scholarly journals Isometry Invariant Shape Recognition of Projectively Perturbed Point Clouds by the Mergegram Extending 0D Persistence

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2121
Author(s):  
Yury Elkin ◽  
Vitaliy Kurlin
Keyword(s):  
General Position ◽  
Shape Recognition ◽  
Rigid Motion ◽  
Point Clouds ◽  
Recognition Problem ◽  
Experimental Demonstration ◽  
Single Linkage ◽  
Projective Transformations ◽  
The Stability ◽  
Invariant Shape

Rigid shapes should be naturally compared up to rigid motion or isometry, which preserves all inter-point distances. The same rigid shape can be often represented by noisy point clouds of different sizes. Hence, the isometry shape recognition problem requires methods that are independent of a cloud size. This paper studies stable-under-noise isometry invariants for the recognition problem stated in the harder form when given clouds can be related by affine or projective transformations. The first contribution is the stability proof for the invariant mergegram, which completely determines a single-linkage dendrogram in general position. The second contribution is the experimental demonstration that the mergegram outperforms other invariants in recognizing isometry classes of point clouds extracted from perturbed shapes in images.

scholarly journals Experimental Demonstration of the Stability of Berry’s Phase for a Spin-1/2Particle

2009 ◽  
Vol 102 (3) ◽  
Author(s):  
S. Filipp ◽  
J. Klepp ◽  
Y. Hasegawa ◽  
C. Plonka-Spehr ◽  
U. Schmidt ◽  
...  
Keyword(s):  
Experimental Demonstration ◽  
Berry's Phase ◽  
Berry’S Phase ◽  
The Stability

scholarly journals Three problems in robotics

2002 ◽  
Vol 216 (1) ◽  
pp. 73-80 ◽  
Author(s):  
J M Selig
Keyword(s):  
Least Squares ◽  
Potential Function ◽  
Equilibrium Position ◽  
Screw Theory ◽  
Rigid Motion ◽  
The Body ◽  
The Third ◽  
Second Derivatives ◽  
Spring System ◽  
The Stability

Three rather different problems in robotics are studied using the same technique from screw theory. The first problem concerns systems of springs. The potential function is differentiated in the direction of an arbitrary screw to find the equilibrium position. The second problem is almost identical in terms of the computations; the least-squares solution to the problem of finding the rigid motion undergone by a body given only data about points on the body is sought. In the third problem the Jacobian of a Stewart platform is found. Again, this is achieved by differentiating with respect to a screw. Furthermore, second-order properties of the first two problems are studied. The Hessian of second derivatives is computed, and hence the stability properties of the equilibrium positions of the spring system are found.

scholarly journals FACETS : A CLOUDCOMPARE PLUGIN TO EXTRACT GEOLOGICAL PLANES FROM UNSTRUCTURED 3D POINT CLOUDS

2016 ◽  
Vol XLI-B5 ◽  
pp. 799-804 ◽  
Author(s):  
T.J. B. Dewez ◽  
D. Girardeau-Montaut ◽  
C. Allanic ◽  
J. Rohmer
Keyword(s):  
Point Cloud ◽  
Point Clouds ◽  
Third Party ◽  
Fast Marching ◽  
Software Environment ◽  
Tension Parameter ◽  
3D Point Clouds ◽  
The Stability ◽  
Planar Facet ◽  
Gis Software

Geological planar facets (stratification, fault, joint…) are key features to unravel the tectonic history of rock outcrop or appreciate the stability of a hazardous rock cliff. Measuring their spatial attitude (dip and strike) is generally performed by hand with a compass/clinometer, which is time consuming, requires some degree of censoring (i.e. refusing to measure some features judged unimportant at the time), is not always possible for fractures higher up on the outcrop and is somewhat hazardous. 3D virtual geological outcrop hold the potential to alleviate these issues. Efficiently segmenting massive 3D point clouds into individual planar facets, inside a convenient software environment was lacking. FACETS is a dedicated plugin within CloudCompare v2.6.2 (<a href="http://cloudcompare.org/"target="_blank">http://cloudcompare.org/</a> ) implemented to perform planar facet extraction, calculate their dip and dip direction (i.e. azimuth of steepest decent) and report the extracted data in interactive stereograms. Two algorithms perform the segmentation: Kd-Tree and Fast Marching. Both divide the point cloud into sub-cells, then compute elementary planar objects and aggregate them progressively according to a planeity threshold into polygons. The boundaries of the polygons are adjusted around segmented points with a tension parameter, and the facet polygons can be exported as 3D polygon shapefiles towards third party GIS software or simply as ASCII comma separated files. One of the great features of FACETS is the capability to explore planar objects but also 3D points with normals with the stereogram tool. Poles can be readily displayed, queried and manually segmented interactively. The plugin blends seamlessly into CloudCompare to leverage all its other 3D point cloud manipulation features. A demonstration of the tool is presented to illustrate these different features. While designed for geological applications, FACETS could be more widely applied to any planar objects.

scholarly journals BIM FROM LASER SCANS… NOT JUST FOR BUILDINGS: NURBS-BASED PARAMETRIC MODELING OF A MEDIEVAL BRIDGE

2016 ◽  
Vol III-5 ◽  
pp. 51-56 ◽  
Author(s):  
L. Barazzetti ◽  
F. Banfi ◽  
R. Brumana ◽  
M. Previtali ◽  
F. Roncoroni
Keyword(s):  
Point Clouds ◽  
Parametric Modeling ◽  
Structural Elements ◽  
Building Information Modelling ◽  
Communications Networks ◽  
Civil Infrastructures ◽  
Irregular Shapes ◽  
Building Information ◽  
Water And Wastewater ◽  
The Stability

Building Information Modelling is not limited to buildings. BIM technology includes civil infrastructures such as roads, dams, bridges, communications networks, water and wastewater networks and tunnels. This paper describes a novel methodology for the generation of a detailed BIM of a complex medieval bridge. The use of laser scans and images coupled with the development of algorithms able to handle irregular shapes allowed the creation of advanced parametric objects, which were assembled to obtain an accurate BIM. The lack of existing object libraries required the development of specific families for the different structural elements of the bridge. Finally, some applications aimed at assessing the stability and safety of the bridge are illustrated and discussed. The BIM of the bridge can incorporate this information towards a new “BIMonitoring” concept to preserve the geometric complexity provided by point clouds, obtaining a detailed BIM with object relationships and attributes.

scholarly journals Registration of spatio-temporal point clouds of plants for phenotyping

PLoS ONE ◽  
2021 ◽  
Vol 16 (2) ◽  
pp. e0247243
Author(s):  
Nived Chebrolu ◽  
Federico Magistri ◽  
Thomas Läbe ◽  
Cyrill Stachniss
Keyword(s):  
Plant Traits ◽  
Scale Up ◽  
Rigid Motion ◽  
Point Clouds ◽  
Plant Performance ◽  
Sensor Data ◽  
Plant Phenotyping ◽  
Compact Representation ◽  
3D Point Clouds ◽  
Over Time

Plant phenotyping is a central task in crop science and plant breeding. It involves measuring plant traits to describe the anatomy and physiology of plants and is used for deriving traits and evaluating plant performance. Traditional methods for phenotyping are often time-consuming operations involving substantial manual labor. The availability of 3D sensor data of plants obtained from laser scanners or modern depth cameras offers the potential to automate several of these phenotyping tasks. This automation can scale up the phenotyping measurements and evaluations that have to be performed to a larger number of plant samples and at a finer spatial and temporal resolution. In this paper, we investigate the problem of registering 3D point clouds of the plants over time and space. This means that we determine correspondences between point clouds of plants taken at different points in time and register them using a new, non-rigid registration approach. This approach has the potential to form the backbone for phenotyping applications aimed at tracking the traits of plants over time. The registration task involves finding data associations between measurements taken at different times while the plants grow and change their appearance, allowing 3D models taken at different points in time to be compared with each other. Registering plants over time is challenging due to its anisotropic growth, changing topology, and non-rigid motion in between the time of the measurements. Thus, we propose a novel approach that first extracts a compact representation of the plant in the form of a skeleton that encodes both topology and semantic information, and then use this skeletal structure to determine correspondences over time and drive the registration process. Through this approach, we can tackle the data association problem for the time-series point cloud data of plants effectively. We tested our approach on different datasets acquired over time and successfully registered the 3D plant point clouds recorded with a laser scanner. We demonstrate that our method allows for developing systems for automated temporal plant-trait analysis by tracking plant traits at an organ level.

scholarly journals On Learning Sets of Symmetric Elements (Extended Abstract)

2021 ◽  
Author(s):  
Haggai Maron ◽  
Or Litany ◽  
Gal Chechik ◽  
Ethan Fetaya
Keyword(s):  
Shape Recognition ◽  
Point Clouds ◽  
Approach To Learning ◽  
Series Of Experiments ◽  
The Common ◽  
Equivariant Functions ◽  
Siamese Networks ◽  
Universal Approximators ◽  
Learning Architectures ◽  
Learning Sets

Learning from unordered sets is a fundamental learning setup, recently attracting increasing attention. Research in this area has focused on the case where elements of the set are represented by feature vectors, and far less emphasis has been given to the common case where set elements themselves adhere to their own symmetries. That case is relevant to numerous applications, from deblurring image bursts to multi-view 3D shape recognition and reconstruction. In this paper, we present a principled approach to learning sets of general symmetric elements. We first characterize the space of linear layers that are equivariant both to element reordering and to the inherent symmetries of elements, like translation in the case of images. We further show that networks that are composed of these layers, called Deep Sets for Symmetric Elements layers (DSS), are universal approximators of both invariant and equivariant functions, and that these networks are strictly more expressive than Siamese networks. DSS layers are also straightforward to implement. Finally, we show that they improve over existing set-learning architectures in a series of experiments with images, graphs, and point clouds.

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