Regularization Schema Research Articles

Dense monocular Simultaneous Localization and Mapping by direct surfel optimization

This work presents a novel approach for monocular dense Simultaneous Localization and Mapping. The surface to be estimated is represented as a piecewise planar surface, defined as a group of surfels each having as parameters its position and normal. These parameters are then directly estimated from the raw camera pixels measurements, by a Gauss-Newton iterative process. The representation of the surface as a group of surfels has several advantages. It allows the recovery of robust and accurate pixel depths, without the need to use a computationally demanding depth regularization schema. This has the further advantage of avoiding the use of a physically unlikely surface smoothness prior. New surfels can be correctly initialized from the information present in nearby surfels, avoiding also the need to use an expensive initialization routine commonly needed in Gauss-Newton methods. The method was written in the GLSL shading language, allowing the usage of GPU thus achieving real-time. The method was tested against several datasets, showing both its depth and normal estimation correctness, and its scene reconstruction quality. The results presented here showcase the usefulness of the more physically grounded piecewise planar scene depth prior, instead of the more commonly pixel depth independence and smoothness prior.

On Fractional Asymptotical Regularization of Linear Ill-Posed Problems in Hilbert Spaces

Abstract In this paper, we study a fractional-order variant of the asymptotical regularization method, called Fractional Asymptotical Regularization (FAR), for solving linear ill-posed operator equations in a Hilbert space setting. We assign the method to the general linear regularization schema and prove that under certain smoothness assumptions, FAR with fractional order in the range (1, 2) yields an acceleration with respect to comparable order optimal regularization methods. Based on the one-step Adams-Moulton method, a novel iterative regularization scheme is developed for the numerical realization of FAR. Two numerical examples are given to show the accuracy and the acceleration effect of FAR.

Hyperspectral Image Restoration via Iteratively Regularized Weighted Schatten <inline-formula> <tex-math notation="LaTeX">$p$</tex-math> </inline-formula>-Norm Minimization

Hyperspectral images (HSIs) are inevitably corrupted by mixture noise during their acquisition process, in which various kinds of noise, e.g., Gaussian noise, impulse noise, dead lines, and stripes, may exist concurrently. In this paper, mixture noise removal is well illustrated by the task of recovering the low-rank and sparse components of a given matrix, which is constructed by stacking vectorized HSI patches from all the bands at the same position. Instead of applying a traditional nuclear norm, a nonconvex low-rank regularizer, i.e., weighted Schatten p -norm (WSN), is introduced to not only give better approximation to the original low-rank assumption but also to consider the importance of different rank components. The resulted nonconvex low-rank matrix approximation (LRMA) model falls into the applicable scope of an augmented Lagrangian method, and its WSN minimization subproblem can be efficiently solved by generalized iterated shrinkage algorithm. Moreover, the proposed model is integrated into an iterative regularization schema to produce final results, leading to a completed HSI restoration framework. Extensive experimental testing on simulated and real data shows, both qualitatively and quantitatively, that the proposed method has achieved highly competent objective performance compared with several state-of-the-art HSI restoration methods.

Towards a Normal Form and a Query Language for Extended Relations Defined by Regular Expressions

This paper introduces a generalized data base concept that unites relational and semi structured data models. As an important theoretical result we could find a quadratic decision algorithm for the implication problem of functional and join dependencies defined on the united data model. As practical contribution we presented a normal form for the new data model as a tool for data base design. With our novel representations of regular expressions, a more effective searching method could be developed. XML elements are described by XML schema languages such as a DTD or an XML Schema definition. The instances of these elements are semi-structured tuples. A semi-structured tuple is an ordered list of (attribute: value) pairs. We may think of a semi-structured tuple as a sentence of a formal language, where the values are the terminal symbols and the attribute names are the non-terminal symbols. In the authors' former work (Szabó and Benczúr, 2015) they introduced the notion of the extended tuple as a sentence from a regular language generated by a grammar where the non-terminal symbols of the grammar are the attribute names of the tuple. Sets of extended tuples are the extended relations. The authors then introduced the dual language, which generates the tuple types allowed to occur in extended relations. They defined functional dependencies (regular FD - RFD) over extended relations. In this paper they rephrase the RFD concept by directly using regular expressions over attribute names to define extended tuples. By the help of a special vertex labeled graph associated to regular expressions the specification of substring selection for the projection operation can be defined. The normalization for regular schemas is more complex than it is in the relational model, because the schema of an extended relation can contain an infinite number of tuple types. However, the authors can define selection, projection and join operations on extended relations too, so a lossless-join decomposition can be performed. They extended their previous model to deal with XML schema indicators too, e.g., with numerical constraints. They added line and set constructors too, in order to extend their model with more general projection and selection operators. This model establishes a query language with table join functionality for collected XML element data.

Tikhonov, Ivanov and Morozov regularization for support vector machine learning

Learning according to the structural risk minimization principle can be naturally expressed as an Ivanov regularization problem. Vapnik himself pointed out this connection, when deriving an actual learning algorithm from this principle, like the well-known support vector machine, but quickly suggested to resort to a Tikhonov regularization schema, instead. This was, at that time, the best choice because the corresponding optimization problem is easier to solve and in any case, under certain hypothesis, the solutions obtained by the two approaches coincide. On the other hand, recent advances in learning theory clearly show that the Ivanov regularization scheme allows a more effective control of the learning hypothesis space and, therefore, of the generalization ability of the selected hypothesis. We prove in this paper the equivalence between the Ivanov and Tikhonov approaches and, for the sake of completeness, their connection to Morozov regularization, which has been show to be useful when effective estimation of the noise in the data is available. We also show that this equivalence is valid under milder conditions on the loss function with respect to Vapnik's original proposal. These results allows us to derive several methods for performing SRM learning according to an Ivanov or Morozov regularization scheme, but using Tikhonov-based solvers, which have been thoroughly studied in the last decades and for which very efficient implementations have been proposed.

Sharp converse results for the regularization error using distance functions

In the analysis of ill-posed inverse problems the impact of solution smoothness on accuracy and convergence rates plays an important role. For linear ill-posed operator equations in Hilbert spaces and with focus on the linear regularization schema we will establish relations between different kinds of measuring solution smoothness in a point-wise or integral manner. In particular, we discuss the interplay of distribution functions, profile functions that express the regularization error, index functions generating source conditions and distance functions associated with benchmark source conditions. We show that typically the distance functions and the profile functions carry the same information as the distribution functions, and that this is not the case for general source conditions. The theoretical findings are accompanied with examples exhibiting applications and limitations of the approach. A detailed understanding of solution smoothness will also be helpful for the treatment and convergence analysis of nonlinear ill-posed problems.

Openness in shared hypermedia workspaces

Group work requires much flexibility regarding both the organization of shared workspaces and the organization of collaborative work. Shared hypermedia workspaces can provide this flexibility. However, this requires the provision of openness with respect to both the hypermedia workspace and the collaboration support offered in such a collaborative open hypermedia system. In this paper we address the issue of how to identify key requirements of open collaborative hypermedia systems. We start with a scenario in order to come up with a preliminary set of requirements. We then apply a regular schema to generate a more comprehensive set of requirements for open collaborative hypermedia systems.

Evaluation of operators defined by regular schemas

We consider different techniques of organizing the evaluation of operators defined by regular schemas. The proposed techniques are based on an abstract machine (a discrete process generator) with nondeterministic operation.

On accessing object-oriented databases: expressive power, complexity, and restrictions

A formal framework for studying the expressive power and complexity of OODB queries is developed. Three approaches to modeling sets are articulated and compared. The class of regular OODB schemas supports the explicit representation of set-valued types. Using an object-based semantics for sets, the regular schemas correspond to most implemented OODB systems in the literature; a value-based semantics for sets is also introduced. Without restrictions, both of these approaches support the specification of all computable queries. Assuming that the new operator is prohibited, the query language of the regular OODB schemas under the object-based semantics is complete in PSPACE; and under the value-based semantics it has hyper-exponential complexity. The third approach to modeling sets is given by the algebraic OODB model, in which multi-valued attributes rather than set-valued types are supported. method implementations can use operators stemming from the relational algebra, and do not have side-effects. The query language of algebraic OODBs is more powerful than the relational algebra but has complexity bounded by PTIME. The expressive power and complexity of data access for other variations of OODBs are also considered. Finally, a new relational query language, called algebra + pointwise recursion , is introduced. This is equivalent to the algebraic OODB language, and can compute generalized transitive closure.

Structured programming in symbolic multiprocessing

This article applies Glushkov's systems of algorithmic algebras (SAA) to symbolic multiprocessing. Regular schemata on abstract memory types are used to formalize the main control techniques for parallel computations in slipway and pipeline multiprocessing. The expressive power of the proposed SAA apparatus is demonstrated for the reader-writer problem, the dynamic communication problem, the firing line problem, and parallel parsing. Structured design grammars combining the SAA apparatus with formal language models are applied for direct and inverse transformation from synchronous to asynchronous regular schemata and back. It is determined that program design based on structured design grammars preserves all the advantages of structured programming and enables partial program verification using top-down, bottom-up, and mixed parsers, the optimization of programs by prespecified criteria using the apparatus of identity transformations developed within the framework of SAA theory, and the joint multilevel (top-down, bottom-up, and mixed) design of structured algorithms and programs.

Embriologia dellaPeperomia maculosaHook.

Summary The author describes the embryo-sac of Pepsremia maculosa Hook, providing his study with drawings which illustrate its various stages. During the megasporogenesis which, owing to the lack of divisory walls, closes with the building of a tetrade of megaspores, the author notices the delay of the chromosones in reaching their respective poles which however has no irflaence on the genesis of the embryo-sac. The vacuolization begins before the end of the omeotypic division which deviates from the normal course, as the vacuolization always follows the omcotypic division. The somatogenic division is abolished and at its place the tetrade of megaspores undergoes a long rest which however does not result in any increase of the volume of the tetrade. The polarization is most irregular and does not develop after any regular schema but follows the most different proceedings. An uncertain polarization determines alterations which if they do not appear during the quite regular gametogenical divisions are to be...