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

2005 ◽  
Vol 37 (3) ◽  
pp. 571-603 ◽  
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.

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

2005 ◽  
Vol 37 (03) ◽  
pp. 571-603 ◽  
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 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.

A Novel Embedded System Architecture for Fire Detection Based on Image Processing

2014 ◽  
Vol 608-609 ◽  
pp. 454-458
Author(s):  
Wei Bai ◽  
Chen Yuan Hu
Keyword(s):  
Image Processing ◽  
Embedded System ◽  
System Architecture ◽  
Cooperative Control ◽  
Processing System ◽  
Fire Detection ◽  
System Level ◽  
High Definition ◽  
The Embedded System ◽  
Pass Through

This paper presents novel logic/software co-work architecture for embedded high definition image processing platform, which is built by the considerations of system level, board hardware level, and the tasks partition between CPU processing and programmable logic based on the latest launched System on Chip Field Programmable Gate Array (Soc FPGA) – Xilinx ZC7020. For this case, we comprehensive analyze of the critical data paths: the uniform Advanced Extensible Interface (AXI) processing between processing system (PS) and processing logic (PL), including high definition video pass through PL to PS and PS software processing send to PL for speed up. We have included the transplant of opensource Linux, multiprocessing cooperative control and boot loader in PS side. Since the general platform is proposed, a fire detection approach based on high definition image processing is implemented. Experiment results indicated the feasibility and universality of the embedded system architecture.

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

2018 ◽  
Vol 34 (6-8) ◽  
pp. 1021-1030 ◽  
Author(s):  
Enkhbayar Altantsetseg ◽  
Oyundolgor Khorloo ◽  
Kouichi Konno
Keyword(s):  
Point Clouds ◽  
Dimensional Error ◽  
Rigid Registration ◽  
Error Metrics ◽  
Higher Dimensional

scholarly journals Evaluation of feature-based methods for automated network orientation

2014 ◽  
Vol XL-5 ◽  
pp. 47-54 ◽  
Author(s):  
F.I. Apollonio ◽  
A. Ballabeni ◽  
M. Gaiani ◽  
F. Remondino
Keyword(s):  
Image Processing ◽  
3D Reconstruction ◽  
Processing Time ◽  
Point Clouds ◽  
Large Networks ◽  
Sift Algorithm ◽  
3D Point Clouds ◽  
Network Orientation ◽  
Feature Based ◽  
Automated Image Processing

Every day new tools and algorithms for automated image processing and 3D reconstruction purposes become available, giving the possibility to process large networks of unoriented and markerless images, delivering sparse 3D point clouds at reasonable processing time. In this paper we evaluate some feature-based methods used to automatically extract the tie points necessary for calibration and orientation procedures, in order to better understand their performances for 3D reconstruction purposes. The performed tests – based on the analysis of the SIFT algorithm and its most used variants – processed some datasets and analysed various interesting parameters and outcomes (e.g. number of oriented cameras, average rays per 3D points, average intersection angles per 3D points, theoretical precision of the computed 3D object coordinates, etc.).

scholarly journals Polynomial approximation on spheres - generalizing de la Vallée-Poussin

2011 ◽  
Vol 11 (4) ◽  
pp. 540-552 ◽  
Author(s):  
Ian H. Sloan
Keyword(s):  
Trigonometric Polynomial ◽  
Polynomial Approximation ◽  
Piecewise Linear ◽  
Continuous Functions ◽  
Fast Convergence ◽  
Piecewise Polynomial ◽  
Smooth Functions ◽  
Higher Dimensional ◽  
Trigonometric Polynomial Approximation ◽  
De La Vallée Poussin

AbstractFor trigonometric polynomial approximation on a circle, the century-old de la Vallée-Poussin construction has attractive features: it exhibits uniform convergence for all continuous functions as the degree of the trigonometric polynomial goes to infinity, yet it also has arbitrarily fast convergence for sufficiently smooth functions. This paper presents an explicit generalization of the de la Vallée-Poussin construction to higher dimensional spheres S^d ≤ R^{d+1}. The generalization replaces the C^∞ filter introduced by Rustamov by a piecewise polynomial of minimal degree. For the case of the circle the filter is piecewise linear, and recovers the de la Vallée-Poussin construction, while for the general sphere S^d the filter is a piecewise polynomial of degree d and smoothness C^{d−1}. In all cases the approximation converges uniformly for all continuous functions, and has arbitrarily fast convergence for smooth functions.

scholarly journals 3D RECORDING AND MODELLING OF MIDDLE-AGE FORTRESS IN DENSE VEGETATION ENVIRONMENT

2017 ◽  
Vol XLII-2/W5 ◽  
pp. 415-420
Author(s):  
M. Koehl ◽  
Y. Courtois ◽  
S. Guillemin
Keyword(s):  
World War I ◽  
Middle Ages ◽  
Laser Scanning ◽  
Digital Terrain Model ◽  
Point Clouds ◽  
Major Step ◽  
Terrain Model ◽  
Dense Vegetation ◽  
Aerial Photogrammetry ◽  
Pass Through

The Schwartzenbourg castle is a Middle-Ages fortress which was built in 1261. It is situated above the valley of Munster in Alsace, France. It was mainly used as a fortified place and a jail. In the early 15th century, the structure has deteriorated. Even after some repairs, it fell into ruins during the Thirty Years’ war (1618-1648) and stayed uninhabited. During World War I, the German army used the place as a vantage point and also built a blockhouse inside the ruins. Nowadays, the ruins are gradually collapsing and the remains of the old walls are completely covered by thick plants.<br><br> The goal of this project was to create a 3D-model of the site before closing its access, which became too dangerous for people. This modelling is divided into two elements: on one hand, a digital terrain model (DTM) of the site in order to replace the castle and to analyze the background of its original environment; on the other hand, a 3D modelling of the ruins of the castle invaded by the vegetation. Indeed, the main difficulty of the measurement is obviously the dense vegetation which hides the castle. Held back for years outside the castle, it has now become an integral part of the ruins. This vegetation is finally today usually the first threat of heritage buildings. After a preliminary inspection of the site as well as difficulties of the project, the first step consisted of the survey of the whole environment of the site. We will therefore describe the different phases of the survey with the initial implementation of a georeferenced network on site. We will present the terrestrial laser scanning (TLS) surveys, then complementary surveys carried out by aerial photogrammetry. To be implemented, we had to wait for an advanced autumn in order to have as few leaves on trees as possible. The major step of processing of point clouds described in this paper is then the extraction of a DTM by using techniques to pass through the vegetation, or better to segment the points into different classes, one of these that would be the soil i.e. DTM, another consists into wall parts of the ruins.

scholarly journals Determining the Optimal Number of Ground Control Points for Varying Study Sites through Accuracy Evaluation of Unmanned Aerial System-Based 3D Point Clouds and Digital Surface Models

Drones ◽  
2020 ◽  
Vol 4 (3) ◽  
pp. 49 ◽  
Author(s):  
Jae Jin Yu ◽  
Dong Woo Kim ◽  
Eun Jung Lee ◽  
Seung Woo Son
Keyword(s):  
Image Processing ◽  
Point Clouds ◽  
Optimal Number ◽  
Ground Control ◽  
Control Points ◽  
Widespread Application ◽  
Ground Control Points ◽  
3D Point Clouds ◽  
Surface Models ◽  
Study Sites

The rapid development of drone technologies, such as unmanned aerial systems (UASs) and unmanned aerial vehicles (UAVs), has led to the widespread application of three-dimensional (3D) point clouds and digital surface models (DSMs). Due to the number of UAS technology applications across many fields, studies on the verification of the accuracy of image processing results have increased. In previous studies, the optimal number of ground control points (GCPs) was determined for a specific area of a study site by increasing or decreasing the amount of GCPs. However, these studies were mainly conducted in a single study site, and the results were not compared with those from various study sites. In this study, to determine the optimal number of GCPs for modeling multiple areas, the accuracy of 3D point clouds and DSMs were analyzed in three study sites with different areas according to the number of GCPs. The results showed that the optimal number of GCPs was 12 for small and medium sites (7 and 39 ha) and 18 for the large sites (342 ha) based on the overall accuracy. If these results are used for UAV image processing in the future, accurate modeling will be possible with minimal effort in GCPs.

Point derivations and cohomologies of Lipschitz algebras

2019 ◽  
Vol 62 (4) ◽  
pp. 1173-1187
Author(s):  
Kazuhiro Kawamura
Keyword(s):  
Metric Spaces ◽  
Banach Algebras ◽  
Studia Math ◽  
Lipschitz Functions ◽  
Homological Dimension ◽  
Smooth Functions ◽  
Infinite Dimensional ◽  
Higher Dimensional ◽  
Geodesic Metric ◽  
Dual Module

AbstractFor a compact metric space (K, d), LipK denotes the Banach algebra of all complex-valued Lipschitz functions on (K, d). We show that the continuous Hochschild cohomology Hn(LipK, (LipK)*) and Hn(LipK, ℂe) are both infinite-dimensional vector spaces for each n ≥ 1 if the space K contains a certain infinite sequence which converges to a point e ∈ K. Here (LipK)* is the dual module of LipK and ℂe denotes the complex numbers with a LipK-bimodule structure defined by evaluations of LipK-functions at e. Examples of such metric spaces include all compact Riemannian manifolds, compact geodesic metric spaces and infinite compact subsets of ℝ. In particular, the (small) global homological dimension of LipK is infinite for every such space. Our proof uses the description of point derivations by Sherbert [‘The structure of ideals and point derivations in Banach algebras of Lipschitz functions’, Trans. Amer. Math. Soc.111 (1964), 240–272] and directly constructs non-trivial cocycles with the help of alternating cocycles of Johnson [‘Higher-dimensional weak amenability’, Studia Math.123 (1997), 117–134]. An alternating construction of cocycles on the basis of the idea of Kleshchev [‘Homological dimension of Banach algebras of smooth functions is equal to infinity’, Vest. Math. Mosk. Univ. Ser. 1. Mat. Mech.6 (1988), 57–60] is also discussed.

Feature extraction from 3D lidar point clouds using image processing methods

2011 ◽  
Author(s):  
Ling Zhu ◽  
Ashton Shortridge ◽  
David Lusch ◽  
Ruoming Shi
Keyword(s):  
Image Processing ◽  
Feature Extraction ◽  
Point Clouds ◽  
Processing Methods ◽  
3D Lidar

scholarly journals Microsaccades during high speed continuous visual search

2020 ◽  
Vol 13 (5) ◽  
Author(s):  
Jacob G. Martin ◽  
Charles E. Davis ◽  
Maximilian Riesenhuber ◽  
Simon J. Thorpe
Keyword(s):  
Visual Search ◽  
High Speed ◽  
Stimulus Onset ◽  
Visual Hierarchy ◽  
The Face ◽  
Cluttered Background ◽  
Random Location ◽  
Pass Through ◽  
Task Oriented ◽  
Inverted Face

Here, we provide an analysis of the microsaccades that occurred during continuous visual search and targeting of small faces that we pasted either into cluttered background photos or into a simple gray background.  Subjects continuously used their eyes to target singular 3-degree upright or inverted faces in changing scenes.  As soon as the participant’s gaze reached the target face, a new face was displayed in a different and random location.  Regardless of the experimental context (e.g. background scene, no background scene), or target eccentricity (from 4 to 20 degrees of visual angle), we found that the microsaccade rate dropped to near zero levels within only 12 milliseconds after stimulus onset.  There were almost never any microsaccades after stimulus onset and before the first saccade to the face.  One subject completed 118 consecutive trials without a single microsaccade.  However, in about 20% of the trials, there was a single microsaccade that occurred almost immediately after the preceding saccade’s offset.  These microsaccades were task oriented because their facial landmark targeting distributions matched those of saccades within both the upright and inverted face conditions.  Our findings show that a single feedforward pass through the visual hierarchy for each stimulus is likely all that is needed to effectuate prolonged continuous visual search.  In addition, we provide evidence that microsaccades can serve perceptual functions like correcting saccades or effectuating task-oriented goals during continuous visual search.

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