@inproceedings{BrackxDeKnockDeSchepper,
  author    = {Brackx, Fred and De Knock, B. and De Schepper, Hennie},
  title     = {A MULTI--DIMENSIONAL HILBERT TRANSFORM IN ANISOTROPIC CLIFFORD ANALYSIS},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.2929},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29297},
  pages     = {15},
  abstract  = {In earlier research, generalized multidimensional Hilbert transforms have been constructed in m-dimensional Euclidean space, in the framework of Clifford analysis. Clifford analysis, centred around the notion of monogenic functions, may be regarded as a direct and elegant generalization to higher dimension of the theory of the holomorphic functions in the complex plane. The considered Hilbert transforms, usually obtained as a part of the boundary value of an associated Cauchy transform in m+1 dimensions, might be characterized as isotropic, since the metric in the underlying space is the standard Euclidean one. In this paper we adopt the idea of a so-called anisotropic Clifford setting, which leads to the introduction of a metric dependent m-dimensional Hilbert transform, showing, at least formally, the same properties as the isotropic one. The Hilbert transform being an important tool in signal analysis, this metric dependent setting has the advantage of allowing the adjustment of the co-ordinate system to possible preferential directions in the signals to be analyzed. A striking result to be mentioned is that the associated anisotropic (m+1)-dimensional Cauchy transform is no longer uniquely determined, but may stem from a diversity of (m+1)-dimensional "mother" metrics.},
  subject      = {Architektur <Informatik>},
  language  = {en}
}
@inproceedings{BrackxDeSchepperDeSchepperetal.,
  author    = {Brackx, Fred and De Schepper, Hennie and De Schepper, Nele and Sommen, Frank},
  title     = {HERMITIAN CLIFFORD-HERMITE WAVELETS},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.2931},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29313},
  pages     = {13},
  abstract  = {The one-dimensional continuous wavelet transform is a successful tool for signal and image analysis, with applications in physics and engineering. Clifford analysis offers an appropriate framework for taking wavelets to higher dimension. In the usual orthogonal case Clifford analysis focusses on monogenic functions, i.e. null solutions of the rotation invariant vector valued Dirac operator ∂, defined in terms of an orthogonal basis for the quadratic space Rm underlying the construction of the Clifford algebra R0,m. An intrinsic feature of this function theory is that it encompasses all dimensions at once, as opposed to a tensorial approach with products of one-dimensional phenomena. This has allowed for a very specific construction of higher dimensional wavelets and the development of the corresponding theory, based on generalizations of classical orthogonal polynomials on the real line, such as the radial Clifford-Hermite polynomials introduced by Sommen. In this paper, we pass to the Hermitian Clifford setting, i.e. we let the same set of generators produce the complex Clifford algebra C2n (with even dimension), which we equip with a Hermitian conjugation and a Hermitian inner product. Hermitian Clifford analysis then focusses on the null solutions of two mutually conjugate Hermitian Dirac operators which are invariant under the action of the unitary group. In this setting we construct new Clifford-Hermite polynomials, starting in a natural way from a Rodrigues formula which now involves both Dirac operators mentioned. Due to the specific features of the Hermitian setting, four different types of polynomials are obtained, two types of even degree and two types of odd degree. These polynomials are used to introduce a new continuous wavelet transform, after thorough investigation of all necessary properties of the involved polynomials, the mother wavelet and the associated family of wavelet kernels.},
  subject      = {Architektur <Informatik>},
  language  = {en}
}
@inproceedings{BrackxDeSchepperSommen,
  author    = {Brackx, Fred and De Schepper, Nele and Sommen, Frank},
  title     = {Clifford-Hermite and Two-Dimensional Clifford-Gabor Filters For Early Vision},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.2930},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29303},
  pages     = {22},
  abstract  = {Image processing has been much inspired by the human vision, in particular with regard to early vision. The latter refers to the earliest stage of visual processing responsible for the measurement of local structures such as points, lines, edges and textures in order to facilitate subsequent interpretation of these structures in higher stages (known as high level vision) of the human visual system. This low level visual computation is carried out by cells of the primary visual cortex. The receptive field profiles of these cells can be interpreted as the impulse responses of the cells, which are then considered as filters. According to the Gaussian derivative theory, the receptive field profiles of the human visual system can be approximated quite well by derivatives of Gaussians. Two mathematical models suggested for these receptive field profiles are on the one hand the Gabor model and on the other hand the Hermite model which is based on analysis filters of the Hermite transform. The Hermite filters are derivatives of Gaussians, while Gabor filters, which are defined as harmonic modulations of Gaussians, provide a good approximation to these derivatives. It is important to note that, even if the Gabor model is more widely used than the Hermite model, the latter offers some advantages like being an orthogonal basis and having better match to experimental physiological data. In our earlier research both filter models, Gabor and Hermite, have been developed in the framework of Clifford analysis. Clifford analysis offers a direct, elegant and powerful generalization to higher dimension of the theory of holomorphic functions in the complex plane. In this paper we expose the construction of the Hermite and Gabor filters, both in the classical and in the Clifford analysis framework. We also generalize the concept of complex Gaussian derivative filters to the Clifford analysis setting. Moreover, we present further properties of the Clifford-Gabor filters, such as their relationship with other types of Gabor filters and their localization in the spatial and in the frequency domain formalized by the uncertainty principle.},
  subject      = {Architektur <Informatik>},
  language  = {en}
}
@inproceedings{BraunesDonath,
  author    = {Braunes, J{\"o}rg and Donath, Dirk},
  title     = {COMPUTERGEST{\"U}TZTE PLANUNG IM BESTAND VON DER DIGITALEN BESTANDSERFASSUNG ZUR PLANUNGSUNTERST{\"U}TZUNG IM CAAD},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.2933},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29338},
  pages     = {10},
  abstract  = {F{\"u}r eine gesicherte Planung im Bestand, sind eine F{\"u}lle verschiedenster Informationen zu ber{\"u}cksichtigen, welche oft erst w{\"a}hrend des Planungs- oder Bauprozesses gewonnen werden. Voraussetzung hierf{\"u}r bildet immer eine Bestandserfassung. Zwar existieren Computerprogramme zur Unterst{\"u}tzung der Bestandserfassung, allerdings handelt es sich hierbei ausschließlich um Insell{\"o}sungen. Der Export der aufgenommenen Daten in ein Planungssystem bedingt Informationsverluste. Trotz der potentiellen M{\"o}glichkeit aktueller CAAD/BIM Systeme zur Verwaltung von Bestandsdaten, sind diese vorrangig f{\"u}r die Neubauplanung konzipiert. Die durchg{\"a}ngige Bearbeitung von Sanierungsprojekten von der Erfassung des Bestandes {\"u}ber die Entwurfs- und Genehmigungsplanung bis zur Ausf{\"u}hrungsplanung innerhalb eines CAAD/BIM Systems wird derzeit nicht ad{\"a}quat unterst{\"u}tzt. An der Professur Informatik in der Architektur (InfAR) der Fakult{\"a}t Architektur der Bauhaus-Universit{\"a}t Weimar entstanden im Rahmen des DFG Sonderforschungsbereich 524 "Werkzeuge und Konstruktionen f{\"u}r die Revitalisierung von Bauwerken" in den letzten Jahren Konzepte und Prototypen zur fachlich orientierten Unterst{\"u}tzung der Planung im Bestand. Der Fokus lag dabei in der Erfassung aller planungsrelevanter Bestandsdaten und der Abbildung dieser in einem dynamischen Bauwerksmodell. Aufbauend auf diesen Forschungsarbeiten befasst sich der Artikel mit der kontextbezogenen Weiterverwendung und gezielten Bereitstellung von Bestandsdaten im Prozess des Planens im Bestand und der Integration von Konzepten der planungsrelevanten Bestandserfassung in markt{\"u}bliche CAAD/BIM Systeme.},
  subject      = {Architektur <Informatik>},
  language  = {de}
}
@inproceedings{BrossmannMueller,
  author    = {Broßmann, Marko and M{\"u}ller, Karl-Heinz},
  title     = {STOCHASTISCHE ANALYSE VON STAHLBETONBALKEN IM GRENZZUSTAND DER ADAPTION UNTER BER{\"u}CKSICHTIGUNG DER STEIFIGKEITSDEGRADATION},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.2934},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29341},
  pages     = {20},
  abstract  = {Am Beispiel eines 3-feldrigen Durchlauftr{\"a}gers wird die Versagenswahrscheinlichkeit von wechselnd belasteten Stahlbetonbalken bez{\"u}glich des Grenzzustandes der Adaption (Einspielen, shakedown) untersucht. Die Adaptionsanalyse erfolgt unter Ber{\"u}cksichtigung der beanspruchungschabh{\"a}ngigen Degradation der Biegesteifigkeit infolge Rissbildung. Die damit verbundene mechanische Problemstellung kann auf die Adaptionsanalyse linear elastisch - ideal plastischer Balkentragwerke mit unbekannter aber begrenzter Biegesteifigkeit zur{\"u}ckgef{\"u}hrt werden. Die Versagenswahrscheinlichkeit wird unter Ber{\"u}cksichtigung stochastischer Tragwerks- und Belastungsgr{\"o}ßen berechnet. Tragwerkseigenschaften und st{\"a}ndige Lasten gelten als zeitunabh{\"a}ngige Zufallsgr{\"o}ßen. Zeitlich ver{\"a}nderliche Lasten werden als nutzungsdauerbezogene Extremwerte POISSONscher Rechteck-Pulsprozesse unter Ber{\"u}cksichtigung zeitlicher {\"U}berlagerungseffekte modelliert, so dass die Versagenswahrscheinlichkeit ebenfalls eine nutzungsdauerbezogene Gr{\"o}ße ist. Die mechanischen Problemstellungen werden numerisch mit der mathematischen Optimierung gel{\"o}st. Die Versagenswahrscheinlichkeit wird auf statistischem Weg mit der Monte-Carlo-Methode gesch{\"a}tzt.},
  subject      = {Architektur <Informatik>},
  language  = {de}
}
@inproceedings{BultheelJansenMaesetal.,
  author    = {Bultheel, Adhemar and Jansen, M. and Maes, J. and Van Aerschot, W. and Vanraes, E.},
  title     = {SUBDIVIDE AND CONQUER RESOLUTION},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.2909},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29091},
  pages     = {47},
  abstract  = {This contribution will be freewheeling in the domain of signal, image and surface processing and touch briefly upon some topics that have been close to the heart of people in our research group. A lot of the research of the last 20 years in this domain that has been carried out world wide is dealing with multiresolution. Multiresolution allows to represent a function (in the broadest sense) at different levels of detail. This was not only applied in signals and images but also when solving all kinds of complex numerical problems. Since wavelets came into play in the 1980's, this idea was applied and generalized by many researchers. Therefore we use this as the central idea throughout this text. Wavelets, subdivision and hierarchical bases are the appropriate tools to obtain these multiresolution effects. We shall introduce some of the concepts in a rather informal way and show that the same concepts will work in one, two and three dimensions. The applications in the three cases are however quite different, and thus one wants to achieve very different goals when dealing with signals, images or surfaces. Because completeness in our treatment is impossible, we have chosen to describe two case studies after introducing some concepts in signal processing. These case studies are still the subject of current research. The first one attempts to solve a problem in image processing: how to approximate an edge in an image efficiently by subdivision. The method is based on normal offsets. The second case is the use of Powell-Sabin splines to give a smooth multiresolution representation of a surface. In this context we also illustrate the general method of construction of a spline wavelet basis using a lifting scheme.},
  subject      = {Architektur <Informatik>},
  language  = {en}
}
@inproceedings{CacaoConstalesKrausshar,
  author    = {Cacao, Isabel and Constales, Denis and Kraußhar, Rolf S{\"o}ren},
  title     = {BESSEL FUNCTIONS AND HIGHER DIMENSIONAL DIRAC TYPE EQUATIONS},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.2936},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29366},
  pages     = {8},
  abstract  = {In this paper we study the structure of the solutions to higher dimensional Dirac type equations generalizing the known λ-hyperholomorphic functions, where λ is a complex parameter. The structure of the solutions to the system of partial differential equations (D- λ) f=0 show a close connection with Bessel functions of first kind with complex argument. The more general system of partial differential equations that is considered in this paper combines Dirac and Euler operators and emphasizes the role of the Bessel functions. However, contrary to the simplest case, one gets now Bessel functions of any arbitrary complex order.},
  subject      = {Architektur <Informatik>},
  language  = {en}
}
@inproceedings{ChangChang,
  author    = {Chang, Wei-Tsang and Chang, Teng-Wen},
  title     = {TIME-BASED FORM TRANSFORMATION WITH FOLDING SPACE},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.2937},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29371},
  pages     = {10},
  abstract  = {Design activity could be treated as state transition computationally. In stepwise processing, in-between form-states are not easily observed. However, in this research time-based concept is introduced and applied in order to bridge the gap. In architecture, folding is one method of form manipulation and architects also want to search for alternatives by this operation. Besides, folding operation has to be defined and parameterized before time factor is involved as a variable of folding. As a result, time-based transformation provides sequential form states and redirects design activity.},
  subject      = {Architektur <Informatik>},
  language  = {en}
}
@inproceedings{ConstalesKrausshar,
  author    = {Constales, Denis and Kraußhar, Rolf S{\"o}ren},
  title     = {ON THE NAVIER-STOKES EQUATION WITH FREE CONVECTION IN STRIP DOMAINS AND 3D TRIANGULAR CHANNELS},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.2938},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29387},
  pages     = {12},
  abstract  = {The Navier-Stokes equations and related ones can be treated very elegantly with the quaternionic operator calculus developed in a series of works by K. Guerlebeck, W. Sproeossig and others. This study will be extended in this paper. In order to apply the quaternionic operator calculus to solve these types of boundary value problems fully explicitly, one basically needs to evaluate two types of integral operators: the Teodorescu operator and the quaternionic Bergman projector. While the integral kernel of the Teodorescu transform is universal for all domains, the kernel function of the Bergman projector, called the Bergman kernel, depends on the geometry of the domain. With special variants of quaternionic holomorphic multiperiodic functions we obtain explicit formulas for three dimensional parallel plate channels, rectangular block domains and regular triangular channels. The explicit knowledge of the integral kernels makes it then possible to evaluate the operator equations in order to determine the solutions of the boundary value problem explicitly.},
  subject      = {Architektur <Informatik>},
  language  = {en}
}
@inproceedings{CruzFalcaoMalonek,
  author    = {Cruz, J. F. and Falc{\~a}o, M. Irene and Malonek, Helmuth Robert},
  title     = {3D-MAPPINGS AND THEIR APPROXIMATION BY SERIES OF POWERS OF A SMALL PARAMETER},
  editor    = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten},
  organization    = {Bauhaus-Universit{\"a}t Weimar},
  doi       = {10.25643/bauhaus-universitaet.2940},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29406},
  pages     = {14},
  abstract  = {In classical complex function theory the geometric mapping property of conformality is closely linked with complex differentiability. In contrast to the planar case, in higher dimensions the set of conformal mappings is only the set of M{\"o}bius transformations. Unfortunately, the theory of generalized holomorphic functions (by historical reasons they are called monogenic functions) developed on the basis of Clifford algebras does not cover the set of M{\"o}bius transformations in higher dimensions, since M{\"o}bius transformations are not monogenic. But on the other side, monogenic functions are hypercomplex differentiable functions and the question arises if from this point of view they can still play a special role for other types of 3D-mappings, for instance, for quasi-conformal ones. On the occasion of the 16th IKM 3D-mapping methods based on the application of Bergman's reproducing kernel approach (BKM) have been discussed. Almost all authors working before that with BKM in the Clifford setting were only concerned with the general algebraic and functional analytic background which allows the explicit determination of the kernel in special situations. The main goal of the abovementioned contribution was the numerical experiment by using a Maple software specially developed for that purpose. Since BKM is only one of a great variety of concrete numerical methods developed for mapping problems, our goal is to present a complete different from BKM approach to 3D-mappings. In fact, it is an extension of ideas of L. V. Kantorovich to the 3-dimensional case by using reduced quaternions and some suitable series of powers of a small parameter. Whereas until now in the Clifford case of BKM the recovering of the mapping function itself and its relation to the monogenic kernel function is still an open problem, this approach avoids such difficulties and leads to an approximation by monogenic polynomials depending on that small parameter.},
  subject      = {Architektur <Informatik>},
  language  = {en}
}