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Enhancing seismic feature orientations: A novel approach using directional derivatives and Hilbert transform of gradient structure tensor

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JOURNAL OF APPLIED GEOPHYSICS 2024年 230卷

作者： Singh, Gagandeep Mohanty, William K. Routray, Aurobinda Mahadik, Rahul Singh, S. K. Oil & Nat Gas Corp Ltd ONGC Geophys Surface Dehra Dun India Indian Inst Technol Dept Geol & Geophys Kharagpur India Indian Inst Technol Kharagpur Kharagpur India

Seismic dip calculation serves as a widely employed technique in the realms of seismic interpretation and reservoir characterization, strategically employed to highlight faults and attributes within the seismic volume. Among the various methodologies utilized for estimating structural dip and azimuth, the gradient structure tensor (GST) stands out. This approach involves leveraging the dominant eigenvector of the positive definite GST matrix to ascertain the inline and crossline dip of seismic data. In the initial phase of our innovative proposal, we employed the spectral balancing technique to enhance the fidelity of seismic data. Subsequently, leveraging this groundwork, we introduced an Analytical Directional gradient structure tensor technique, a distinctive adaptation of GST. This novel approach involves the calculation of directive derivatives in both perpendicular and parallel directions to seismic features. By incorporating directive derivatives, our method excels in capturing subtle stratigraphic nuances, particularly in the dipping direction of interest. To validate the accuracy and effectiveness of our approach, we present compelling evidence through the examination of synthetic and real-field seismic volume outcomes. This underscores the robustness and reliability of our proposed method in enhancing the precision of seismic dip calculations and providing valuable insights into subsurface geological features.

关键词： Fault detection gradient structure tensor Seismic data interpretation Spectral balancing

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Optimal Differentiators for the Algorithm of Orientation Estimation on the Basis of a gradient structure tensor

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OPTOELECTRONICS INSTRUMENTATION AND DATA PROCESSING 2012年第1期48卷 1-8页

作者： Gruzman, I. S. Novosibirsk State Tech Univ Pr Karla Marksa 20 Novosibirsk 630092 Russia

A method of constructing optimal mask differentiating filters minimizing the level of the root-mean-square or systematic error of estimation of the anisotropic structure orientation observed in the presence of additive white noise is proposed. Results of a comparative analysis of the accuracy of gradient algorithms are presented. It is demonstrated that the use of optimal differentiating filters substantially increases the accuracy of the orientation estimation algorithm.

关键词： optimal mask differentiating filters gradient structure tensor

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Estimation of the Trajectory of a Mark-Making Object Based on the gradient structure tensor

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OPTOELECTRONICS INSTRUMENTATION AND DATA PROCESSING 2011年第1期47卷 1-6页

作者： Gruzman, I. S. Karpushin, V. B. Novosibirsk State Tech Univ Pr Karla Marksa 20 Novosibirsk 630092 Russia

An estimation algorithm for the trajectory of a mark-making object is developed which does not require interactive selection of the region of marks. An adequate measure of the straightness of marks is proposed which allows quantitative evaluation of the performance of the estimation algorithms. Results of experimental studies are given that support the possibility of using the gradient structure tensor to estimate moving object trajectories from images obtained during motion analysis.

关键词： gradient structure tensor mark-making object line straightening motion analysis

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Efficiency of Estimation of Anisotropic Texture Orientation on the Basis of a gradient structure tensor

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OPTOELECTRONICS INSTRUMENTATION AND DATA PROCESSING 2011年第6期47卷 527-532页

作者： Gruzman, I. S. Novosibirsk State Tech Univ Pr Karla Marksa 20 Novosibirsk 630092 Russia

An approximate method is developed for calculating the systematic and root-mean-square errors of the algorithm for estimating the anisotropic texture orientation on the basis of a gradient structure tensor. It is demonstrated that the method is highly accurate and computationally efficient, as compared to the method of computer modeling.

关键词： gradient structure tensor estimation of orientation systematic and root-mean-square errors

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Critical Points Extraction from Building Facades by Analyzing gradient structure tensor

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REMOTE SENSING 2021年第16期13卷

作者： Chen, Dong Li, Jing Di, Shaoning Peethambaran, Jiju Xiang, Guiqiu Wan, Lincheng Li, Xianghong Nanjing Forestry Univ Coll Civil Engn Nanjing 210037 Peoples R China Cent South Univ Sch Geosci & Info Phys Changsha 410083 Peoples R China St Marys Univ Dept Math & Comp Sci Halifax NS B3P 2M6 Canada

This paper proposes a building facade contouring method from LiDAR (Light Detection and Ranging) scans and photogrammetric point clouds. To this end, we calculate the confidence property at multiple scales for an individual point cloud to measure the point cloud's quality. The confidence property is utilized in the definition of the gradient for each point. We encode the individual point gradient structure tensor, whose eigenvalues reflect the gradient variations in the local neighborhood areas. The critical point clouds representing the building facade and rooftop (if, of course, such rooftops exist) contours are then extracted by jointly analyzing dual-thresholds of the gradient and gradient structure tensor. Based on the requirements of compact representation, the initial obtained critical points are finally downsampled, thereby achieving a tradeoff between the accurate geometry and abstract representation at a reasonable level. Various experiments using representative buildings in Semantic3D benchmark and other ubiquitous point clouds from ALS DublinCity and Dutch AHN3 datasets, MLS TerraMobilita/iQmulus 3D urban analysis benchmark, UAV-based photogrammetric dataset, and GeoSLAM ZEB-HORIZON scans have shown that the proposed method generates building contours that are accurate, lightweight, and robust to ubiquitous point clouds. Two comparison experiments also prove the superiority of the proposed method in terms of topological correctness, geometric accuracy, and representation compactness.

关键词： critical points gradient gradient structure tensor simplification building facade Semantic3D DublinCity Dutch AHN3 potogrammetric point clouds GeoSLAM

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Measurement of structural anisotropy in femoral trabecular bone using clinical-resolution CT images

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JOURNAL OF BIOMECHANICS 2013年第15期46卷 2659-2666页

作者： Kersh, Mariana E. Zysset, Philippe K. Pahr, Dieter H. Wolfram, Uwe Larsson, David Pandy, Marcus G. Univ Melbourne Dept Mech Engn Parkville Vic 3010 Australia Univ Bern Inst Surg Technol & Biomech CH-3014 Bern Switzerland Vienna Univ Technol Inst Lightweight Design & Struct Biomech A-1040 Vienna Austria

Discrepancies in finite-element model predictions of bone strength may be attributed to the simplified modeling of bone as an isotropic structure due to the resolution limitations of clinical-level Computed Tomography (CT) data. The aim of this study is to calculate the preferential orientations of bone (the principal directions) and the extent to which bone is deposited more in one direction compared to another (degree of anisotropy). Using 100 femoral trabecular samples, the principal directions and degree of anisotropy were calculated with a gradient structure tensor (GST) and a Sobel structure tensor (SST) using clinical-level CT. The results were compared against those calculated with the gold standard Mean-Intercept-Length (MIL) fabric tensor using micro-CT. There was no significant difference between the GST and SST in the calculation of the main principal direction (median error=28 degrees), and the error was inversely correlated to the degree of transverse isotropy (r= -0.34, p < 0.01). The degree of anisotropy measured using the structure tensors was weakly correlated with the MIL-based measurements (r=0.2, p < 0.001). Combining the principal directions with the degree of anisotropy resulted in a significant increase in the correlation of the tensor distributions (r=0.79, p < 0.001). Both structure tensors were robust against simulated noise, kernel sizes, and bone volume fraction. We recommend the use of the GST because of its computational efficiency and ease of implementation. This methodology has the promise to predict the structural anisotropy of bone in areas with a high degree of anisotropy, and may improve the in vivo characterization of bone. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Clinical quantitative computed tomography Finite-element model gradient structure tensor Sobel structure tensor Trabecular bone strength

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On curvature estimation of ISO surfaces in 3D gray-value images and the computation of shape descriptors

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2004年第8期26卷 1088-1094页

作者： Rieger, B Timmermans, FJ van Vliet, LJ Verbeek, PW Delft Univ Technol Dept Appl Phys Pattern Recognit Grp NL-2628 CJ Delft Netherlands

In this paper, we present a novel method to estimate curvature of iso gray-level surfaces in gray-value images. Our method succeeds where standard isophote curvature estimation methods fail. There is neither a segmentation of the surface needed nor a parametric model assumed. Our estimator works on the orientation field of the surface. This orientation field and a description of local structure is obtained by the gradient structure tensor. The estimated orientation field has discontinuities mod pi. It is mapped via the Knutsson mapping to a continuous representation. The principal curvatures of the surface, a coordinate invariant property, are computed in this mapped representation. From these curvatures, locally the bending energy is computed to describe the surface shape. An extensive evaluation shows that our curvature estimation is robust even in the presence of noise, independent of the scale of the object and furthermore the relative error stays small.

关键词： principal curvatures surface area local surface measures gradient structure tensor Knutsson mapping

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Curvature of n-dimensional space curves in grey-value images

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IEEE TRANSACTIONS ON IMAGE PROCESSING 2002年第7期11卷 738-745页

作者： Rieger, B van Vliet, LJ Delft Univ Technol Dept Appl Phys Pattern Recognit Grp NL-2628 Delft Netherlands

Local curvature represents an important shape parameter of space curves which are well described by differential geometry. We have developed an estimator for local curvature of space curves embedded in n-dimensional (n-D) grey-value images. There is neither a segmentation of the curve needed nor a parametric model assumed. Our estimator works on the orientation field of the space curve. This orientation field and a description of local structure is obtained by the gradient structure tensor. The orientation field has discontinuities;walking around a closed contour yields two such discontinuities in orientation. This field is mapped via the Knutsson mapping to a continuous representation;from a n-D vector to a symmetric n(2)-D tensor field. The curvature of a space curve, a coordinate invariant property, is computed in this tensor field representation. An extensive evaluation shows that our curvature estimation is unbiased even in the presence of noise, independent of the scale of the object and furthermore the relative error stays small.

关键词： curvature gradient structure tensor Knutsson mapping space curves in n-D

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Detection in seismic data using curvelet transform and tensor-based elliptical adaptive structuring elements

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JOURNAL OF APPLIED GEOPHYSICS 2020年 172卷

作者： Boustani, Bahareh Javaherian, Abdolrahim Nabi-Bidhendi, Majid Torabi, Siyavash Amindavar, Hamid Reza Amirkabir Univ Technol Dept Petr Engn Tehran Iran Univ Tehran Inst Geophys Tehran Iran DMT Petrol GmbH & Co KGKarl Wiechert Allee D-7630625 Hannover Germany Amirkabir Univ Technol Dept Elect Engn Tehran Iran

Channels are one of the vital issues in the exploration of oil and gas. They can be considered as reservoirs if they are filled with porous and permeable material and placed in a suitable position. A detailed study of the channels can help identify the sedimentation processes of the area, the intensity, and direction of the sea currents. Manual interpretation of the channels is difficult and requires skill. Therefore, in this paper, the adaptive curvelet and morphological gradient algorithm (ACMG) is used for the automatic interpretation of the channels. First, the morphological gradient is applied to extract the edges of the channels;then, the curvelet transform is used to increase the signal-to-noise ratio. The morphological top-hat operator extracts the local maxima of curvelet subbands. In this workflow, we applied an elliptical adaptive structuring element (EASE) based on gradient structure tensor (GST). For the construction of the 2D GST, the horizontal and vertical gradients of the image were calculated by the first-order Gaussian derivative. The eigenvalue decomposition of each structure tensor can provide an estimate of the direction and anisotropy rate of the image objects. Hence, parameters of the elliptical structuring element are obtained by eigenvalue decomposition of the GST. To evaluate ACMG, we compared the final output with the results of the non-adaptive curvelet and morphological gradient algorithm (CMG). Also, we compared it with the common edge-detectors such as Canny, Sobel, Laplacian of Gaussian, and similarity attribute. The comparison shows that both CMG and ACMG well extracted the edge of the channels with the higher signal-to-noise ratio. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Channel edge Elliptical adaptive structuring element gradient structure tensor Morphological gradient Curvelet transform Top-hat

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Fault Enhancement Method of Seismic Data

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1st International Conference on Energy and Environmental Protection (ICEEP 2012)

作者： Feng Lei Li Guang-ming Henan Polytech Univ Sch Resources & Environm Jiaozuo Henan Province Peoples R China

ISBN: (纸本)9783037854167

With the deepening of the degree of oil exploitation, investigation of geological structure is particularly important, especially those faults that have an important impact on the exploration and development of oil. However, seismic data is affected by various kinds of factors in the progress of data acquisition, which reduces SNR and interfere with the accuracy of geological structure interpretation. This paper based on image processing provides fault enhancement medthod. It can reduce random factors impact and depicte fault more clearly. This method combine anisotropy and orientation information of image, then use generalized Kuwahara filter to enhance fault. This technique has a most important value in seismic fault interpretation.

关键词： generalized Kuwahara filter fault enhance gradient structure tensor

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