The principal independent components of images

This paper proposes a new approach for the encoding of images by only a few important components. Classically, this is done by the Principal Component Analysis (PCA). Recently, the Independent Component Analysis (ICA) has found strong interest in the neural network community. Applied to images, we aim for the most important source patterns with the highest occurrence probability or highest information called principal independent components (PIC). For the example of a synthetic image composed by characters this idea selects the salient ones. For natural images it does not lead to an acceptable reproduction error since no a-priori probabilities can be computed. Combining the traditional principal component criteria of PCA with the independence property of ICA we obtain a better encoding. It turns out that this definition of PIC implements the classical demand of Shannon’s rate distortion theory

Image encoding by independent principal components

The encoding of images by semantic entities is still an unresolved task. This paper proposes the encoding of images by only a few important components or image primitives. Classically, this can be done by the Principal Component Analysis (PCA). Recently, the Independent Component Analysis (ICA) has found strong interest in the signal processing and neural network community. Using this as pattern primitives we aim for source patterns with the highest occurrence probability or highest information. For the example of a synthetic image composed by characters this idea selects the salient ones. For natural images it does not lead to an acceptable reproduction error since no a-priori probabilities can be computed. Combining the traditional principal component criteria of PCA with the independence property of ICA we obtain a better encoding. It turns out that the Independent Principal Components (IPC) in contrast to the Principal Independent Components (PIC) implement the classical demand of Shannon’s rate distortion theory

MASCOT: a mechanism for attention-based scale-invariant object recognition in images

The efficient management of large multimedia databases requires the development of new techniques to process, characterize, and search for multimedia objects. Especially in the case of image data, the rapidly growing amount of documents prohibits a manual description of the images’ content. Instead, the automated characterization is highly desirable to support annotation and retrieval of digital images. However, this is a very complex and still unsolved task. To contribute to a solution of this problem, we have developed a mechanism for recognizing objects in images based on the query by example paradigm. Therefore, the most salient image features of an example image representing the searched object are extracted to obtain a scale-invariant object model. The use of this model provides an efficient and robust strategy for recognizing objects in images independently of their size. Further applications of the mechanism are classical recognition tasks such as scene decomposition or object tracking in video sequences

Project SEMACODE : a scale-invariant object recognition system for content-based queries in image databases

For the efficient management of large image databases, the automated characterization of images and the usage of that characterization for searching and ordering tasks is highly desirable. The purpose of the project SEMACODE is to combine the still unsolved problem of content-oriented characterization of images with scale-invariant object recognition and modelbased compression methods. To achieve this goal, existing techniques as well as new concepts related to pattern matching, image encoding, and image compression are examined. The resulting methods are integrated in a common framework with the aid of a content-oriented conception. For the application, an image database at the library of the university of Frankfurt/Main (StUB; about 60000 images), the required operations are developed. The search and query interfaces are defined in close cooperation with the StUB project “Digitized Colonial Picture Library”. This report describes the fundamentals and first results of the image encoding and object recognition algorithms developed within the scope of the project

Quantum Critical Exponents for a Disordered Three-Dimensional Weyl Node

Three-dimensional Dirac and Weyl semimetals exhibit a disorder-induced quantum phase transition between a semimetallic phase at weak disorder and a diffusive-metallic phase at strong disorder. Despite considerable effort, both numerically and analytically, the critical exponents $\nu$ and $z$ of this phase transition are not known precisely. Here we report a numerical calculation of the critical exponent $\nu=1.47\pm0.03$ using a minimal single-Weyl node model and a finite-size scaling analysis of conductance. Our high-precision numerical value for $\nu$ is incompatible with previous numerical studies on tight-binding models and with one- and two-loop calculations in an $\epsilon$-expansion scheme. We further obtain $z=1.49\pm0.02$ from the scaling of the conductivity with chemical potential

Joint inversion scheme with an adaptive coupling strategy - applications on synthetic and real data sets

Joint inversion strategies for geophysical data have become increasingly popular since they allow to combine complementary information from different data sets in an efficient way. However, for joint inversion algorithms that use methods that are sensitive to different parameters it is important that they are not restricted to specific survey arrays and subsurface conditions. Hence, joint inversion schemes are needed that 1) adequately balance data from the different methods and 2) use links between the parameter models that are suited for a wide range of applications. Here, we combine MT, seismic tomography and gravity data in a non-linear joint inversion that accounts for these critical issues. Data from the different methods are inverted separately and are joined through constrains accounting for parameter relationships. An advantage of performing the inversions separately (and not together in one matrix) is that no relative weighting between the data sets is required. To avoid that the convergence behavior of the inversions is profoundly disturbed by the coupling, the strengths of the associated constraints are re-adjusted at each iteration. As criteria to control the adaption of the coupling strengths we used a general version of the well-known discrepancy principle. Adaption of the coupling strengths makes the joint inversion scheme also applicable to subsurface conditions, for which the assumed relationships are only a rough first order approximation. So, the coupling between the different parameter models is automatically reduced if for some structures the true rock property behaviors differ significantly from the assumed relationships (e.g. the atypical density-velocity behavior of salt). We have tested our scheme first on different synthetic 2-D models for which the assumed parameter relationships are everywhere valid. We observe that the adaption of the coupling strengths makes the convergence of the inversions very robust and that the final results are close to the true models. In a next step the scheme has been applied on models for which the assumed parameter relationships are invalid for some structures. For these structures deviations from the relationships are present in the final results; however, for the remaining structures the relative behaviors of the physical parameters are still approximately described by the assumed relationship. Finally, we applied our joint inversion scheme on seismic, MT and gravity data collected offshore the Faroe Islands, where basalt intrusions are present

Weyl node with random vector potential

We study Weyl semimetals in the presence of generic disorder, consisting of a random vector potential as well as a random scalar potential. We derive renormalization group flow equations to second order in the disorder strength. These flow equations predict a disorder-induced phase transition between a pseudo-ballistic weak-disorder phase and a diffusive strong-disorder phase for sufficiently strong random scalar potential or for a pure three-component random vector potential. We verify these predictions using a numerical study of the density of states near the Weyl point and of quantum transport properties at the Weyl point. In contrast, for a pure single-component random vector potential the diffusive strong-disorder phase is absent.Comment: published version with minor change