Morphological Counterparts of Linear Shift-Invariant Scale-Spaces

It is well-known that there are striking analogies between linear shift-invariant systems and morphological systems for image analysis. So far, however, the relations between both system theories are mainly understood on a pure convolution / erosion level. A formal connection on the level of differential or pseudodifferential equations and their induced scale-spaces is still missing. The goal of our paper is to close this gap. We present a simple and fairly general dictionary that allows to translate any linear shift-invariant evolution equation into its morphological counterpart and vice versa. It is based on a scale-space representation by means of the symbol of its (pseudo)differential operator. Introducing a novel transformation, the Cramér–Fourier transform, puts us in a position to relate the symbol to the structuring function of a morphological scale-space of Hamilton–Jacobi type. As an application of our general theory, we derive the morphological counterparts of many linear shift-invariant scale-spaces, such as the Poisson scale-space, \(\alpha \)-scale-spaces, summed \(\alpha \)-scale-spaces, relativistic scale-spaces, and their anisotropic variants. Our findings are illustrated by experiments.     

An auto-generated real-time iteration algorithm for nonlinear MPC in the microsecond range

In this paper, we present an automatic C-code generation strategy for real-time nonlinear model predictive control (NMPC), which is designed for applications with kilohertz sample rates. The corresponding code export module has been implemented within the software package ACADO Toolkit. It is capable of exporting fixed step-size integrators together with their sensitivities as well as a real-time Gauss–Newton method. Here, we employ the symbolic representation of optimal control problems in ACADO in order to auto-generate plain C-code which is optimized for final production. The exported code has been tested for model predictive control scenarios comprising constrained nonlinear dynamic systems with four states and a control horizon of ten samples. The numerical simulations show a promising performance of the exported code being able to provide feedback in much less than a millisecond.     

On improving the efficiency of tensor voting

This paper proposes two alternative formulations to reduce the high computational complexity of tensor voting, a robust perceptual grouping technique used to extract salient information from noisy data. The first scheme consists of numerical approximations of the votes, which have been derived from an in-depth analysis of the plate and ball voting processes. The second scheme simplifies the formulation while keeping the same perceptual meaning of the original tensor voting: The stick tensor voting and the stick component of the plate tensor voting must reinforce surfaceness, the plate components of both the plate and ball tensor voting must boost curveness, whereas junctionness must be strengthened by the ball component of the ball tensor voting. Two new parameters have been proposed for the second formulation in order to control the potentially conflictive influence of the stick component of the plate vote and the ball component of the ball vote. Results show that the proposed formulations can be used in applications where efficiency is an issue since they have a complexity of order O(1). Moreover, the second proposed formulation has been shown to be more appropriate than the original tensor voting for estimating saliencies by appropriately setting the two new parameters.     

A New Algorithm for Finding Trees with Many Leaves

We present an algorithm that finds out-trees and out-branchings with at least k leaves in directed graphs. These problems are known as Directed Maximum Leaf Out-Tree and Directed Maximum Leaf Out-Branching, respectively, and—in the case of undirected graphs—as Maximum Leaf Spanning Tree. The run time of our algorithm is O(4 ^k nm) on directed graphs and O(poly(n)+4 ^k k ²) on undirected graphs. This improves over the previously fastest algorithms for these problems with run times of 2 ^O(klog k) poly(n) and O(poly(n)+6.75 ^k poly(k)) respectively.     

Knowledge visualization for evaluation tasks

Although various methods for the evaluation of intelligent systems have been proposed in the past, almost no techniques are present that support the manual inspection of knowledge bases by the domain specialist. Manual knowledge base inspection is an important and frequently applied method in knowledge engineering. Since it can hardly be performed in an automated manner, it is a time-consuming and costly task. In this paper, we discuss a collection of appropriate visualization techniques that help developers to interactively browse and analyze the knowledge base in order to find deficiencies and semantic errors in their implementation. We describe standard visualization methods adapted to specifically support the analysis of the static knowledge base structure, but also of the usage of knowledge base objects such as questions or solutions. Additionally, we introduce a novel visualization technique that supports the validation of the derivation and interview behavior of a knowledge system in a semi-automatic manner. The application of the presented methods was motivated by the daily practice of knowledge base development.     

Metaphors and Context-Aware Information Access

Metaphors are often used to provide the user with a mental model to ease the use of computers. An example of such a metaphor is the commonly used “Desktop Metaphor”. Metaphors also can be used to ease context-aware information access for the users of mobile information systems. In this paper we present a taxonomy that allows the categorisation of such metaphors. Furthermore, we give an overview of existing metaphors and their implementations. After introducing some new metaphors we conclude our considerations with a classification of new and existing metaphors using our taxonomy.     

An Internet-based negotiation server for e-commerce

This paper describes the design and implementation of a replicable, Internet-based negotiation server for conducting bargaining-type negotiations between enterprises involved in e-commerce and e-business. Enterprises can be buyers and sellers of products/services or participants of a complex supply chain engaged in purchasing, planning, and scheduling. Multiple copies of our server can be installed to complement the services of Web servers. Each enterprise can install or select a trusted negotiation server to represent his/her interests. Web-based GUI tools are used during the build-time registration process to specify the requirements, constraints, and rules that represent negotiation policies and strategies, preference scoring of different data conditions, and aggregation methods for deriving a global cost-benefit score for the item(s) under negotiation. The registration information is used by the negotiation servers to automatically conduct bargaining type negotiations on behalf of their clients. In this paper, we present the architecture of our implementation as well as a framework for automated negotiations, and describe a number of communication primitives which are used in the underlying negotiation protocol. A constraint satisfaction processor (CSP) is used to evaluate a negotiation proposal or counterproposal against the registered requirements and constraints of a client company. In case of a constraint violation, an event is posted to trigger the execution of negotiation strategic rules, which either automatically relax the violated constraint, ask for human intervention, invoke an application, or perform other remedial operations. An Event-Trigger-Rule (ETR) server is used to manage events, triggers, and rules. Negotiation strategic rules can be added or modified at run-time. A cost-benefit analysis component is used to perform quantitative analysis of alternatives. The use of negotiation servers to conduct automated negotiation has been demonstrated in the context of an integrated supply chain scenario. Received: 30 October 2000 / Accepted: 12 January 2001 Published online: 2 August 2001     

Relations Between Regularization and Diffusion Filtering

Regularization may be regarded as diffusion filtering with an implicit time discretization where one single step is used. Thus, iterated regularization with small regularization parameters approximates a diffusion process. The goal of this paper is to analyse relations between noniterated and iterated regularization and diffusion filtering in image processing. In the linear regularization framework, we show that with iterated Tikhonov regularization noise can be better handled than with noniterated. In the nonlinear framework, two filtering strategies are considered: the total variation regularization technique and the diffusion filter technique of Perona and Malik. It is shown that the Perona-Malik equation decreases the total variation during its evolution. While noniterated and iterated total variation regularization is well-posed, one cannot expect to find a minimizing sequence which converges to a minimizer of the corresponding energy functional for the Perona–Malik filter. To overcome this shortcoming, a novel regularization technique of the Perona–Malik process is presented that allows to construct a weakly lower semi-continuous energy functional. In analogy to recently derived results for a well-posed class of regularized Perona–Malik filters, we introduce Lyapunov functionals and convergence results for regularization methods. Experiments on real-world images illustrate that iterated linear regularization performs better than noniterated, while no significant differences between noniterated and iterated total variation regularization have been observed.     

Group awareness and self-presentation in computer-supported information exchange

A common challenge in many situations of computer-supported collaborative learning is increasing the willingness of those involved to share their knowledge with other group members. As a prototypical situation of computer-supported information exchange, a shared-database setting was chosen for the current study. This information-exchange situation represented a social dilemma: while the contribution of information to a shared database induced costs and provided no benefit for the individual, the entire group suffered when all members decided to withhold information. In order to alleviate the information-exchange dilemma, a group-awareness tool was employed. It was hypothesized that participants would use group awareness for self-presentational purposes. For the examination of this assumption, the personality variable ‘protective self-presentation’ (PSP) was measured. An interaction effect of group awareness and PSP was found: when an awareness tool provided information concerning the contribution behavior of each individual, this tool was used as a self-presentation opportunity. In order to understand this effect in more detail, single items of the PSP-scale were analyzed.     

Artists portray human faces with the Fourier statistics of complex natural scenes

When artists portray human faces, they generally endow their portraits with properties that render the faces esthetically more pleasing. To obtain insight into the changes introduced by artists, we compared Fourier power spectra in photographs of faces and in portraits by artists. Our analysis was restricted to a large set of monochrome or lightly colored portraits from various Western cultures and revealed a paradoxical result. Although face photographs are not scale-invariant, artists draw human faces with statistical properties that deviate from the face photographs and approximate the scale-invariant, fractal-like properties of complex natural scenes. This result cannot be explained by systematic differences in the complexity of patterns surrounding the faces or by reproduction artifacts. In particular, a moderate change in gamma gradation has little influence on the results. Moreover, the scale-invariant rendering of faces in artists' portraits was found to be independent of cultural variables, such as century of origin or artistic techniques. We suggest that artists have implicit knowledge of image statistics and prefer natural scene statistics (or some other rules associated with them) in their creations. Fractal-like statistics have been demonstrated previously in other forms of visual art and may be a general attribute of esthetic visual stimuli.