Rigid registration of noisy point clouds based on higher-dimensional error metrics

Given a class Γ of curves in [0, 1]2, we ask: in a cloud of n uniform random points, how many points can lie on some curve γ ∈ Γ? Classes studied here include curves of length less than or equal to L, Lipschitz graphs, monotone graphs, twice-differentiable curves, and graphs of smooth functions with m-bounded derivatives. We find, for example, that there are twice-differentiable curves containing as many as O P (n 1/3) uniform random points, but not essentially more than this. More generally, we consider point clouds in higher-dimensional cubes [0, 1] d and regular hypersurfaces of specified codimension, finding, for example, that twice-differentiable k-dimensional hypersurfaces in R d may contain as many as O P (n k/(2d-k)) uniform random points. We also consider other notions of ‘incidence’, such as curves passing through given location/direction pairs, and find, for example, that twice-differentiable curves in R 2 may pass through at most O P (n 1/4) uniform random location/direction pairs. Idealized applications in image processing and perceptual psychophysics are described and several open mathematical questions are identified for the attention of the probability community.

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Wide Angle Rigid Registration Using a Comparative Tensor Shape Factor

International Journal of Image and Graphics ◽

10.1142/s0219467817500061 ◽

2017 ◽

Vol 17 (01) ◽

pp. 1750006 ◽

Cited By ~ 2

Author(s):

Luciano W. X. Cejnog ◽

Fernando A. A. Yamada ◽

Marcelo Bernardes Vieira

Keyword(s):

Euclidean Distance ◽

Additive Noise ◽

Point Clouds ◽

Local Geometry ◽

Rigid Registration ◽

Weight Variation ◽

Orientation Tensors ◽

Point Search ◽

Proposed Modification ◽

Made In

This work aims to enhance a classic method for rigid registration, the iterative closest point (ICP), modifying the closest point search in order to consider approximated information of local geometry combined to the Euclidean distance, originally used. For this, a preprocessing stage is applied, in which the local geometry is encoded in second-order orientation tensors. We define the CTSF, a similarity factor between tensors. Our method uses a strategy of weight variation between the CTSF and the Euclidean distance, in order to establish correspondences. Quantitative tests were made in point clouds with different geometric features, with variable levels of additive noise and outliers and in partial overlapping situations. Results show that the proposed modification increases the convergence probability of the method for higher angles, making the method comparable to state-of-art techniques.

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Connect the dots: how many random points can a regular curve pass through?

Advances in Applied Probability ◽

10.1239/aap/1127483737 ◽

2005 ◽

Vol 37 (3) ◽

pp. 571-603 ◽

Cited By ~ 8

Author(s):

Ery Arias-Castro ◽

David L. Donoho ◽

Xiaoming Huo ◽

Craig A. Tovey

Keyword(s):

Image Processing ◽

Point Clouds ◽

Regular Curve ◽

Smooth Functions ◽

Higher Dimensional ◽

Random Location ◽

Pass Through ◽

Lipschitz Graphs

Given a class Γ of curves in [0, 1]2, we ask: in a cloud of n uniform random points, how many points can lie on some curve γ ∈ Γ? Classes studied here include curves of length less than or equal to L, Lipschitz graphs, monotone graphs, twice-differentiable curves, and graphs of smooth functions with m-bounded derivatives. We find, for example, that there are twice-differentiable curves containing as many as OP(n1/3) uniform random points, but not essentially more than this. More generally, we consider point clouds in higher-dimensional cubes [0, 1]d and regular hypersurfaces of specified codimension, finding, for example, that twice-differentiable k-dimensional hypersurfaces in Rd may contain as many as OP(nk/(2d-k)) uniform random points. We also consider other notions of ‘incidence’, such as curves passing through given location/direction pairs, and find, for example, that twice-differentiable curves in R2 may pass through at most OP(n1/4) uniform random location/direction pairs. Idealized applications in image processing and perceptual psychophysics are described and several open mathematical questions are identified for the attention of the probability community.

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Comparing Seven Methodogies for Rigid Alignment of Point Clouds with Focus on Frame-to-Frame Registration in Depth Sequences

Journal of Interactive Systems ◽

10.5753/jis.2018.703 ◽

2018 ◽

Vol 9 (2) ◽

pp. 1

Author(s):

Fernando Akio Yamada ◽

Gilson Antonio Giraldi ◽

Marcelo Bernardes Vieira ◽

Liliane Rodrigues Almeida ◽

Antonio Lopes Apolinário Jr.

Keyword(s):

Missing Data ◽

Mean Squared Error ◽

Ground Truth ◽

Point Clouds ◽

Video Sequences ◽

Depth Information ◽

Rigid Registration ◽

Temporal Sampling ◽

3D Data ◽

Depth Video

Pairwise rigid registration aims to find the rigid transformation that best registers two surfaces represented by point clouds. This work presents a comparison between seven algorithms, with different strategies to tackle rigid registration tasks. We focus on the frame-to-frame problem, in which the point clouds are extracted from a video sequence with depth information generating partial overlapping 3D data. We use both point clouds and RGB-D video streams in the experimental results. The former is considered under different viewpoints with the addition of a case-study simulating missing data. Since the ground truth rotation is provided, we discuss four different metrics to measure the rotation error in this case. Among the seven considered techniques, the Sparse ICP and Sparse ICP-CTSF outperform the other five ones in the point cloud registration experiments without considering incomplete data. However, the evaluation facing missing data indicates sensitivity for these methods against this problem and favors ICP-CTSF in such situations. In the tests with video sequences, the depth information is segmented in the first step, to get the target region. Next, the registration algorithms are applied and the average root mean squared error, rotation and translation errors are computed. Besides, we analyze the robustness of the algorithms against spatial and temporal sampling rates. We conclude from the experiments using a depth video sequences that ICP-CTSF is the best technique for frame-to-frame registration.

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Pheno4D: A spatio-temporal dataset of maize and tomato plant point clouds for phenotyping and advanced plant analysis

PLoS ONE ◽

10.1371/journal.pone.0256340 ◽

2021 ◽

Vol 16 (8) ◽

pp. e0256340

Author(s):

David Schunck ◽

Federico Magistri ◽

Radu Alexandru Rosu ◽

André Cornelißen ◽

Nived Chebrolu ◽

...

Keyword(s):

High Resolution ◽

3D Reconstruction ◽

Point Clouds ◽

Training Data ◽

Plant Phenotyping ◽

Growth Stages ◽

Plant Analysis ◽

Rigid Registration ◽

3D Point Clouds ◽

Spatio Temporal

Understanding the growth and development of individual plants is of central importance in modern agriculture, crop breeding, and crop science. To this end, using 3D data for plant analysis has gained attention over the last years. High-resolution point clouds offer the potential to derive a variety of plant traits, such as plant height, biomass, as well as the number and size of relevant plant organs. Periodically scanning the plants even allows for performing spatio-temporal growth analysis. However, highly accurate 3D point clouds from plants recorded at different growth stages are rare, and acquiring this kind of data is costly. Besides, advanced plant analysis methods from machine learning require annotated training data and thus generate intense manual labor before being able to perform an analysis. To address these issues, we present with this dataset paper a multi-temporal dataset featuring high-resolution registered point clouds of maize and tomato plants, which we manually labeled for computer vision tasks, such as for instance segmentation and 3D reconstruction, providing approximately 260 million labeled 3D points. To highlight the usability of the data and to provide baselines for other researchers, we show a variety of applications ranging from point cloud segmentation to non-rigid registration and surface reconstruction. We believe that our dataset will help to develop new algorithms to advance the research for plant phenotyping, 3D reconstruction, non-rigid registration, and deep learning on raw point clouds. The dataset is freely accessible at https://www.ipb.uni-bonn.de/data/pheno4d/.

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Automatic non-rigid registration of multi-strip point clouds from mobile laser scanning systems

International Journal of Remote Sensing ◽

10.1080/01431161.2017.1410248 ◽

2017 ◽

Vol 39 (6) ◽

pp. 1713-1728 ◽

Cited By ~ 7

Author(s):

Li Yan ◽

Junxiang Tan ◽

Hua Liu ◽

Hong Xie ◽

Changjun Chen

Keyword(s):

Laser Scanning ◽

Point Clouds ◽

Rigid Registration ◽

Scanning Systems

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Parametric process optimization to improve the accuracy and mechanical properties of 3D printed parts

MRS Advances ◽

10.1557/adv.2018.647 ◽

2018 ◽

Vol 4 (24) ◽

pp. 1383-1392

Author(s):

Amirhossein Hakamivala ◽

Amirali Nojoomi ◽

Alieh Aminian ◽

Arghavan Farzadi ◽

Noor Azuan Abu Osman

Keyword(s):

Mechanical Properties ◽

Compressive Strength ◽

Response Surface Methodology ◽

Vertical Direction ◽

Dimensional Accuracy ◽

Efficient Design ◽

Dimensional Error ◽

Higher Dimensional ◽

3D Printed ◽

Cost Efficient

ABSTRACTInvestigating the mechanical properties and dimensional accuracy of 3D printed parts is an important step towards achieving optimum printing conditions. This condition, which leads to the fabrication of parts with appropriate mechanical properties and accuracy, is achieved by studying the effect of different process parameters on the final structure. In this work, Response Surface Methodology (RSM) was employed to design specified experiments to investigate the effects of layer thickness, printing orientation and delay, on the compressive strength and dimensional error of the parts. The results show that an increase in the delay time in X orientation results in better binder spreading and uniformity followed by improvement in the compression strength. Furthermore, more binder spreads in the vertical direction leads to the higher dimensional error in the Z direction. The results proved that the RSM provides a time and cost-efficient design to print the prototypes with optimum strength and dimensional error.

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