Automatic object and image alignment using Fourier Descriptors

Duan, Weisheng; Kuester, Falko; Gaudiot, Jean‐Luc; Hammami, Omar

doi:10.1016/j.imavis.2008.01.009

Cited by 20 publications

(13 citation statements)

References 26 publications

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“…The shape similarity is measured using the Euclidean distance between the normalized Fourier descriptors (FDs) of two contours. FDs are typically used in image retrieval and pattern recognition because of their insensitivity to geometric translation, rotation, and scaling [64][65][66][67]. We employ the normalized Fourier descriptor (nFD) to measure the approximate shape similarity between two contours based on the assumption that the shape differences among the intact contour clusters are only produced by geometric translations and scaling, whereas the damaged contour clusters do not follow this assumption.…”

Section: Feature Definitionmentioning

confidence: 99%

“…The Fourier coefficients a(k) are normalized to make them invariant to the translation, rotation, and scaling of contours [67]. The normalized FDs are defined as in Equation (8).…”

Section: Feature Definitionmentioning

confidence: 99%

“…Translation invariance can be achieved by omitting the Fourier coefficient a(0) and using the other Fourier coefficients because translation affects only the first Fourier coefficient a(0), and the other FDs retain their values [64]. The FDs are made invariant against rotation by taking the magnitude of each Fourier coefficient, and they are made scale invariant by dividing all Fourier coefficients by the magnitude of a(1) [64,67]. The normalized FD na(k), defined in Equation (8), also omits the second Fourier coefficient because it is a constant value of 1.…”

Section: Feature Definitionmentioning

confidence: 99%

“…In most cases, these two contours contain a different number of points, and their normalized Fourier coefficients are not same; therefore, the Euclidean distance cannot be directly calculated. To solve this problem, both contours are first sampled such that they have the same number of points before FDs are applied to the two contours [67]. The shape chaos index is calculated based on an entropy definition whereby the probability is defined as the ratio between the number of contours with similar shapes and the total number of contours in the contour cluster, as detailed in Section 2.2.1.…”

Section: Feature Definitionmentioning

confidence: 99%

See 3 more Smart Citations

A 3D Shape Descriptor Based on Contour Clusters for Damaged Roof Detection Using Airborne LiDAR Point Clouds

Zhu

et al. 2016

Remote Sensing

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Abstract:The rapid and accurate assessment of building damage states using only post-event remote sensing data is critical when performing loss estimation in earthquake emergency response. Damaged roof detection is one of the most efficient methods of assessing building damage. In particular, airborne LiDAR is often used to detect roofs damaged by earthquakes, especially for certain damage types, due to its ability to rapidly acquire accurate 3D information on individual roofs. Earthquake-induced roof damages are categorized into surface damages and structural damages based on the geometry features of the debris and the roof structure. However, recent studies have mainly focused on surface damage; little research has been conducted on structural damage. This paper presents an original 3D shape descriptor of individual roofs for detecting roofs with surface damage and roofs exhibiting structural damage by identifying spatial patterns of compact and regular contours for intact roofs, as well as jagged and irregular contours for damaged roofs. The 3D shape descriptor is extracted from building contours derived from airborne LiDAR point clouds. First, contour clusters are extracted from contours that are generated from a dense DSM of individual buildings derived from point clouds. Second, the shape chaos indexes of contour clusters are computed as the information entropy through a contour shape similarity measurement between two contours in a contour cluster. Finally, the 3D shape descriptor is calculated as the weighted sum of the shape chaos index of each contour cluster corresponding to an individual roof. Damaged roofs are detected solely using the 3D shape descriptor with the maximum entropy threshold. Experiments using post-event airborne LiDAR point clouds of the 2010 Haiti earthquake suggest that the proposed damaged roof detection technique using the proposed 3D shape descriptor can detect both roofs exhibiting surface damage and roofs exhibiting structural damage with a high accuracy.

show abstract

Section: Feature Definitionmentioning

confidence: 99%

“…The Fourier coefficients a(k) are normalized to make them invariant to the translation, rotation, and scaling of contours [67]. The normalized FDs are defined as in Equation (8).…”

Section: Feature Definitionmentioning

confidence: 99%

Section: Feature Definitionmentioning

confidence: 99%

Section: Feature Definitionmentioning

confidence: 99%

See 2 more Smart Citations

A 3D Shape Descriptor Based on Contour Clusters for Damaged Roof Detection Using Airborne LiDAR Point Clouds

Zhu

et al. 2016

Remote Sensing

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show abstract

“…Note that the variable is not used in this study. After (15) was expanded, the kinematic equation of the stage becomes…”

Section: Concept Of Floating Center Transformationmentioning

confidence: 99%

Development of a High Precision Edge Alignment System for Touch-Panel Glass Substrates

Lee

Liu

Chen

2014

Advances in Mechanical Engineering

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There are two kinds of alignment systems, marked and unmarked. The glass substrate for touch panels is categorized as an unmarked work piece. Vision based glass substrate alignment (GSA) relies on the edge of the glass. Traditional GSA systems compensate first for angular and then for linear error. This reduces alignment accuracy and increases alignment time and edge detection usually takes longer than 10 ms. This study proposes an effortless edge detection method. This method is very simple and can significantly reduce the time taken to detect the edge to about 6 ms using a 1.3 megapixel image. In this study, a floating center idea is used to control the glass substrate on a high precision coplanar alignment stage. According to the method, users can set the rotation center anywhere as long as it is on the working ( ) plane. Tolerance prognosis is also considered in this study to help the operator decide if the substrate is usable or should be rejected. The experimental results show alignment repeatability of the , , and axes to be 1 m, 1 m, and 5 arcsec, respectively.

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Specific Document Sign Location Detection Based on Point Matching and Clustering

Xiong

2018

Advances in Visual Computing

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Automatic object and image alignment using Fourier Descriptors

Cited by 20 publications

References 26 publications

A 3D Shape Descriptor Based on Contour Clusters for Damaged Roof Detection Using Airborne LiDAR Point Clouds

A 3D Shape Descriptor Based on Contour Clusters for Damaged Roof Detection Using Airborne LiDAR Point Clouds

Development of a High Precision Edge Alignment System for Touch-Panel Glass Substrates

Specific Document Sign Location Detection Based on Point Matching and Clustering

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