Quantum Kolmogorov Complexity

In this paper we give a definition for quantum Kolmogorov complexity. In the classical setting, the Kolmogorov complexity of a string is the length of the shortest program that can produce this string as its output. It is a measure of the amount of innate randomness (or information) contained in the string. We define the quantum Kolmogorov complexity of a qubit string as the length of the shortest quantum input to a universal quantum Turing machine that produces the initial qubit string with high fidelity. The definition of Vitanyi (Proceedings of the 15th IEEE Annual Conference on Computational Complexity, 2000) measures the amount of classical information, whereas we consider the amount of quantum information in a qubit string. We argue that our definition is natural and is an accurate representation of the amount of quantum information contained in a quantum state.Comment: 14 pages, LaTeX2e, no figures, \usepackage{amssymb,a4wide}. To appear in the Proceedings of the 15th IEEE Annual Conference on Computational Complexit

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

Black-Box Complexity: Breaking the O(nlog⁡n)O(n \log n) Barrier of LeadingOnes

We show that the unrestricted black-box complexity of the $n$-dimensional XOR- and permutation-invariant LeadingOnes function class is $O(n \log (n) / \log \log n)$. This shows that the recent natural looking $O(n\log n)$ bound is not tight. The black-box optimization algorithm leading to this bound can be implemented in a way that only 3-ary unbiased variation operators are used. Hence our bound is also valid for the unbiased black-box complexity recently introduced by Lehre and Witt (GECCO 2010). The bound also remains valid if we impose the additional restriction that the black-box algorithm does not have access to the objective values but only to their relative order (ranking-based black-box complexity).Comment: 12 pages, to appear in the Proc. of Artificial Evolution 2011, LNCS 7401, Springer, 2012. For the unrestricted black-box complexity of LeadingOnes there is now a tight $\Theta(n \log\log n)$ bound, cf. http://eccc.hpi-web.de/report/2012/087

Temporal Extension of Scale Pyramid and Spatial Pyramid Matching for Action Recognition

Historically, researchers in the field have spent a great deal of effort to create image representations that have scale invariance and retain spatial location information. This paper proposes to encode equivalent temporal characteristics in video representations for action recognition. To achieve temporal scale invariance, we develop a method called temporal scale pyramid (TSP). To encode temporal information, we present and compare two methods called temporal extension descriptor (TED) and temporal division pyramid (TDP) . Our purpose is to suggest solutions for matching complex actions that have large variation in velocity and appearance, which is missing from most current action representations. The experimental results on four benchmark datasets, UCF50, HMDB51, Hollywood2 and Olympic Sports, support our approach and significantly outperform state-of-the-art methods. Most noticeably, we achieve 65.0% mean accuracy and 68.2% mean average precision on the challenging HMDB51 and Hollywood2 datasets which constitutes an absolute improvement over the state-of-the-art by 7.8% and 3.9%, respectively

Pooling-Invariant Image Feature Learning

Unsupervised dictionary learning has been a key component in state-of-the-art computer vision recognition architectures. While highly effective methods exist for patch-based dictionary learning, these methods may learn redundant features after the pooling stage in a given early vision architecture. In this paper, we offer a novel dictionary learning scheme to efficiently take into account the invariance of learned features after the spatial pooling stage. The algorithm is built on simple clustering, and thus enjoys efficiency and scalability. We discuss the underlying mechanism that justifies the use of clustering algorithms, and empirically show that the algorithm finds better dictionaries than patch-based methods with the same dictionary size

Land cover mapping at very high resolution with rotation equivariant CNNs: towards small yet accurate models

In remote sensing images, the absolute orientation of objects is arbitrary. Depending on an object's orientation and on a sensor's flight path, objects of the same semantic class can be observed in different orientations in the same image. Equivariance to rotation, in this context understood as responding with a rotated semantic label map when subject to a rotation of the input image, is therefore a very desirable feature, in particular for high capacity models, such as Convolutional Neural Networks (CNNs). If rotation equivariance is encoded in the network, the model is confronted with a simpler task and does not need to learn specific (and redundant) weights to address rotated versions of the same object class. In this work we propose a CNN architecture called Rotation Equivariant Vector Field Network (RotEqNet) to encode rotation equivariance in the network itself. By using rotating convolutions as building blocks and passing only the the values corresponding to the maximally activating orientation throughout the network in the form of orientation encoding vector fields, RotEqNet treats rotated versions of the same object with the same filter bank and therefore achieves state-of-the-art performances even when using very small architectures trained from scratch. We test RotEqNet in two challenging sub-decimeter resolution semantic labeling problems, and show that we can perform better than a standard CNN while requiring one order of magnitude less parameters