A novel method of combined interval analysis and homotopy continuation in indoor building reconstruction

Jamali, Ali; Castro, Francesc Antón; Mioc, Darka

doi:10.1080/0305215x.2018.1472253

Cited by 4 publications

(4 citation statements)

References 23 publications

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“…3D terrain modelling using piecewise cubic interpolation and smoothing piecewise cubic interpolation is shown in Figures 2 and 3 respectively. A homotopy is a continuous deformation of geometric figures or paths or more generally, functions: a function (or a path, or a geometric figure) is continuously deformed into another one (Allgower and Georg, 1990;Jamali et al, 2017;Jamali et al, 2018). A homotopy between two continuous functions f0 and f1 from a topological space X to a topological space Y is defined as a continuous map H: X × [0, 1] → Y from the Cartesian product of the topological space X with the unit interval [0, 1] to Y such that H (x, 0) = f0, and H (x, 1) = f1, where x ∈ X.…”

Section: Continuous Deformationmentioning

confidence: 99%

Topological 3d Elevation Data Interpolation of Aster Gdem Based on Continuous Deformation

Jamali

Castro

2018

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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<p><strong>Abstract.</strong> In Geographic Information Science, polynomial methods such as linear estimation and non-polynomial methods including Inverse Distance Weighting and Kriging have been used for elevation data interpolation. In this paper, 3D data interpolation using linear and non-linear homotopy continuation as well as advanced polynomial interpolation methods are researched. Continuous deformations that reconstruct straight lines or algebraic curves between any pair of 3D data are presented. The implemented topological mathematical algorithm for 3D elevation data interpolation is compared to Inverse Distance Weighting and Triangulated Irregular Network (TIN) methods. The presented linear and non-linear mathematical algorithms show better results compared to Inverse Distance Weighting and TIN in terms of Root Mean Square Error and L-infinity.</p>

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Section: Continuous Deformationmentioning

confidence: 99%

Topological 3d Elevation Data Interpolation of Aster Gdem Based on Continuous Deformation

Jamali

Castro

2018

Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci.

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“…Therefore, the proposed system is an efficient and accurate solution for indoor 3D mapping.surveying process requires skilled personnel and sufficient knowledge of the survey area to pick optimal stations, good network design for marker placement, etc. [5][6][7][8].Mobile measurement technology integrates positioning, attitude determination, and measurement, which realizes the measurement in motion, improves the degrees of freedom of the measurement platform, and greatly reduces the time and labor costs. A typical mobile measurement system (MMS) consists of laser scanners, optical cameras, the global navigation satellite system (GNSS) and a high-grade inertial measurement unit (IMU) mounted on a vehicle.…”

mentioning

confidence: 99%

“…surveying process requires skilled personnel and sufficient knowledge of the survey area to pick optimal stations, good network design for marker placement, etc. [5][6][7][8].…”

mentioning

confidence: 99%

“…To build the textured model, the common process is to build a model from point clouds and then map images to the model. There are many literature entries that discuss the construction of structured models from point clouds [7,[22][23][24]. Additionally, it is the most widely used method for fitting and segmenting point clouds by relying on the systematic surfaces of artificial buildings.…”

mentioning

confidence: 99%

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Panoramic Image and Three-Axis Laser Scanner Integrated Approach for Indoor 3D Mapping

Zhao

Wang

et al. 2018

Remote Sensing

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High-precision indoor three-dimensional maps are a prerequisite for building information models, indoor location-based services, etc., but the indoor mapping solution is still in the stage of technological experiment and application scenario development. In this paper, indoor mapping equipment integrating a three-axis laser scanner and panoramic camera is designed, and the corresponding workflow and critical technologies are described. First, hardware design and software for controlling the operations and calibration of the spatial relationship between sensors are completed. Then, the trajectory of the carrier is evaluated by a simultaneous location and mapping framework, which includes reckoning of the real-time position and attitude of the carrier by a filter fusing the horizontally placed laser scanner data and inertial measurement data, as well as the global optimization by a closed-loop adjustment using a graph optimization algorithm. Finally, the 3D point clouds and panoramic images of the scene are reconstructed from two tilt-mounted laser scanners and the panoramic camera by synchronization of the position and attitude of the carrier. The experiment was carried out in a five-story library using the proposed prototype system; the results demonstrate accuracies of up to 3 cm for 2D maps, and up to 5 cm for 3D maps, and the produced point clouds and panoramic images can be utilized for modeling and further works related to large-scale indoor scenes. Therefore, the proposed system is an efficient and accurate solution for indoor 3D mapping.surveying process requires skilled personnel and sufficient knowledge of the survey area to pick optimal stations, good network design for marker placement, etc. [5][6][7][8].Mobile measurement technology integrates positioning, attitude determination, and measurement, which realizes the measurement in motion, improves the degrees of freedom of the measurement platform, and greatly reduces the time and labor costs. A typical mobile measurement system (MMS) consists of laser scanners, optical cameras, the global navigation satellite system (GNSS) and a high-grade inertial measurement unit (IMU) mounted on a vehicle. The trajectory of the vehicle is determined using GNSS and IMU, and the measurement results of scanners and cameras are reconstructed to a unified geographic frame by the relative position and attitude between units. The acquisition technology of large-scale outdoor point clouds using MMS has matured, and this type of system has been commercially available for several years and can achieve good accuracy [9][10][11][12]. Unfortunately, such a system cannot be directly used for indoor applications due to its reliance on GNSS, which obviously is not available indoors.With the boom of machine vision and the robotics industry, simultaneous location and mapping (SLAM) is extensively studied. SLAM solves the chicken-and-egg problem in an unknown environment by positioning according to the motion estimation and the existing map while simultaneously building an incrementa...

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Topological 3D Spatial Interpolation Based on the Interval-Valued Homotopy Continuation

Jamali

Castro

Karaş

2023

Lecture Notes in Networks and Systems

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A novel method of combined interval analysis and homotopy continuation in indoor building reconstruction

Cited by 4 publications

References 23 publications

Topological 3d Elevation Data Interpolation of Aster Gdem Based on Continuous Deformation

Topological 3d Elevation Data Interpolation of Aster Gdem Based on Continuous Deformation

Panoramic Image and Three-Axis Laser Scanner Integrated Approach for Indoor 3D Mapping

Topological 3D Spatial Interpolation Based on the Interval-Valued Homotopy Continuation

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