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.

Reverse Geometry Hybrid Contact Lens Fitting in a Case of Donor-Host Misalignment after Keratoplasty

Purpose: To report the successful outcome obtained after fitting a new hybrid contact lens in a cornea with an area of donor-host misalignment and significant levels of irregular astigmatism after penetrating keratoplasty (PKP). Materials and methods: A 41-year-old female with bilateral asymmetric keratoconus underwent PKP in her left eye due to the advanced status of the disease. One year after surgery, the patient referred a poor visual acuity and quality in this eye. The fitting of different types of rigid gas permeable contact lenses was performed, but with an unsuccessful outcome due to contact lens stability problems and uncomfortable wear. Scheimpflug imaging evaluation revealed that a donor-host misalignment was present at the nasal area. Contact lens fitting with a reverse geometry hybrid contact lens (Clearkone, SynergEyes Carlsbad) was then fitted. Visual, refractive, and ocular aberrometric outcomes were evaluated during a 1-year period after the fitting. Results: Uncorrected distance visual acuity improved from a prefitting value of 20/200 to a best corrected postfitting value of 20/20. Prefitting manifest refraction was +5.00 sphere and -5.50 cylinder at 75°, with a corrected distance visual acuity of 20/30. Higher order root mean square (RMS) for a 5 mm pupil changed from a prefitting value of 6.83 µm to a postfitting value of 1.57 µm (5 mm pupil). The contact lens wearing was referred as comfortable, with no anterior segment alterations. Conclusion: The SynergEyes Clearkone contact lens seems to be another potentially useful option for the visual rehabilitation after PKP, especially in cases of donor-host misalignment.

3D geometry of growth strata in a fault-propagation fold: insights into space–time evolution of the Crevillente Fault (Abanilla-Alicante sector), Betic Cordillera, Spain

This work presents a 3D geometric model of growth strata cropping out in a fault-propagation fold associated with the Crevillente Fault (Abanilla-Alicante sector) from the Bajo Segura Basin (eastern Betic Cordillera, southern Spain). The analysis of this 3D model enables us to unravel the along-strike and along-section variations of the growth strata, providing constraints to assess the fold development, and hence, the fault kinematic evolution in space and time. We postulate that the observed along-strike dip variations are related to lateral variation in fault displacement. Along-section variations of the progressive unconformity opening angles indicate greater fault slip in the upper Tortonian–Messinian time span; from the Messinian on, quantitative analysis of the unconformity indicate a constant or lower tectonic activity of the Crevillente Fault (Abanilla-Alicante sector); the minor abundance of striated pebbles in the Pliocene-Quaternary units could be interpreted as a decrease in the stress magnitude and consequently in the tectonic activity of the fault. At a regional scale, comparison of the growth successions cropping out in the northern and southern limits of the Bajo Segura Basin points to a southward migration of deformation in the basin. This means that the Bajo Segura Fault became active after the Crevillente Fault (Abanilla-Alicante sector), for which activity on the latter was probably decreasing according to our data. Consequently, we propose that the seismic hazard at the northern limit of the Bajo Segura Basin should be lower than at the southern limit.

Structural Analysis with ANSYS on Stone Constructions in the Historical Spanish Heritage

According to the importance of rehabilitation and recovery of Architectural Heritage in the live of people, this paper is aimed to strengthen the traditional methods of stone vaults calculation taking advantage of the technological characteristics of the powerful program ANSYS Workbench. As an example of this, it could find out the possible pathologies that could arise during the construction history of the building. To limit this research, the upper vault of the main chapel of the Santiago parish church in Orihuela -Alicante- is selected as a reference which is a Jeronimo Quijano´s important building work in the XVI century in the Renaissance. Moreover, it is an innovative stone masonry vault that consists of 8 double intercrossed arches with each other and braced by severies. During the seventeenth century there was a lantern in the central cap and it is unknown why it was removed. Its construction could justify the original constructive solution with intercrossed arches that freed the center to create a more enlightened and comfortable presbytery. By similarity with other Quijano’s works, it is considered a small lantern drilling the central spherical cap. It is proposed to carry out a comparative study of it with different architectural solutions from the same period and based on several common parameters such as: a vault of square plant with spherical surround, intercrossed arches, a possible lantern, the dimension of the permitted space, similar states of loads and compact limestone masonry. The three solutions are mainly differentiated by their size and the type of lantern and its comparison lets us know which one is the most resistant and stable. The other two building works maintain some connection with the Quijano's professional scope. It has selected the particular case of the Communion chapel of the Basilica in Elche (a large prismatic lantern with a large cylindrical drum that starts from the own arches and an upper hemispherical dome), for its conservation, its proximity to Orihuela and its implementation during the century XVIII. Finally, a significant Dome Spanish Renaissance complete the selection: a cross vault of the Benavides Chapel of the Saint Francisco Convent in Baeza - Jaén-, designed by Andres of Vandelvira in the sixteenth century (a large hemispherical dome that starts from the own arcs). To simplify the calculation and standardize the work that have to be contrasted, all of them were considered with some similar characteristics: 30 cm constant thickness, the intercrossed arches were specifically analyzed and had identical loads, Young's modulus and Poisson's ratio. Regarding the calculation solutions, in general terms, the compressive stresses predominate, influencing on it the joint collaboration of the filling material on the vault, the vault itself, the thick side walls, the buttresses and the top cover weight . In addition, the three solutions are suitable, being the Orihuela one the safest and the Baeza one the riskiest for its large dimensions. Thus, the idea of intercrossed arches with suitable thickness would allow carry out the heaviest lantern and this would confirm it as a Renaissance architectural typology built in stone.