Geometric 3D point cloud compression

The use of 3D data in mobile robotics applications provides valuable information about the robot’s environment but usually the huge amount of 3D information is unmanageable by the robot storage and computing capabilities. A data compression is necessary to store and manage this information but preserving as much information as possible. In this paper, we propose a 3D lossy compression system based on plane extraction which represent the points of each scene plane as a Delaunay triangulation and a set of points/area information. The compression system can be customized to achieve different data compression or accuracy ratios. It also supports a color segmentation stage to preserve original scene color information and provides a realistic scene reconstruction. The design of the method provides a fast scene reconstruction useful for further visualization or processing tasks.

Calmness of the Feasible Set Mapping for Linear Inequality Systems

In this paper we deal with parameterized linear inequality systems in the n-dimensional Euclidean space, whose coefficients depend continuosly on an index ranging in a compact Hausdorff space. The paper is developed in two different parametric settings: the one of only right-hand-side perturbations of the linear system, and that in which both sides of the system can be perturbed. Appealing to the backgrounds on the calmness property, and exploiting the specifics of the current linear structure, we derive different characterizations of the calmness of the feasible set mapping, and provide an operative expresion for the calmness modulus when confined to finite systems. In the paper, the role played by the Abadie constraint qualification in relation to calmness is clarified, and illustrated by different examples. We point out that this approach has the virtue of tackling the calmness property exclusively in terms of the system’s data.

Discontinuity spacing analysis in rock masses using 3D point clouds

The complete characterization of rock masses implies the acquisition of information of both, the materials which compose the rock mass and the discontinuities which divide the outcrop. Recent advances in the use of remote sensing techniques – such as Light Detection and Ranging (LiDAR) – allow the accurate and dense acquisition of 3D information that can be used for the characterization of discontinuities. This work presents a novel methodology which allows the calculation of the normal spacing of persistent and non-persistent discontinuity sets using 3D point cloud datasets considering the three dimensional relationships between clusters. This approach requires that the 3D dataset has been previously classified. This implies that discontinuity sets are previously extracted, every single point is labeled with its corresponding discontinuity set and every exposed planar surface is analytically calculated. Then, for each discontinuity set the method calculates the normal spacing between an exposed plane and its nearest one considering 3D space relationship. This link between planes is obtained calculating for every point its nearest point member of the same discontinuity set, which provides its nearest plane. This allows calculating the normal spacing for every plane. Finally, the normal spacing is calculated as the mean value of all the normal spacings for each discontinuity set. The methodology is validated through three cases of study using synthetic data and 3D laser scanning datasets. The first case illustrates the fundamentals and the performance of the proposed methodology. The second and the third cases of study correspond to two rock slopes for which datasets were acquired using a 3D laser scanner. The second case study has shown that results obtained from the traditional and the proposed approaches are reasonably similar. Nevertheless, a discrepancy between both approaches has been found when the exposed planes members of a discontinuity set were hard to identify and when the planes pairing was difficult to establish during the fieldwork campaign. The third case study also has evidenced that when the number of identified exposed planes is high, the calculated normal spacing using the proposed approach is minor than those using the traditional approach.

Discontinuity Set Extractor

Disponible en Github: https://github.com/adririquelme/DSE

Convergence analysis and validation of low cost distance metrics for computational cost reduction of the Iterative Closest Point algorithm

The Iterative Closest Point algorithm (ICP) is commonly used in engineering applications to solve the rigid registration problem of partially overlapped point sets which are pre-aligned with a coarse estimate of their relative positions. This iterative algorithm is applied in many areas such as the medicine for volumetric reconstruction of tomography data, in robotics to reconstruct surfaces or scenes using range sensor information, in industrial systems for quality control of manufactured objects or even in biology to study the structure and folding of proteins. One of the algorithm’s main problems is its high computational complexity (quadratic in the number of points with the non-optimized original variant) in a context where high density point sets, acquired by high resolution scanners, are processed. Many variants have been proposed in the literature whose goal is the performance improvement either by reducing the number of points or the required iterations or even enhancing the complexity of the most expensive phase: the closest neighbor search. In spite of decreasing its complexity, some of the variants tend to have a negative impact on the final registration precision or the convergence domain thus limiting the possible application scenarios. The goal of this work is the improvement of the algorithm’s computational cost so that a wider range of computationally demanding problems from among the ones described before can be addressed. For that purpose, an experimental and mathematical convergence analysis and validation of point-to-point distance metrics has been performed taking into account those distances with lower computational cost than the Euclidean one, which is used as the de facto standard for the algorithm’s implementations in the literature. In that analysis, the functioning of the algorithm in diverse topological spaces, characterized by different metrics, has been studied to check the convergence, efficacy and cost of the method in order to determine the one which offers the best results. Given that the distance calculation represents a significant part of the whole set of computations performed by the algorithm, it is expected that any reduction of that operation affects significantly and positively the overall performance of the method. As a result, a performance improvement has been achieved by the application of those reduced cost metrics whose quality in terms of convergence and error has been analyzed and validated experimentally as comparable with respect to the Euclidean distance using a heterogeneous set of objects, scenarios and initial situations.

On the Result of Invariance of the Closure Set of the Real Projections of the Zeros of an Important Class of Exponential Polynomials

In this paper we provide the proof of a practical point-wise characterization of the set RP defined by the closure set of the real projections of the zeros of an exponential polynomial P(z) = Σn j=1 cjewjz with real frequencies wj linearly independent over the rationals. As a consequence, we give a complete description of the set RP and prove its invariance with respect to the moduli of the c′ js, which allows us to determine exactly the gaps of RP and the extremes of the critical interval of P(z) by solving inequations with positive real numbers. Finally, we analyse the converse of this result of invariance.

New York, N.Y. and vicinity, 1961 : Harlem, N.Y.-N.J. (8 Sheet Set) (Raster Image)

This layer is a georeferenced raster image of the United States Geological Survey 7.5 minute topographic sheet map entitled: New York and vicinity : Harlem, N.Y.-N.J., 1956. It is part of an 8 sheet map set covering the metropolitan New York City area. It was published in 1961. Scale 1:24,000. The source map was compiled from 1:24,000-scale maps of Mount Vernon 1956, Yonkers 1956, Central Park 1956, and Flushing 1955 7.5 minute quadrangles. Hydrography compiled from USC&GS charts 222 (1955), 223 (1954), 748 (1955), 226, 274, 745, 746, and 747 (1956). The image inside the map neatline is georeferenced to the surface of the earth and fit to the Universal Transverse Mercator (UTM) Zone 18N NAD27 projection. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. USGS maps are typical topographic maps portraying both natural and manmade features. They show and name works of nature, such as mountains, valleys, lakes, rivers, vegetation, etc. They also identify the principal works of humans, such as roads, railroads, boundaries, transmission lines, major buildings, etc. Relief is shown with standard contour intervals of 10 and 20 feet; depths are shown with contours and soundings. Please pay close attention to map collar information on projections, spheroid, sources, dates, and keys to grid numbering and other numbers which appear inside the neatline. This layer is part of a selection of digitally scanned and georeferenced historic maps from The Harvard Map Collection as part of the Imaging the Urban Environment project. Maps selected for this project represent major urban areas and cities of the world, at various time periods. These maps typically portray both natural and manmade features at a large scale. The selection represents a range of regions, originators, ground condition dates, scales, and purposes.

New York, N.Y. and vicinity, 1961 : Oyster Bay, N.Y.-Conn. (8 Sheet Set) (Raster Image)

This layer is a georeferenced raster image of the United States Geological Survey 7.5 minute topographic sheet map entitled: New York and vicinity : Oyster Bay, N.Y.-Conn., 1955. It is part of an 8 sheet map set covering the metropolitan New York City area. It was published in 1961. Scale 1:24,000. The source map was prepared by the Geological Survey from 1:24,000-scale maps of Bayville 1954, Mamaroneck 1955, Sea Cliff 1954, and Hicksville 1954 7.5 minute quadrangles compiled by the Army Map Service. The Mamaroneck quadrangle was previously compiled by the Geological Survey in 1933 and 1934. Culture revised by the Geological Survey. Hydrography compiled from USC&GS charts 222 (1955), 223 (1954, 1955), and 224 (1954). The image inside the map neatline is georeferenced to the surface of the earth and fit to the Universal Transverse Mercator (UTM) Zone 18N NAD27 projection. All map collar and inset information is also available as part of the raster image, including any inset maps, profiles, statistical tables, directories, text, illustrations, index maps, legends, or other information associated with the principal map. USGS maps are typical topographic maps portraying both natural and manmade features. They show and name works of nature, such as mountains, valleys, lakes, rivers, vegetation, etc. They also identify the principal works of humans, such as roads, railroads, boundaries, transmission lines, major buildings, etc. Relief is shown with standard contour intervals of 10 and 20 feet; depths are shown with contours and soundings. Please pay close attention to map collar information on projections, spheroid, sources, dates, and keys to grid numbering and other numbers which appear inside the neatline. This layer is part of a selection of digitally scanned and georeferenced historic maps from The Harvard Map Collection as part of the Imaging the Urban Environment project. Maps selected for this project represent major urban areas and cities of the world, at various time periods. These maps typically portray both natural and manmade features at a large scale. The selection represents a range of regions, originators, ground condition dates, scales, and purposes.

Eastern Policy of the EU: the Visegrad Countries' Perspective. OSW Point of View, February 2003

1. After its enlargement, scheduled for 2004, the European Union will face a completely new situation at its eastern borders. This new situation calls for a new concept of the EU eastern activities, i.e. for development of the new Eastern Policy of the EU. 2. Due to a number of specific features such as geographical location, closeness of ties, direct risk factors etc., the Visegrad countries will and should be particularly interested in the process of formulating the new EU Eastern Policy. Consequently, they should be the co-makers of this policy. 3. The new EU Eastern Policy should differ fundamentally from the Union's traditional eastern relations. Firstly, its scope should not cover the entire CIS area: instead, the policy should focus on some of the European successor states of the former Soviet Union, namely Belarus, Russia and Ukraine, as well as Moldova, following the accession of Romania. It does not seem advisable to exclude the Russian Federation from this policy and to develop and implement a separate policy towards it. The new Eastern Policy should be an autonomous component and one of the most important elements in the overall foreign policy of the EU. 4. Secondly, the new Eastern Policy should be founded on the following two pillars: a region-oriented strategy, which could be called the Eastern Dimension, and reshaped strategies for individual countries. The Eastern Dimension should set up a universal framework of co-operation, defining its basic mechanisms and objectives. These should include: the adaptation assistance programme, JHA, transborder co-operation, social dialogue and transport infrastructures. The approach, however, should be kept flexible, taking into account the specific situation of each country. This purpose should be served by keeping in place the existing bilateral institutional contacts between the EU and each of its eastern neighbours, and by developing a national strategy for each neighbour.

A new Visegrad Group in the new European Union - possibilities and opportunities for development. OSW Point of View, June 2003

The Visegrad Group has fulfilled the tasks it was set when established. It seems unjustified, therefore, to ponder the need for it to function further. However, it is advisable to lay out new tasks, suitable for the group's operation in the new European reality - following EU accession of Visegrad countries in May 2004.

'The power gained, we will never surrender': Russian ruling elite versus the succession and economic crisis. OSW Point of View (Policy Brief), October 2009

Even though the economic crisis proved harmful to the Russian economy and people's living standards, it has nonetheless failed to make the elite revise its policy. Despite some problems, the government has managed to sustain economic and political stability, thanks to the reserves it amassed in the times of prosperity, and to the propaganda campaign that protected it, above all Vladimir Putin. The crisis failed to force the elite to implement deeper structural and political reforms. Moreover, it has actually reinforced existing tendencies, such as state control over the economy and its oil-oriented character, the elite's economic expansion at the expense of private businesses, and the preservation of political power. Thus, the crisis has so far failed to dismantle Putinism, indeed quite the reverse - it has in fact contributed to its becoming 'set in stone'.

Georgian drift. The crisis of Georgia's way westwards. OSW POINT OF VIEW 57, 2016-02-22

For several years Georgia has been experiencing processes which may be interpreted as symptoms of a deepening, multidimensional social and political crisis. Reforms have lost momentum, stagnation has set in, and in some areas the situation has begun to revert to the pre-revolution status (including rising crime levels). The Georgian political system has found itself in a serious crisis, while society has become increasingly frustrated and apathetic, mainly because people’s standards of living have been stagnating. This political and social malaise has been breeding Euro-scepticism and disenchantment with the West. A country that had been firmly navigating westwards, Georgia has now started drifting and slipping into malaise. This risks reversing what the country has achieved so far in the internal dimension, increasing instability and triggering a crisis in the pro-Western vector of Tbilisi’s foreign policy. While that may not necessarily mean a turn towards Russia, in the present situation it has been easier for Moscow to pursue its own interests in the region. Should Tbilisi’s pro-Western course become reversed or permanently stagnant, that would entail grave consequences for the country itself and beyond. It would be a defeat for the West and would undermine the European aspirations of countries like Ukraine or Moldova.

Single- vs. multiple-set resistance training: Recent developments in the controversy

Galvao, D.A., and D.R. Taaffe. Single- vs. multiple-set resistance training: recent developments in the controversy. J. Strength Cond. Res. 18(3):660-667. 2004.-The number of sets in a resistance training program remains a major point of discussion and controversy. Studies prior to 1998 demonstrated inconsistent findings between single-set and multiple-set programs; however, recent evidence suggests that multiple sets promote additional benefits following short- and long-term training. The rationale supporting multiple sets is that the number of sets is part of the exercise volume equation, and the volume of exercise is crucial in producing the stimulus necessary to elicit specific physiological adaptations. The purpose of this paper is to present an overview of recent resistance training studies comparing single and multiple sets. However, it should be noted that studies to date have been conducted in young and middle-aged adults, and it remains to be determined if the additional benefits accrued with multiple-set training also occurs for older adults, especially the frail elderly.

Global behavior of positive solutions of nonlinear three-point boundary value problems

We investigate the structure of the positive solution set for nonlinear three-point boundary value problems of the form u('') + h(t) f(u) = 0, u(0) = 0, u(1) = lambdau(eta), where eta epsilon (0, 1) is given lambda epsilon (0, 1/n) is a parameter, f epsilon C ([0, infinity), [0, infinity)) satisfies f (s) > 0 for s > 0, and h epsilon C([0, 1], [0, infinity)) is not identically zero on any subinterval of [0, 1]. Our main results demonstrate the existence of continua of positive solutions of the above problem. (C) 2004 Elsevier Ltd. All rights reserved.

Generalized Variational Inequalities for Upper Hemicontinuous and Demi Operators with Applications to Fixed Point Theorems in Hilbert Spaces

∗ The final version of this paper was sent to the editor when the author was supported by an ARC Small Grant of Dr. E. Tarafdar.