Hanns Schulz-Mirbach

Bio: Hanns Schulz-Mirbach is an academic researcher from University of Hamburg. The author has contributed to research in topics: Invariant (mathematics) & Primary field. The author has an hindex of 3, co-authored 3 publications receiving 207 citations.

Haag duality in conformal quantum field theory

Abstract: Haag duality is established in conformal quantum field theory for observable fields on the compactified light ray S1 and Minkowski space S1×S1, respectively. This result provides the foundation for an algebraic approach to the classification of conformal theories. Haag duality can fail, however, for the restriction of conformal fields to the underlying non-compact spaces ℝ, respectively ℝ×ℝ. A prominent example is the stress energy tensor with central charge c>1.

Invariant Features for Gray Scale Images

Abstract: Invariant features are image characteristics which remain unchanged under the action of a transformation group. We consider in this paper image rotations and translations and present algorithms for constructing invariant features. After briefly sketching the theoretical background we develop algorithms for recognizing several objects in a single scene without the necessity to segment the image beforehand. The objects can be rotated and translated independently. Moderate occlusions are tolerable. Furthermore we show how to use these techniques for the recognition of articulated objects. The methods work directly with the gray values and do not rely on the extraction of geometric primitives like edges or corners in a preprocessing step. All algorithms have been implemented and tested both on synthetic and real image data. We present some illustrative experimental results.

Fast Adaptive Calculation of Invariant Features

Abstract: The paper presents algorithms for the fast adaptive calculation of invariant features. These are pattern characteristics that remain unchanged under the action of a transformation group. First it is explained how to construct such features by integrating complex valued functions over the transformation group. Motivated by this technique we devise algorithms for adaptively calculating invariant features especially suited for a given application. The basic tool is a new network structure with adaptable nodes allowing the fast calculation of an invariant feature with the computational complexity of cal O(N) (N the size of the input data). The algorithms have been implemented and tested both on real and synthetic data. By an experimental comparison with other techniques for calculating invariants we elucidate the abilities of our adaptive algorithms.

Features for image retrieval: an experimental comparison

Abstract: An experimental comparison of a large number of different image descriptors for content-based image retrieval is presented. Many of the papers describing new techniques and descriptors for content-based image retrieval describe their newly proposed methods as most appropriate without giving an in-depth comparison with all methods that were proposed earlier. In this paper, we first give an overview of a large variety of features for content-based image retrieval and compare them quantitatively on four different tasks: stock photo retrieval, personal photo collection retrieval, building retrieval, and medical image retrieval. For the experiments, five different, publicly available image databases are used and the retrieval performance of the features is analyzed in detail. This allows for a direct comparison of all features considered in this work and furthermore will allow a comparison of newly proposed features to these in the future. Additionally, the correlation of the features is analyzed, which opens the way for a simple and intuitive method to find an initial set of suitable features for a new task. The article concludes with recommendations which features perform well for what type of data. Interestingly, the often used, but very simple, color histogram performs well in the comparison and thus can be recommended as a simple baseline for many applications.

Nets of subfactors

Abstract: A subtheory of a quantum field theory specifies von Neumann subalgebras $\mathcal{A(O)}$ (the ‘observables’ in the space-time region ${\mathcal O}$) of the von Neumann algebras $\mathcal{B(O)}$ (the 'field' localized in ${\mathcal O}$). Every local algebra being a (type III1) factor, the inclusion $\mathcal{A(O)} \subset \mathcal{B(O)}$ is a subfactor. The assignment of these local subfactors to the space-time regions is called a ‘net of subfactors’. The theory of subfactors is applied to such nets. In order to characterize the ‘relative position’ of the subtheory, and in particular to control the restriction and induction of superselection sectors, the canonical endomorphism is studied. The crucial observation is this: the canonical endomorphism of a single local subfactor extends to an endomorphism of the field net, which in turn restricts to a localized endomorphism of the observable net. The method allows one to characterize, and reconstruct, local extensions ℬ of a given theory ${\mathcal A}$ in term...

Integral Invariants for Shape Matching

Abstract: For shapes represented as closed planar contours, we introduce a class of functionals which are invariant with respect to the Euclidean group and which are obtained by performing integral operations. While such integral invariants enjoy some of the desirable properties of their differential counterparts, such as locality of computation (which allows matching under occlusions) and uniqueness of representation (asymptotically), they do not exhibit the noise sensitivity associated with differential quantities and, therefore, do not require presmoothing of the input shape. Our formulation allows the analysis of shapes at multiple scales. Based on integral invariants, we define a notion of distance between shapes. The proposed distance measure can be computed efficiently and allows warping the shape boundaries onto each other; its computation results in optimal point correspondence as an intermediate step. Numerical results on shape matching demonstrate that this framework can match shapes despite the deformation of subparts, missing parts and noise. As a quantitative analysis, we report matching scores for shape retrieval from a database

Operator algebras and conformal field theory

Abstract: We define and study two-dimensional, chiral conformal field theory by the methods of algebraic field theory. We start by characterizing the vacuum sectors of such theories and show that, under very general hypotheses, their algebras of local observables are isomorphic to the unique hyperfinite type III1 factor. The conformal net determined by the algebras of local observables is proven to satisfy Haag duality. The representation of the Moebius group (and presumably of the entire Virasoro algebra) on the vacuum sector of a conformal field theory is uniquely determined by the Tomita-Takesaki modular operators associated with its vacuum state and its conformal net. We then develop the theory of Moebius covariant representations of a conformal net, using methods of Doplicher, Haag and Roberts. We apply our results to the representation theory of loop groups. Our analysis is motivated by the desire to find a “background-independent” formulation of conformal field theories.

Robust vision-based localization by combining an image-retrieval system with Monte Carlo localization

Abstract: In this paper, we present a vision-based approach to mobile robot localization that integrates an image-retrieval system with Monte Carlo localization. The image-retrieval process is based on features that are invariant with respect to image translations and limited scale. Since it furthermore uses local features, the system is robust against distortion and occlusions, which is especially important in populated environments. To integrate this approach with the sample-based Monte Carlo localization technique, we extract for each image in the database a set of possible viewpoints using a two-dimensional map of the environment. Our technique has been implemented and tested extensively. We present practical experiments illustrating that our approach is able to globally localize a mobile robot, to reliably keep track of the robot's position, and to recover from localization failures. We furthermore present experiments designed to analyze the reliability and robustness of our approach with respect to larger errors in the odometry.