On a new method for finding generalized equivalence transformations for differential equations involving arbitrary functions

A new efficient method for finding generalized equivalence transformations for a class of differential equation systems via its related extended classical symmetries is presented. This technique can be further adapted to find the equivalence transformations for the mathematical model. It applies to classes of differential systems whose arbitrary functions involve all equations’ independent variables. As a consequence, any symbolic manipulation program designed to find classical Lie symmetries can also be used to determine generalized equivalence transformations and equivalence transformations, respectively, without any modification of the program. The method has been implemented as the maple routine gendefget and is based on the maple package desolv(by Carminati and Vu). The nonlinear stationary heat conduction parameter identification problem is considered as an example.     

Sparse Non‐rigid Registration of 3D Shapes

Non‐rigid registration of 3D shapes is an essential task of increasing importance as commodity depth sensors become more widely available for scanning dynamic scenes. Non‐rigid registration is much more challenging than rigid registration as it estimates a set of local transformations instead of a single global transformation, and hence is prone to the overfitting issue due to underdetermination. The common wisdom in previous methods is to impose an ?₂‐norm regularization on the local transformation differences. However, the ?₂‐norm regularization tends to bias the solution towards outliers and noise with heavy‐tailed distribution, which is verified by the poor goodness‐of‐fit of the Gaussian distribution over transformation differences. On the contrary, Laplacian distribution fits well with the transformation differences, suggesting the use of a sparsity prior. We propose a sparse non‐rigid registration (SNR) method with an ?₁‐norm regularized model for transformation estimation, which is effectively solved by an alternate direction method (ADM) under the augmented Lagrangian framework. We also devise a multi‐resolution scheme for robust and progressive registration. Results on both public datasets and our scanned datasets show the superiority of our method, particularly in handling large‐scale deformations as well as outliers and noise.     

Goto and Concurrency Introducing Safe Jumps in Esterel

Esterel is a design language for the specification of real time embedded systems. Based on the synchronous concurrency paradigm, its semantics describes execution as a succession of instants of computation. In this work, we consider the introduction of a new gotopause instruction in the language, which acts as a non-instantaneous jump instruction compatible with concurrency. It allows the programmer to activate state control points anywhere in the program, from where the execution is resumed in the next instant. In order to provide the formal semantics of the extended language, we first define a state semantics of Esterel, which we prove observationally equivalent to the original logical behavioral semantics. Including gotopause in the state semantics is then straightforward. We sketch two key applications of our new primitive: a direct encoding of automata and a quasi-linear rewriting of programs eliminating schizophrenic behaviors.     

Fusing multiple image transformations and a thermal sensor with kinect to improve person detection ability

This paper proposes a novel approach to combine data from multiple low-cost sensors to detect people in a mobile robot. Robust detection of people is a key capability required for robots working in environments with people. Several works have shown the benefits of fusing data from complementary sensors. The Kinect sensor provides a rich data set at a significantly low cost, however, it has some limitations for its use on a mobile platform, mainly that people detection algorithms rely on images captured by a static camera. To cope with these limitations, this work is based on the fusion of Kinect and a thermical sensor (thermopile) mounted on top of a mobile platform. We propose the implementation of an evolutionary selection of sequences of image transformation to detect people through supervised classifiers. Experimental results carried out with a mobile platform in a manufacturing shop floor show that the percentage of wrong classified using only Kinect is drastically reduced with the classification algorithms and with the combination of the three information sources. Extra experiments are presented as well to show the benefits of the image transformation sequence idea here presented.     

Higher-Order Nets for Mobile Policies

Since the early 80's the combination of Petri nets and rule-based transformations has been extensively researched to obtain new concepts and results. In this paper we consider rules as tokens leading to the concept of higher-order nets for mobile policies. The rules are used on the one hand for the specification of policy rules and on the other hand for the modification of policy rules, i.e. for the definition of new rules by reusing existing rules. So the higher-order net models distribution and modification of policy rules in a systematic and structured way. We give HasCasl-specifications of rules and (local) transformations in the sense of the double-pushout approach and illustrate our concept by a small system inspired by the case study of a tax refund process [E. Bertino, E. Ferrari, E., and V. Atluri. The Specification and Enforcement of Authorization Constraints in Workflow Management Systems. ACM Transactions on Information and System Security 2 (1) (1999) 65–104].     

Equational tree transformations

We define an equational relation as the union of some components of the least solution of a system of equations of tree transformations in a pair of algebras. We focus on equational tree transformations which are equational relations obtained by considering the least solutions of such systems in pairs of term algebras. We characterize equational tree transformations in terms of tree transformations defined by different bimorphisms. To demonstrate the robustness of equational tree transformations, we give equational definitions of some well-known tree transformation classes for which bimorphism characterizations also exist. These are the class of alphabetic tree transformations, the class of linear and nondeleting extended top-down tree transformations, and the class of bottom-up tree transformations and its linear and linear and nondeleting subclasses. Finally, we prove that a relation is equational if and only if it is the morphic image of an equational tree transformation.     

Multi‐Scale Geometry Interpolation

Interpolating vertex positions among triangle meshes with identical vertex‐edge graphs is a fundamental part of many geometric modelling systems. Linear vertex interpolation is robust but fails to preserve local shape. Most recent approaches identify local affine transformations for parts of the mesh, model desired interpolations of the affine transformations, and then optimize vertex positions to conform with the desired transformations. However, the local interpolation of the rotational part is non‐trivial for more than two input configurations and ambiguous if the meshes are deformed significantly. We propose a solution to the vertex interpolation problem that starts from interpolating the local metric (edge lengths) and mean curvature (dihedral angles) and makes consistent choices of local affine transformations using shape matching applied to successively larger parts of the mesh. The local interpolation can be applied to any number of input vertex configurations and due to the hierarchical scheme for generating consolidated vertex positions, the approach is fast and can be applied to very large meshes.     

Mobility‐Trees for Indoor Scenes Manipulation

In this work, we introduce the ‘mobility‐tree’ construct for high‐level functional representation of complex 3D indoor scenes. In recent years, digital indoor scenes are becoming increasingly popular, consisting of detailed geometry and complex functionalities. These scenes often consist of objects that reoccur in various poses and interrelate with each other. In this work we analyse the reoccurrence of objects in the scene and automatically detect their functional mobilities. ‘Mobility’ analysis denotes the motion capabilities (i.e. degree of freedom) of an object and its subpart which typically relates to their indoor functionalities. We compute an object's mobility by analysing its spatial arrangement, repetitions and relations with other objects and store it in a ‘mobility‐tree’. Repetitive motions in the scenes are grouped in ‘mobility‐groups’, for which we develop a set of sophisticated controllers facilitating semantical high‐level editing operations. We show applications of our mobility analysis to interactive scene manipulation and reorganization, and present results for a variety of indoor scenes.     

Transformations of Petri Nets

The aim of this paper is an introduction to the area of Petri net transformations, a rule-based approach for dynamic changes of the net structure of Petri nets. This is especially important for the stepwise construction of Petri nets in the sense of the software development process in software engineering. The concept of Petri net transformations is based on that of graph transformations and high-level replacement systems and it is introduced within a small case study logistics.