equivalences. Effectively, the hierarchy of nested structures of equivalences, by definition too invariant under the gauge group, is obtained by applying an exchange principle for a free energy of the physical field dynamics (represented through the equivalences) that in turn is linked to a statistical partition function. This principle is operationalised as a topological current of free energy between different regions of the physical field dynamics. It translates for each equivalence into a process governed by a system of integral and/or partial differential equations (PDES) with local and global initial-boundary conditions (IBC). The scaled physical field dynamics is concisely classified in terms of local and non-local equivalences, conserved densities or curvatures of the dynamic scale-space paradigm that in generally are not coinciding with all initial equivalences. Our dynamic scale-space paradigm distinguishes itself intrinsically from the standard ones that are mainly developed for scalar fields. A dynamic scale-space paradigm is also operationalised for non-scalar fields like curvature and torsion tensor fields and even more complex nonlocal and global topological fields supported by the physical field dynamics. The description of the dynamic scale-spaces are given in terms of again equivalences, and the paradigms in terms of symmetries, curvatures and conservation laws. The topological characteristics of the paradigm form then a representation of the logical framework.A simple example of a dynamic scale-space paradigm is presented for a time-sequence of two-dimensional satellite images in the visual spectrum. The segmentation of the sequence in fore- and background dynamics at various scales is demonstrated together with a detection of ridges, courses and inflection lines allowing a concise triangulation of the image. Furthermore, the segmentation procedure of a dynamic scale-space is made explicit allowing a true hierarchically description in terms of nested equivalences.How to unify all the existing scale-space paradigms using our frame work is illustrated. This unification comes about by a choice of gauge and renormalisation group, and setting up a suitable scale-space paradigm that might be user-defined.How to extend and to generalise the existing scale-space paradigm is elaborated on. This is illustrated by pointing out how to retain a pure topological or covariant scale-space paradigm from an initially segmented image that instead of a scalar field also can represent a density field coinciding with dislocation and disclination fields capturing the cutting and pasting procedures underlying the image formation.

Local and Multilocal Scale-Space Description

A new method is presented for solving equivalence problems for the extended jet of finite order of the scale-space corresponding to a 2-dimensional input image and the groups of spatially homogeneous affine and orthogonal transformations of local cartesian coordinate frames. By means of this method complete and irreducible sets of algebraic invariants are found that may describe any local and (or) multilocal affine or orthogonal invariant of scale-space. Consequently these sets may form bases for topological descriptions of scale-space.