Local and Global Feature Extraction for Invariant Object Recognition

Perceiving the world visually is a basic act for humans, but for computers it is still an unsolved problem. The variability present innatural environments is an obstacle for effective computer vision. The goal of invariant object recognition is to recognise objects in a digital image despite variations in, for example, pose, lighting or occlusion. In this study, invariant object recognition is considered from the viewpoint of feature extraction. Thedifferences between local and global features are studied with emphasis on Hough transform and Gabor filtering based feature extraction. The methods are examined with respect to four capabilities: generality, invariance, stability, and efficiency. Invariant features are presented using both Hough transform and Gabor filtering. A modified Hough transform technique is also presented where the distortion tolerance is increased by incorporating local information. In addition, methods for decreasing the computational costs of the Hough transform employing parallel processing and local information are introduced.

Me Alexander I... Suuri Ruhtinas Suomen maasa... Wakutus-Kirja... Annettu Borgåsa sinä 15/27 päiwänä Maaliskuusa 1809

Turku 1809, Frenckell

Hans Kejserliga Majestäts Alexander I:s Tal hållet wid Landtdagens slut, i Borgå, den 6/18 Julii 1809 - [Titelsidan]

Åbo 1809, Frenckell

Hans Kejserliga Majestäts Alexander I:s Tal, hållet wid hyllningen i Borgå den 17/29 Martii 1809 - [Titelsidan]

Åbo 1809, Frenckell

Alexander II

London : Methuen & Co.Ltd 1915

Alexander Collan

Suolapaperivedos

A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: explorations and mechanisms for the breakdown of hyperbolicity

In two previous papers [J. Differential Equations, 228 (2006), pp. 530 579; Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), pp. 1261 1300] we have developed fast algorithms for the computations of invariant tori in quasi‐periodic systems and developed theorems that assess their accuracy. In this paper, we study the results of implementing these algorithms and study their performance in actual implementations. More importantly, we note that, due to the speed of the algorithms and the theoretical developments about their reliability, we can compute with confidence invariant objects close to the breakdown of their hyperbolicity properties. This allows us to identify a mechanism of loss of hyperbolicity and measure some of its quantitative regularities. We find that some systems lose hyperbolicity because the stable and unstable bundles approach each other but the Lyapunov multipliers remain away from 1. We find empirically that, close to the breakdown, the distances between the invariant bundles and the Lyapunov multipliers which are natural measures of hyperbolicity depend on the parameters, with power laws with universal exponents. We also observe that, even if the rigorous justifications in [J. Differential Equations, 228 (2006), pp. 530-579] are developed only for hyperbolic tori, the algorithms work also for elliptic tori in Hamiltonian systems. We can continue these tori and also compute some bifurcations at resonance which may lead to the existence of hyperbolic tori with nonorientable bundles. We compute manifolds tangent to nonorientable bundles.

On the computation of reducible invariant tori on a parallel computer

We present an algorithm for the computation of reducible invariant tori of discrete dynamical systems that is suitable for tori of dimensions larger than 1. It is based on a quadratically convergent scheme that approximates, at the same time, the Fourier series of the torus, its Floquet transformation, and its Floquet matrix. The Floquet matrix describes the linearization of the dynamics around the torus and, hence, its linear stability. The algorithm presents a high degree of parallelism, and the computational effort grows linearly with the number of Fourier modes needed to represent the solution. For these reasons it is a very good option to compute quasi-periodic solutions with several basic frequencies. The paper includes some examples (flows) to show the efficiency of the method in a parallel computer. In these flows we compute invariant tori of dimensions up to 5, by taking suitable sections.

För Alexander [Stemmat]

Soitinnus: orkesteri, sekakuoro.

Una propuesta de la integración psicocorporal a través de la técnica Alexander y la danza movimiento terapia

Este trabajo es una propuesta de integración de la Técnica Alexander y la Danza Movimiento Terapia. Partiendo de la realidad de que ambas técnicas tienen como objetivo final la integración de la dimensión de la psique, del cuerpo y de la emoción, para restaurar el equilibrio integral del ser humano que como consecuencia aporta un estado de salud al individuo. Cada una de ellas se posiciona sobre un camino diferente hacia la curación, aunque comparten muchas bases en común. Una de ellas trata del aprendizaje de un método: la Técnica Alexander, y la otra es una forma de psicoterapia para realizar un proceso terapéutico: la Danza Movimiento Terápia. Una se focaliza en la reeducación del uso psicofísico del individuo y en su interacción con el mundo interno y externo (TA) y el otro en la expresión y despliegue psico / corporal / emocional para la transformación y el desarrollo personal, y la curación del trauma (DMT). Como cada una de ellas ha desarrollado un aspecto más profundamente que otro, en el caso de la TA: la estructura psicofísica primaria y estructural orgánica, y la DMT: la emoción: su expresión y capacidad para la transformación. Y es estos aspectos más desarrollados que pueden enriquecer y desarrollar a la otra. Este texto aporta un estudio comparativo entre ambos métodos, los objetivos y la teoría que comparten como los aspectos en los que divergen. Finalmente se propone una hipótesis de integración de la TA, como técnica base de formación psicocorporal del estudiante dentro de un programa de formación de la DMT, y la DMT como técnica psicoterapéutica de acompañamiento de los estudiantes en formación de profesores de la TA.

Tool-supported invariant-based programming

The development of correct programs is a core problem in computer science. Although formal verification methods for establishing correctness with mathematical rigor are available, programmers often find these difficult to put into practice. One hurdle is deriving the loop invariants and proving that the code maintains them. So called correct-by-construction methods aim to alleviate this issue by integrating verification into the programming workflow. Invariant-based programming is a practical correct-by-construction method in which the programmer first establishes the invariant structure, and then incrementally extends the program in steps of adding code and proving after each addition that the code is consistent with the invariants. In this way, the program is kept internally consistent throughout its development, and the construction of the correctness arguments (proofs) becomes an integral part of the programming workflow. A characteristic of the approach is that programs are described as invariant diagrams, a graphical notation similar to the state charts familiar to programmers. Invariant-based programming is a new method that has not been evaluated in large scale studies yet. The most important prerequisite for feasibility on a larger scale is a high degree of automation. The goal of the Socos project has been to build tools to assist the construction and verification of programs using the method. This thesis describes the implementation and evaluation of a prototype tool in the context of the Socos project. The tool supports the drawing of the diagrams, automatic derivation and discharging of verification conditions, and interactive proofs. It is used to develop programs that are correct by construction. The tool consists of a diagrammatic environment connected to a verification condition generator and an existing state-of-the-art theorem prover. Its core is a semantics for translating diagrams into verification conditions, which are sent to the underlying theorem prover. We describe a concrete method for 1) deriving sufficient conditions for total correctness of an invariant diagram; 2) sending the conditions to the theorem prover for simplification; and 3) reporting the results of the simplification to the programmer in a way that is consistent with the invariantbased programming workflow and that allows errors in the program specification to be efficiently detected. The tool uses an efficient automatic proof strategy to prove as many conditions as possible automatically and lets the remaining conditions be proved interactively. The tool is based on the verification system PVS and i uses the SMT (Satisfiability Modulo Theories) solver Yices as a catch-all decision procedure. Conditions that were not discharged automatically may be proved interactively using the PVS proof assistant. The programming workflow is very similar to the process by which a mathematical theory is developed inside a computer supported theorem prover environment such as PVS. The programmer reduces a large verification problem with the aid of the tool into a set of smaller problems (lemmas), and he can substantially improve the degree of proof automation by developing specialized background theories and proof strategies to support the specification and verification of a specific class of programs. We demonstrate this workflow by describing in detail the construction of a verified sorting algorithm. Tool-supported verification often has little to no presence in computer science (CS) curricula. Furthermore, program verification is frequently introduced as an advanced and purely theoretical topic that is not connected to the workflow taught in the early and practically oriented programming courses. Our hypothesis is that verification could be introduced early in the CS education, and that verification tools could be used in the classroom to support the teaching of formal methods. A prototype of Socos has been used in a course at Åbo Akademi University targeted at first and second year undergraduate students. We evaluate the use of Socos in the course as part of a case study carried out in 2007.