scholarly journals Weighted Quasi-Interpolant Spline Approximations of Planar Curvilinear Profiles in Digital Images

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3084
Author(s):  
Andrea Raffo ◽  
Silvia Biasotti
Keyword(s):  
Digital Images ◽  
Spline Approximation ◽  
Detection Algorithm ◽  
Polynomial Spline ◽  
Automatic Method ◽  
Data Perturbation ◽  
Spline Curves ◽  
Curve Approximation ◽  
Local Approximations ◽  
Edge Points

The approximation of curvilinear profiles is very popular for processing digital images and leads to numerous applications such as image segmentation, compression and recognition. In this paper, we develop a novel semi-automatic method based on quasi-interpolation. The method consists of three steps: a preprocessing step exploiting an edge detection algorithm; a splitting procedure to break the just-obtained set of edge points into smaller subsets; and a final step involving the use of a local curve approximation, the Weighted Quasi Interpolant Spline Approximation (wQISA), chosen for its robustness to data perturbation. The proposed method builds a sequence of polynomial spline curves, connected C0 in correspondence of cusps, G1 otherwise. To curb underfitting and overfitting, the computation of local approximations exploits the supervised learning paradigm. The effectiveness of the method is shown with simulation on real images from various application domains.

Extracting Geometric Edges from 3D Point Clouds Based on Normal Vector Change

2014 ◽  
Vol 571-572 ◽  
pp. 729-734
Author(s):  
Jia Li ◽  
Huan Lin ◽  
Duo Qiang Zhang ◽  
Xiao Lu Xue
Keyword(s):  
Point Clouds ◽  
Detection Algorithm ◽  
Growth Strategy ◽  
Normal Vector ◽  
Geometric Morphometric ◽  
3D Point Clouds ◽  
Real Scene ◽  
Edge Points ◽  
Normal Vectors ◽  
Change Intensity

Normal vector of 3D surface is important differential geometric property over localized neighborhood, and its abrupt change along the surface directly reflects the variation of geometric morphometric. Based on this observation, this paper presents a novel edge detection algorithm in 3D point clouds, which utilizes the change intensity and change direction of adjacent normal vectors and is composed of three steps. First, a two-dimensional grid is constructed according to the inherent data acquisition sequence so as to build up the topology of points. Second, by this topological structure preliminary edge points are retrieved, and the potential directions of edges passing through them are estimated according to the change of normal vectors between adjacent points. Finally, an edge growth strategy is designed to regain the missing edge points and connect them into complete edge lines. The results of experiment in a real scene demonstrate that the proposed algorithm can extract geometric edges from 3D point clouds robustly, and is able to reduce edge quality’s dependence on user defined parameters.

L 1 C 1 polynomial spline approximation algorithms for large data sets

2014 ◽  
Vol 67 (4) ◽  
pp. 807-826 ◽  
Author(s):  
Laurent Gajny ◽  
Olivier Gibaru ◽  
Eric Nyiri
Keyword(s):  
Approximation Algorithms ◽  
Spline Approximation ◽  
Large Data ◽  
Polynomial Spline ◽  
Large Data Sets ◽  
Data Sets

scholarly journals Lane Detection Algorithm Based on Road Structure and Extended Kalman Filter

2020 ◽  
Vol 12 (2) ◽  
pp. 1-20
Author(s):  
Jinsheng Xiao ◽  
Wenxin Xiong ◽  
Yuan Yao ◽  
Liang Li ◽  
Reinhard Klette
Keyword(s):  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Region Of Interest ◽  
Detection Algorithm ◽  
Lane Detection ◽  
Strong Light ◽  
Edge Strength ◽  
Straight Line ◽  
Edge Points ◽  
The Stability

Lane detection still demonstrates low accuracy and missing robustness when recorded markings are interrupted by strong light or shadows or missing marking. This article proposes a new algorithm using a model of road structure and an extended Kalman filter. The region of interest is set according to the vanishing point. First, an edge-detection operator is used to scan horizontal pixels and calculate edge-strength values. The corresponding straight line is detected by line parameters voted by edge points. From the edge points and lane mark candidates extracted above, and other constraints, these points are treated as the potential lane boundary. Finally, the lane parameters are estimated using the coordinates of the lane boundary points. They are updated by an extended Kalman filter to ensure the stability and robustness. Results indicate that the proposed algorithm is robust for challenging road scenes with low computational complexity.

Low-Degree B-Spline Approximation of Procedurally Defined Curves

1999 ◽  
Author(s):  
Jun Qu ◽  
Radha Sarma
Keyword(s):  
Spline Approximation ◽  
Optimality Criteria ◽  
Least Square ◽  
B Spline ◽  
Spline Curves ◽  
Low Degree ◽  
Integration Techniques ◽  
Error Metric ◽  
High Level ◽  
The Ideal

Abstract This paper outlines an algorithm for approximating procedurally defined curves with low-degree, integral b-spline curves. The algorithm is based on minimizing a least square error metric between the ideal and approximated curves. Expressions for optimality criteria using the least square error metric are derived from a combination of exact b-spline integration and numerical integration techniques, thereby eliminating the need for sampling the ideal curve. A high-level iterative procedure that doubles knots at each step is proposed to ensure that the deviations between the ideal and approximated curves are within user specified limits. Issues of computational complexity are addressed and several examples are presented that illustrate the effectiveness of the algorithm.

scholarly journals Polynomial Spline-Approximation of Clarke's Model

2004 ◽  
Vol 52 (5) ◽  
pp. 1198-1208 ◽  
Author(s):  
Y.V. Zakharov ◽  
T.C. Tozer ◽  
J.F. Adlard
Keyword(s):  
Spline Approximation ◽  
Polynomial Spline
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