CN109242968A - A kind of river three-dimensional modeling method cut based on the super voxel figure of more attributes - Google Patents
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Abstract
本发明提供了一种基于多属性超体素图割的河道三维建模方法,属于地质体三维模型构建领域。针对单一地震属性对河道刻画的不足,本发明提出了一种基于改进的局部线性嵌入的多属性融合方法,通过ISOLLE算法将优选的多种属性融合成为新的属性,考虑到地震属性数据间存在的非线性关系,采用一种非线性的融合方法,融合后的属性优于之前的多种属性,对河道边缘与区域刻画的准确性都得到了提升,为下一步的分割和重建打下了良好的基础;本发明基于超体素和图割的河道分割方法,通过简单线性迭代算法生成三维超体素,生成的超体素很好的贴合了河道的边缘,并且具有良好的同质性,再结合图割框架得到最终的分割结果,提取等值面的方式得到河道表面的三维模型。
The invention provides a three-dimensional modeling method of a river channel based on a multi-attribute super-voxel graph cut, which belongs to the field of three-dimensional model construction of geological bodies. Aiming at the insufficiency of a single seismic attribute to describe the river channel, the present invention proposes a multi-attribute fusion method based on an improved local linear embedding. The ISOLLE algorithm fuses the preferred attributes into a new attribute. Considering the existence of existing seismic attribute data A nonlinear fusion method is adopted. The fused attributes are better than the previous attributes, and the accuracy of the river edge and region characterization has been improved, laying a good foundation for the next segmentation and reconstruction. The present invention is based on the super-voxel and graph-cut channel segmentation method, and generates three-dimensional super-voxels through a simple linear iterative algorithm. The generated super-voxels fit the edge of the channel well and have good homogeneity. , and then combined with the graph cutting framework to obtain the final segmentation result, and extract the isosurface to obtain the three-dimensional model of the river surface.
Description
技术领域technical field
本发明属于地质体三维模型构建领域,特别涉及一种基于多属性超体素图 割的河道三维建模方法。The invention belongs to the field of three-dimensional model construction of geological bodies, and in particular relates to a three-dimensional modeling method of a river channel based on multi-attribute super-voxel map cuts.
背景技术Background technique
地质体(河道)三维模型构建是地震数据解释中最重要的任务之一,因为 大多数重要的油气藏都存在于地质体周围。地质体的三维模型不仅能够直观地 表现地质体的构造形态以及在三维空间的分布状况,使解释人员能够对地质体 进行定量的分析,同时也为油藏数值模拟、储量计算井位部署提供重要依据。Building a 3D model of a geological body (channel) is one of the most important tasks in seismic data interpretation because most important hydrocarbon reservoirs exist around the geological body. The 3D model of the geological body can not only intuitively express the structural form of the geological body and its distribution in the 3D space, so that the interpreter can quantitatively analyze the geological body, but also provide important information for the numerical simulation of the reservoir and the deployment of the well location for reserves calculation. in accordance with.
边缘检测的方法是用于地质体检测的一种常见方法,采用基于边缘检测的 方法识别盐丘边界,但由于地震数据中存在较大的噪声,这种方法并不能达到 理想的效果。现有技术中还有一种将3D边缘检测器与倾角导向结合的方法用于 地质体的检测,提高了信噪比与边缘连续性,使地质体的边界形状更清晰。但 基于边缘的方法对振幅的变化依赖性较强,在边缘的瞬时振幅变化不明显时, 无法得到很好的检测效果。为了克服这些问题,引入了基于纹理属性的地质体 识别方法。可使用一组纹理属性来预测3D立方体中每个像素属于盐丘的概率, 再通过分割找到盐丘边界。现有技术针对边缘处像素变化较大这一特点,使用 纹理梯度来检测盐丘的边界。但对于基于纹理的方法,窗口的大小对识别结果 有很大的影响,对不同工区来说不具有普适性。有一种组合的边缘与纹理属性 的混合分类方法,兼具边缘法和纹理法的优点,能较好的检测盐丘。进一步将 边缘检测、几何和纹理三种属性结合起来,再通过支持向量机(SVM)进行半 自动的断层检测,检测结果与原始图像较匹配。The edge detection method is a common method for geological body detection. The edge detection-based method is used to identify salt dome boundaries, but due to the large noise in seismic data, this method cannot achieve ideal results. In the prior art, there is also a method combining a 3D edge detector and dip angle steering for the detection of geological bodies, which improves the signal-to-noise ratio and edge continuity, and makes the boundary shape of the geological body clearer. However, the edge-based method has a strong dependence on the change of the amplitude, and cannot obtain a good detection effect when the instantaneous amplitude change of the edge is not obvious. In order to overcome these problems, a geological body identification method based on texture attributes is introduced. A set of texture attributes can be used to predict the probability that each pixel in the 3D cube belongs to a salt dome, and then segmentation can be used to find the salt dome boundary. The prior art uses texture gradients to detect the boundaries of salt domes in view of the large pixel variation at the edge. But for texture-based methods, the size of the window has a great influence on the recognition results, and it is not universal for different work areas. There is a hybrid classification method combining edge and texture attributes, which has the advantages of edge method and texture method, and can better detect salt domes. The three attributes of edge detection, geometry and texture are further combined, and then semi-automatic tomographic detection is carried out through support vector machine (SVM), and the detection results match the original image.
但与盐丘、溶洞等地质体不同,河道本身并没有明显、确定的边界,同时 河道经常变化、交叉,连续性较差,因此以上地质体识别分割的方法并不能很 好的应用在河道分割中。However, unlike geological bodies such as salt domes and karst caves, the river itself does not have an obvious and definite boundary, and at the same time, the river often changes, intersects, and has poor continuity. Therefore, the above methods of identifying and segmenting geological bodies cannot be well applied to river segmentation. middle.
很多学者从地震属性的角度来分割河道。地震属性是通过一定的算法从原 始三维地震数据中提取出的数据体,地震属性从不同的角度反映了地震数据的 特点,不同的地质构造在属性值上显示出不同的特征。首先用地震属性来辅助 分析河道,通过对多个地震属性切片图的对比分析,综合比较划分河道边界。 但在此方法中,数据的信噪比极大地影响了地震属性分辨率与质量,且部分地 震属性对河道的划分并没有帮助。将RGB多属性融合技术应用到河道的识别中, 使河道边缘更加清晰,分辨率提高。通过相干性和谱分解将地震属性分解为三 个频段,分别用不同颜色表示,再通过RGB混频技术进行可视化,能够快速有 效的识别河道。但RGB融合技术只能融合三种属性,具有一定的局限性,在需 要融合更多种属性时不适用,并且大多数研究只是使用可视化技术辅助主观判 断,并没有定性的分割出河道边界。Many scholars divide river channels from the perspective of seismic attributes. Seismic attributes are data volumes extracted from the original 3D seismic data through certain algorithms. Seismic attributes reflect the characteristics of seismic data from different angles, and different geological structures show different characteristics in attribute values. Firstly, the seismic attribute is used to assist in the analysis of the river channel. Through the comparative analysis of multiple seismic attribute slice maps, the river channel boundary is comprehensively compared and compared. However, in this method, the signal-to-noise ratio of the data greatly affects the resolution and quality of seismic attributes, and some seismic attributes are not helpful for channel division. The RGB multi-attribute fusion technology is applied to the identification of the river channel, so that the edge of the river channel is clearer and the resolution is improved. Seismic attributes are decomposed into three frequency bands through coherence and spectral decomposition, which are represented by different colors, and then visualized through RGB mixing technology, which can quickly and effectively identify river channels. However, RGB fusion technology can only fuse three attributes, which has certain limitations. It is not applicable when more attributes need to be fused, and most studies only use visualization technology to assist subjective judgment, and do not qualitatively segment the river boundary.
近年来,很多学者把地质问题与图像结合起来以达到准确分割目的。将改 进的PRC分割算法应用于二维和三维的地震图像中,能够半自动的精确分割盐丘 边界。使用最优路径拾取算法在新图像中提取盐丘边界,该算法通过选择具有 全局最大包络值的最佳路径来跟踪高度不连续的盐丘边界,能够快速更新得到 盐边界。In recent years, many scholars have combined geological problems with images to achieve accurate segmentation. Applying the improved PRC segmentation algorithm to 2D and 3D seismic images, the salt dome boundary can be accurately segmented semi-automatically. Salt dome boundaries are extracted in new images using an optimal path picking algorithm that tracks highly discontinuous salt dome boundaries by selecting the optimal path with the global maximum envelope value, which can be quickly updated to obtain salt boundaries.
基于图像的方法在河道地质体的问题上也同样适用。为了解决河道结构复 杂、连续性差等问题,通过图像处理中steerable pyramid的方法来增强河道的局 部线性特征。有一种置信度和曲率引导的水平集方法从三维地震数据中分割河 道。在融合多种地震属性的基础上,用水平集的方法对溶洞、河道等多种地质 体进行了分割建模。但基于水平集的方法比较依赖初始形状,且计算效率比较 低。Image-based methods are also applicable to the problem of channel geological bodies. In order to solve the problems of complex river channel structure and poor continuity, the local linear features of the river channel are enhanced by the method of steerable pyramid in image processing. There is a confidence- and curvature-guided level-set method for segmenting channels from 3D seismic data. Based on the fusion of various seismic attributes, the method of level set is used to segment and model various geological bodies such as karst caves and river channels. However, the method based on the level set is more dependent on the initial shape, and the computational efficiency is relatively low.
综合来看,现有的对河道地质体的研究大多停留在二维平面的识别检测上, 对河道三维模型构建的研究有些不足。To sum up, most of the existing researches on river channel geological bodies remain on the identification and detection of the two-dimensional plane, and the research on the construction of the three-dimensional model of the river channel is somewhat insufficient.
发明内容SUMMARY OF THE INVENTION
由于单属性数据所携带的地质信息并不完整,所以仅仅在单属性数据上对 河道进行解释往往不够准确。因此需要合理的选取几种可以信息互补的属性, 并采用非线性降维的方法,在降维的同时,不至于损失数据信息。在进行河道 分割时,如果仅仅是基于像素级的分割,分割出的河道边缘连续性较差,不能 很好的解释河道。为了解决现有技术中的问题,本发明提供了一种基于多属性 超体素图割的河道三维建模方法。Because the geological information carried by single-attribute data is incomplete, it is often inaccurate to interpret river channels only on single-attribute data. Therefore, it is necessary to reasonably select several attributes that can complement information, and adopt a nonlinear dimensionality reduction method, so as not to lose data information while reducing dimensionality. When segmenting the river channel, if it is only based on pixel-level segmentation, the segmented channel edge has poor continuity and cannot explain the channel well. In order to solve the problems in the prior art, the present invention provides a three-dimensional modeling method of a river channel based on multi-attribute super-voxel graph cuts.
一种基于多属性超体素图割的河道三维建模方法,包括以下步骤:A three-dimensional modeling method of river channel based on multi-attribute hypervoxel graph cut, comprising the following steps:
步骤1,采用ISOLLE的非线性降维算法融合河道地震属性,得到河道的 属性数据体;Step 1, using the nonlinear dimension reduction algorithm of ISOLLE to fuse the seismic attributes of the river channel to obtain the attribute data body of the river channel;
步骤2,根据所述数据体,通过简单线性迭代聚类算法(SLIC),生成地 质超体素;Step 2, according to the data body, by simple linear iterative clustering algorithm (SLIC), generate geological supervoxel;
步骤3,通过k-means聚类方法,建立目标区域和非目标区域的高斯混合 模型,构建网络图和能量函数,基于最小割准则对地质数据进行分割,得到二 值化的分割结果,并通过提取等值面的方法得到河道地质体的三维模型。Step 3, through the k-means clustering method, establish the Gaussian mixture model of the target area and the non-target area, construct the network graph and energy function, and segment the geological data based on the minimum cut criterion to obtain the binarized segmentation result, and pass The method of extracting the isosurface can obtain the three-dimensional model of the channel geological body.
进一步地,所述步骤1包括以下流程:Further, the step 1 includes the following processes:
步骤11,根据测地距离搜寻与地震数据样本点近邻的k个样本;Step 11, according to the geodetic distance, search for k samples that are close to the seismic data sample point;
根据两点之间的测地距离,在三维数据中搜寻与每个地震数据样本点i测 地距离最相近的k个数据点According to the geodesic distance between two points, search the k data points with the closest geodetic distance to each seismic data sample point i in the 3D data.
dG(xi,xj)=min{LG(xi,xj)}d G (x i ,x j )=min{L G (x i ,x j )}
其中,LG为两点之间某路径的长度,dE为欧氏距离,dG为两点之间的测 地距离;Among them, L G is the length of a path between two points, d E is the Euclidean distance, and d G is the geodesic distance between the two points;
步骤12,构造局部最优化重建权值矩阵;Step 12, constructing a local optimization reconstruction weight matrix;
引入误差函数以衡量重构误差大小,其为An error function is introduced to measure the reconstruction error, which is
其中,xij(j=1,2,...,k)为地震数据点i的k个近邻点,wij为xi和xij之间的权 值,wij符合 Among them, x ij (j=1,2,...,k) is the k nearest neighbors of seismic data point i, w ij is the weight between x i and x ij , and w ij conforms to
对于每个地震数据点,误差为For each seismic data point, the error is
构造局部协方差矩阵Construct the local covariance matrix
结合所述局部协方差矩阵和通过拉格朗日乘子法,得到局部最 优化重建权值矩阵Combine the local covariance matrix and Through the Lagrange multiplier method, the locally optimized reconstruction weight matrix is obtained
当所述局部最优化重建权值矩阵为奇异矩阵时,进行正则化处理When the local optimization reconstruction weight matrix is a singular matrix, perform regularization processing
Qi=Qi+r·IQ i =Q i +r·I
其中,r为正则化参数,I为k×k单位矩阵;Among them, r is the regularization parameter, and I is the k×k unit matrix;
步骤13,将所有地震数据点从高维向低维空间进行映射,通过该地震数据 点的局部重建权值矩阵以及它的k个近邻点计算出该地震数据点在低维空间的 值;Step 13, map all seismic data points from high-dimensional to low-dimensional space, calculate the value of this seismic data point in low-dimensional space by the local reconstruction weight matrix of this seismic data point and its k neighbors;
映射条件满足Mapping conditions are met
其中,ε(Y)为损失函数值,yi为xi输出向量,yij(j=1,2,…,k)为通过测地 距离寻找到的的k个近邻点,同时还满足Among them, ε(Y) is the value of the loss function, y i is the output vector of x i , and y ij (j=1,2,...,k) is the k nearest neighbors found by the geodesic distance.
其中,I为m×m的单位矩阵;损失函数为Among them, I is the identity matrix of m×m; the loss function is
其中,M为N×N的对阵矩阵,表示为Among them, M is an N×N alignment matrix, which is expressed as
M=(1-W)T·(I-W)。M=(1-W) T ·(IW).
进一步地,所述步骤2包括以下流程:Further, the step 2 includes the following processes:
步骤21,初始化聚类中心;Step 21, initialize the cluster center;
设置地质超体素的初始个数为K,将河道工区中地震数据点i的标签初始 化设为-1,即labeil=-1,点i与聚类中心j的距离初始化设为无穷大,即 distij=+∞;Set the initial number of geological supervoxels as K, initialize the label of seismic data point i in the river channel area to -1, that is, label i l=-1, and initialize the distance between point i and cluster center j to infinity, That is, dist ij = +∞;
步骤22,在聚类中心Cj的邻域内,计算各点到Cj的距离;Step 22, in the neighborhood of the cluster center C j , calculate the distance from each point to C j ;
距离为distance is
其中,为地震数据点i和聚类中心Cj在融合后的属性值上的 距离,为地震数据点i与聚类中心Cj在河道三 维空间的空间距离,m为调节属性距离和空间距离权重的参数;in, is the distance between the seismic data point i and the cluster center C j on the fused attribute value, is the spatial distance between the seismic data point i and the cluster center C j in the three-dimensional space of the river channel, and m is the parameter for adjusting the attribute distance and the weight of the spatial distance;
当dij<disti,更新disti=dij,labeli=j;When d ij < dist i , update dist i =d ij , label i =j;
步骤23,更新聚类中心其中Nj为属于第类地质超体素的地震 数据点的个数;Step 23, update the cluster center where N j is the number of seismic data points belonging to the first type of geological supervoxel;
步骤24,计算残差 Step 24, calculate the residuals
步骤25,更新聚类中心,令Cj=C'j,若E小于预设阈值或超过最大迭代次 数,进入下一流程;若E不满足条件,则流程回到所述步骤22;Step 25, update the cluster center, set C j =C' j , if E is less than the preset threshold or exceeds the maximum number of iterations, enter the next process; if E does not meet the conditions, the process returns to the step 22;
步骤26,对于分割出的地质超体素,通过在三维空间中遍历地震数据点的 连通区域,建立邻接矩阵A,将属性直方图作为地质超体素特征;Step 26, for the segmented geological supervoxel, by traversing the connected region of the seismic data points in three-dimensional space, an adjacency matrix A is established, and the attribute histogram is used as the geological supervoxel feature;
对体积不大于阈值的地质超体素i,计算地质超体素i与相邻超体素j之间 的巴氏距离For the geological super-voxel i whose volume is not greater than the threshold, calculate the Babbitt distance between the geological super-voxel i and the adjacent super-voxel j
其中,M为地质超体素灰属性直方图的维度,将地质超体素i合并到距离T 最小的相邻地质超体素中;Among them, M is the dimension of the gray attribute histogram of the geological supervoxel, and the geological supervoxel i is merged into the adjacent geological supervoxel with the smallest distance T;
步骤27,将所有离散的、小于阈值的地质超体素合并完成后,更新邻接矩 阵及地质超体素的属性直方图。Step 27: After merging all discrete geological supervoxels smaller than the threshold, update the adjacency matrix and the attribute histogram of the geological supervoxels.
进一步地,所述步骤3包括以下流程:Further, the step 3 includes the following processes:
步骤31,通过k-means聚类方法,建立目标区域和非目标区域的高斯混合 模型;Step 31, by k-means clustering method, sets up the Gaussian mixture model of target area and non-target area;
标记属于河道的超体素αi=1,其余超体素αi=0;Mark the supervoxel α i = 1 that belongs to the channel, and the remaining supervoxels α i = 0;
通过GLCM四个属性作为特征对地质超体素进行k-means聚类;Perform k-means clustering on geological supervoxels by using four attributes of GLCM as features;
根据聚类结果初始化高斯混合模型中每一个高斯分量的参数,权重ωk,样 本均值uk和协方差∑k,高斯混合模型的密度函数为Initialize the parameters of each Gaussian component in the Gaussian mixture model according to the clustering results, the weight ω k , the sample mean u k and the covariance Σ k , the density function of the Gaussian mixture model is
其中, in,
计算后验概率Calculate the posterior probability
计算高斯分量参数的最大似然估计Compute maximum likelihood estimates of Gaussian component parameters
通过迭代至似然函数收敛,得到河道高斯混合模型和非河道高斯混合模型;By iterating until the likelihood function converges, the channel Gaussian mixture model and the non-channel Gaussian mixture model are obtained;
步骤32,构建网格图和能量函数;Step 32, constructing a grid diagram and an energy function;
采用灰度共生矩阵来计算每个超地质体素的纹理属性。GLCM是图像中两 个灰度值的联合概率分布,选取GLCM的熵、相异性、能量三种属性作为超 体素的特征值,融合了地质超体素区域信息和边缘信息的能量函数为The gray-scale co-occurrence matrix is used to calculate the texture properties of each metageological voxel. GLCM is the joint probability distribution of two grayscale values in the image. The entropy, dissimilarity, and energy of GLCM are selected as the eigenvalues of the supervoxel. The energy function that combines the geological supervoxel region information and edge information is:
其中,C为网格图的分割;Er为区域项,代表网格图汇总t-link边的权值, 反映了地质超体素的区域信息;Eb为边界项,代表了网络图中n-link边的权值, 体现出分割的边界属性;通过构建能量函数,将河道的分割转换成能量函数最 小化问题;Among them, C is the division of the grid map; E r is the regional item, which represents the weights of the t-link edges in the grid map summary, reflecting the regional information of the geological supervoxel; E b is the boundary term, representing the network map. The weight of the n-link edge reflects the boundary attribute of the segmentation; by constructing an energy function, the segmentation of the river channel is converted into an energy function minimization problem;
步骤33,基于最小割准则对地质数据进行分割,并更新高斯混合模型中的 地震数据点和数据点标记αi,迭代结束后输出分割结果,得到河道地质体的二 值化分割结果,通过提取等值面的方法得到河道地质体的三维模型。Step 33: Segment the geological data based on the minimum cut criterion, update the seismic data points and the data point markers α i in the Gaussian mixture model, and output the segmentation results after the iteration to obtain the binarized segmentation results of the channel geological body. The method of isosurface obtains the three-dimensional model of the channel geological body.
本发明的有益效果:本发明提供了一种基于多属性超体素图割的河道三维 建模方法,通过融合几种优选地震属性得到新的数据体,再通过超体素图割的 方法进行二值化分割,最后通过等值面提取得到河道表面。本发明中ISOLLE的 融合方法能有效地融合多种地震属性,合理的地震属性选取有助于信息互补, 更全面地刻画河道地质体,且多属性融合的方式能够保持河道地震数据中的非 线性关系,得到的新属性体为下一步的分割和重建打下了良好的基础;河道地 质超体素具有良好的边缘保持性,地质超体素与图割相结合能准确、快速地分 割河道,通过等值面提取实现了由三维地震数据河道地质体三维模型的转化, 更加直观地展示了河道地质体的空间特征;本发明提出的基于多属性融合超体 素图割的方法实现了对河道地质体的精准刻画,最终得到的三维模型符合地质 规律,且与地质人员得到的结果基本一致,为后续工作奠定了基础。Beneficial effects of the present invention: The present invention provides a three-dimensional modeling method of a river channel based on multi-attribute super-voxel map cuts, obtains a new data volume by fusing several preferred seismic attributes, and then performs the super-voxel map cut method to obtain a new data volume. Binarized segmentation, and finally obtained the channel surface through isosurface extraction. The fusion method of ISOLLE in the present invention can effectively fuse various seismic attributes, and reasonable selection of seismic attributes is helpful for information complementation, more comprehensive description of the channel geological body, and the multi-attribute fusion method can maintain the nonlinearity in the channel seismic data. The obtained new attribute volume lays a good foundation for the next segmentation and reconstruction; the channel geological supervoxel has good edge retention, and the combination of the geological supervoxel and the map cut can accurately and quickly segment the channel. The isosurface extraction realizes the transformation of the three-dimensional model of the channel geological body from the three-dimensional seismic data, and more intuitively displays the spatial characteristics of the channel geological body; the method based on the multi-attribute fusion super-voxel map cut proposed by the present invention realizes the analysis of the channel geological body. The final three-dimensional model conforms to the geological laws and is basically consistent with the results obtained by the geologists, laying a foundation for the follow-up work.
附图说明Description of drawings
图1为本发明的流程图。FIG. 1 is a flow chart of the present invention.
图2为图1中步骤1的流程图。FIG. 2 is a flowchart of step 1 in FIG. 1 .
图3为图1中步骤2的流程图。FIG. 3 is a flowchart of step 2 in FIG. 1 .
图4为初始化的聚类中心图。Figure 4 is the initialized cluster center map.
图5为图1中步骤3的流程图。FIG. 5 is a flowchart of step 3 in FIG. 1 .
具体实施方式Detailed ways
下面结合附图对本发明的实施例做进一步的说明。The embodiments of the present invention will be further described below with reference to the accompanying drawings.
请参阅图1,本发明提供了一种基于多属性超体素图割的河道三维建模方 法,通过以下步骤实现:Please refer to Fig. 1, the present invention provides a kind of river three-dimensional modeling method based on multi-attribute super-voxel graph cut, realizes through the following steps:
步骤1,采用ISOLLE的非线性降维算法融合河道地震属性,得到河道的 属性数据体。Step 1, using the nonlinear dimension reduction algorithm of ISOLLE to fuse the seismic attributes of the river channel to obtain the attribute data volume of the river channel.
本实施例中,在地震解释的过程中不同的属性数据从不同角度刻画地质构 造,通过融合不同属性,可以对储层的地质构造有更精确的解释。由于地震属 性与地质特征的关系通常是非线性的,基于线性变换的PCA方法不能充分地 反映这种非线性关系,降低了预测识别的精度。非线性的LLE降维算法采用 的是欧式距离计算点与点之间的距离,并不能反映点之间的真实结构,且对近 邻个数的选择十分敏感。In this embodiment, in the process of seismic interpretation, different attribute data describe the geological structure from different angles, and by fusing different attributes, the geological structure of the reservoir can be interpreted more accurately. Because the relationship between seismic attributes and geological features is usually nonlinear, the PCA method based on linear transformation cannot fully reflect this nonlinear relationship, which reduces the accuracy of prediction and identification. The nonlinear LLE dimensionality reduction algorithm uses the Euclidean distance to calculate the distance between points, which cannot reflect the real structure between points, and is very sensitive to the choice of the number of neighbors.
本实施例中,采用ISOLLE算法,引入测地距离的概念,将欧式距离用测 地距离替换,在保持了LLE算法处理高维流形数据优势的同时,又提高了在 相应低维空间中数据的紧密性和局部邻域数据的线性特征。本发明将ISOLLE 方法首次应用到三维河道地震数据的多属性融合中,选取几种属性融合成为新 的属性体,扩展到三维空间。In this embodiment, the ISOLLE algorithm is used, the concept of geodesic distance is introduced, and the Euclidean distance is replaced by the geodesic distance. While maintaining the advantages of the LLE algorithm in processing high-dimensional manifold data, the data in the corresponding low-dimensional space is improved. The tightness and linearity of local neighborhood data. The present invention applies the ISOLLE method to the multi-attribute fusion of the three-dimensional channel seismic data for the first time, and selects several attributes for fusion to form a new attribute body, which is extended to the three-dimensional space.
本实施例中,选取了均方根振幅属性、能量属性、纹理同质性,频谱属性, 瞬时频率属性来研究某地震工区的多属性融合问题。再经过归一化处理和傅立 叶变换去噪后得到不同属性的切片图。同一属性在不同时间切片上的表现有好 有坏,不同属性可以弥补彼此的不足。In this embodiment, the root mean square amplitude attribute, energy attribute, texture homogeneity, spectrum attribute, and instantaneous frequency attribute are selected to study the multi-attribute fusion problem of a certain seismic work area. After normalization and Fourier transform denoising, slice images with different attributes are obtained. The performance of the same attribute on different time slices is good or bad, and different attributes can make up for each other's shortcomings.
请参阅图2,步骤1通过以下流程实现:Referring to Figure 2, step 1 is achieved through the following process:
步骤11,根据测地距离搜寻与地震数据样本点近邻的k个样本;Step 11, according to the geodetic distance, search for k samples that are close to the seismic data sample point;
根据两点之间的测地距离,在三维数据中搜寻与每个地震数据样本点i测 地距离最相近的k个数据点According to the geodesic distance between two points, search the k data points with the closest geodetic distance to each seismic data sample point i in the 3D data.
dG(xi,xj)=min{LG(xi,xj)}d G (x i ,x j )=min{L G (x i ,x j )}
其中,LG为两点之间某路径的长度,dE为欧氏距离,dG为两点之间的测 地距离;Among them, L G is the length of a path between two points, d E is the Euclidean distance, and d G is the geodesic distance between the two points;
步骤12,得到地震数据点的局部重建矩阵。局部重建矩阵代表了多属性之 间的局部线性关系,融合后的地震数据点之间也要能够保持这种线性关系。Step 12, obtaining a local reconstruction matrix of the seismic data points. The local reconstruction matrix represents the local linear relationship between multiple attributes, and the fused seismic data points should also be able to maintain this linear relationship.
引入误差函数以衡量重构误差大小,其为An error function is introduced to measure the reconstruction error, which is
其中,xij(j=1,2,...,k)为地震数据点i的k个近邻点,wij为xi和xij之间的权 值,wij符合 Among them, x ij (j=1,2,...,k) is the k nearest neighbors of seismic data point i, w ij is the weight between x i and x ij , and w ij conforms to
对于每个地震数据点,误差为For each seismic data point, the error is
构造局部协方差矩阵Construct the local covariance matrix
结合局部协方差矩阵和通过拉格朗日乘子法,得到局部最优化 重建权值矩阵Combine the local covariance matrix and Through the Lagrange multiplier method, the locally optimized reconstruction weight matrix is obtained
当局部最优化重建权值矩阵为奇异矩阵时,进行正则化处理When the local optimization reconstruction weight matrix is a singular matrix, perform regularization processing
Qi=Qi+r·IQ i =Q i +r·I
其中,r为正则化参数,I为k×k单位矩阵;Among them, r is the regularization parameter, and I is the k×k unit matrix;
步骤13,将所有地震数据点从高维向低维空间进行映射,通过该地震数据 点的局部重建权值矩阵以及它的k个近邻点计算出该地震数据点在低维空间的 值;Step 13, map all seismic data points from high-dimensional to low-dimensional space, calculate the value of this seismic data point in low-dimensional space by the local reconstruction weight matrix of this seismic data point and its k neighbors;
映射条件满足Mapping conditions are met
其中,ε(Y)为损失函数值,yi为xi输出向量,yij(j=1,2,…,k)为通过测地 距离寻找到的的k个近邻点,同时还满足以下两个条件Among them, ε(Y) is the value of the loss function, y i is the output vector of x i , and y ij (j=1,2,...,k) is the k nearest neighbors found by the geodesic distance, and also satisfies the following two conditions
其中,I为m×m的单位矩阵。这里的通常存储在N×N的 稀疏矩阵W中,当xj是xi的近邻点时,wij=wj,若两者不相等,则wij=0。这 两个条件有其各自的意义,第一个保障了对Y的平移不变性;第二个保 障了在低维空间中通过不同坐标所产生的重构误差也可以运用相同的测量标 准。从而防止出现Y=0的退化解。损失函数为where I is an m×m identity matrix. here Usually stored in an N×N sparse matrix W, when x j is a neighbor of x i , w ij =w j , if the two are not equal, then w ij =0. These two conditions have their own meaning, the first guarantees Translation invariance to Y; the second guarantees that the same measure can be applied to the reconstruction error generated by different coordinates in low-dimensional space. Thus, the degenerate solution of Y=0 is prevented from appearing. The loss function is
其中,M为N×N的对阵矩阵,表示为Among them, M is an N×N alignment matrix, which is expressed as
M=(1-W)T·(I-W)。M=(1-W) T ·(IW).
矩阵M具有稀疏、半正定的特点。若要使得损失函数达到最小值,那么 应该取为的最小个非零特征值所对应的特征向量。同时,把的特征值根据由小到 大的顺序进行排列。第一个特征值约等于零,因此舍弃第一个特征值。The matrix M has the characteristics of sparse and positive semi-definite. To make the loss function reach the minimum value, then should be taken as the eigenvector corresponding to the smallest non-zero eigenvalue. At the same time, the eigenvalues are arranged according to the order from small to large. The first eigenvalue is approximately equal to zero, so the first eigenvalue is discarded.
步骤2,根据所述数据体,通过简单线性迭代聚类算法(SLIC),生成地 质超体素。Step 2: Generate geological supervoxels according to the data volume through a simple linear iterative clustering algorithm (SLIC).
本实施例中,基于像素级的分割,并未充分利用像素间的局部关系,在图 像离散化过程中,会带来误差。超像素利用像素之间特征的相似性将像素分组, 用少量的超像素代替大量的像素来表达图片特征,与像素级分割相比,它能保 持原图像的边缘特征。超体素是超像素在三维空间中的扩展。在处理三维地震 数据时,地质超体素的方法克服了在二维切片使用超像素最后合成三维模型时 不平滑等问题,同时减少了分块个数,降低了计算量。In this embodiment, the segmentation based on the pixel level does not make full use of the local relationship between pixels, which will bring errors in the process of image discretization. Superpixels use the similarity of features between pixels to group pixels, and use a small number of superpixels to replace a large number of pixels to express image features. Compared with pixel-level segmentation, it can maintain the edge features of the original image. A supervoxel is an extension of a superpixel in three-dimensional space. When processing 3D seismic data, the geological supervoxel method overcomes the problem of unsmoothness when synthesizing 3D models using superpixels in 2D slices, and at the same time reduces the number of blocks and reduces the amount of computation.
本实施例中,在地震数据体中,距离越近的两个地震数据点,属于同一个 地质体的概率也越大。根据这一特点,我们将相似的地震数据点基于SLIC算 法进行聚类处理生成地质超体素。生成的地质超体素既能保持内部均匀紧凑, 又能保持地质体的边缘特性,降低了后续分割的计算复杂度。在SLIC算法中, 主要步骤就是比较各点与聚类中心Cj的距离进行分类,再更新聚类中心。假设 融合后为Crossline*Inlinc*Time大小的三维数据体,则所有地震数据点的集 V={v1,v2,...,vN},其中vi={gi,xi,yi,zi},gi为地震数据点i融合后的属性值,xi, yi,zi为网格点i在空间中的坐标。In this embodiment, in the seismic data volume, the closer the distance between two seismic data points, the higher the probability of belonging to the same geological body. According to this feature, we cluster similar seismic data points based on the SLIC algorithm to generate geological supervoxels. The generated geological supervoxel can not only keep the interior uniform and compact, but also maintain the edge characteristics of the geological body, which reduces the computational complexity of subsequent segmentation. In the SLIC algorithm, the main step is to compare the distance between each point and the cluster center C j to classify, and then update the cluster center. Assuming that it is a three-dimensional data volume of Crossline*Inlinc*Time size after fusion, the set of all seismic data points V={v 1 , v 2 ,...,v N }, where v i ={ gi , xi , y i , z i }, gi are the attribute values of seismic data point i after fusion, xi , y i , zi are the coordinates of grid point i in space.
请参阅图3,步骤2通过以下流程实现:Referring to Figure 3, step 2 is achieved through the following process:
步骤21,初始化聚类中心;Step 21, initialize the cluster center;
设置地质超体素的初始个数为K,则超体素初始大小为该河道区 域被分为K个小区域。在河道的三维空间中,交错选择种子点如图4所示,这 样可以使种子点在空间内尽可能的均匀分布。则初始聚类中心C={C1,C2,...,CK}, 相邻河道超体素聚类中心的距离为 Set the initial number of geological supervoxels to K, then the initial size of supervoxels is The river area is divided into K small areas. In the three-dimensional space of the river channel, the seed points are alternately selected as shown in Figure 4, so that the seed points can be distributed as evenly as possible in the space. Then the initial cluster center C={C 1 ,C 2 ,...,C K }, the distance between the adjacent river supervoxel cluster centers is
生成的种子点可能会落在河道的边缘,为了避免这种情况发生,计算出在 当前种子点3×3×3邻域中所有网格点的梯度值,将种子点的位置移动到此邻域 梯度最小处。即将聚类中心移动到G(x,y,z)=minG(x,y,z)处。The generated seed point may fall on the edge of the river. In order to avoid this situation, the gradient value of all grid points in the 3×3×3 neighborhood of the current seed point is calculated, and the position of the seed point is moved to this neighborhood. where the domain gradient is minimal. That is, move the cluster center to G(x,y,z)=minG(x,y,z).
以种子点为中心的3×3×3窗口内,计算河道内各地震数据点的属性梯度。 计算方式如下:In a 3×3×3 window centered on the seed point, the attribute gradient of each seismic data point in the channel is calculated. It is calculated as follows:
G(x,y,z)=||I(x+1,y,z)-I(x-1,y,z)||2 G(x,y,z)=||I(x+1,y,z)-I(x-1,y,z)|| 2
+||I(x,y+1,z)-I(x,y-1,z)||2 +||I(x,y+1,z)-I(x,y-1,z)|| 2
+||I(x,y,z+1)-I(x,y,z-1)||2 +||I(x,y,z+1)-I(x,y,z-1)|| 2
式中,I(x,y,z)表示在河道工区内坐标为(x,y,z)时的属性值。G(x,y,z)表 示在河道工区内坐标为(x,y,z)时基于属性值计算出的梯度值。In the formula, I(x, y, z) represents the attribute value when the coordinates are (x, y, z) in the river work area. G(x, y, z) represents the gradient value calculated based on the attribute value when the coordinates are (x, y, z) in the river work area.
将河道工区中地震数据点i的标签初始化设为-1,即labeli=-1;Initialize the label of seismic data point i in the river work area to -1, that is, label i = -1;
点i与聚类中心j的距离初始化设为无穷大,即distij=+∞。The distance between point i and cluster center j is initially set to infinity, that is, dist ij =+∞.
步骤22,在聚类中心Cj的邻域内,计算各点到Cj的距离;Step 22, in the neighborhood of the cluster center C j , calculate the distance from each point to C j ;
对所有的聚类中心Cj,在2S×2S×2S的邻域内,各点到聚类中心Cj的距 离为For all cluster centers C j , in the neighborhood of 2S×2S×2S, the distance from each point to the cluster center C j is
其中,为地震数据点i和聚类中心Cj在融合后的属性值上的 距离,为地震数据点i与聚类中心Cj在河道三 维空间的空间距离,m为调节属性距离和空间距离权重的参数;in, is the distance between the seismic data point i and the cluster center C j on the fused attribute value, is the spatial distance between the seismic data point i and the cluster center C j in the three-dimensional space of the river channel, and m is the parameter for adjusting the attribute distance and the weight of the spatial distance;
当dij<disti,更新disti=dij,labeli=j;When d ij < dist i , update dist i =d ij , label i =j;
步骤23,更新聚类中心其中Nj为属于第类地质超体素的地震 数据点的个数;Step 23, update the cluster center where N j is the number of seismic data points belonging to the first type of geological supervoxel;
步骤24,计算残差 Step 24, calculate the residuals
步骤25,更新聚类中心,令Cj=C'j,若E小于预设阈值或超过最大迭代次 数,进入下一流程;若E不满足条件,则流程回到所述步骤22;Step 25, update the cluster center, set C j =C' j , if E is less than the preset threshold or exceeds the maximum number of iterations, enter the next process; if E does not meet the conditions, the process returns to the step 22;
步骤26,对于分割出的地质超体素,通过在三维空间中遍历地震数据点的 连通区域,建立邻接矩阵A,将属性直方图作为地质超体素特征;Step 26, for the segmented geological supervoxel, by traversing the connected region of the seismic data points in three-dimensional space, an adjacency matrix A is established, and the attribute histogram is used as the geological supervoxel feature;
对体积不大于阈值的地质超体素i,计算地质超体素i与相邻超体素j之间 的巴氏距离For the geological super-voxel i whose volume is not greater than the threshold, calculate the Babbitt distance between the geological super-voxel i and the adjacent super-voxel j
其中,M为地质超体素灰属性直方图的维度,将地质超体素i合并到距离T 最小的相邻地质超体素中;Among them, M is the dimension of the gray attribute histogram of the geological supervoxel, and the geological supervoxel i is merged into the adjacent geological supervoxel with the smallest distance T;
步骤27,将所有离散的、小于阈值的地质超体素合并完成后,更新邻接矩 阵及地质超体素的属性直方图。Step 27: After merging all discrete geological supervoxels smaller than the threshold, update the adjacency matrix and the attribute histogram of the geological supervoxels.
本实施例中,考虑将相似的数据点进行聚类,看做河道的最小单位来进行 分割。将融合后的河道数据体进行三维超体素分割,设定不同的地质超体素个 数K,可以得到不同的结果。当设定地质超体素的数量K较小时,分割出的地 质超体素在河道边缘不够贴合。当K较大时,河道内外的区分模糊,并且不能 有效的降低图割的计算量。因此我们将超体素的数量K设置为150,分割出的 超体地体素能够很好的贴合河道的边缘,并且地质超体素的同质性也更好。当 然,K也可以设为其它数值。In this embodiment, similar data points are considered to be clustered, and the division is performed as the smallest unit of the river channel. The fused channel data volume is divided into three-dimensional supervoxels, and different geological supervoxels K are set, and different results can be obtained. When the number K of geological supervoxels is set to be small, the segmented geological supervoxels do not fit well at the channel edge. When K is large, the distinction between inside and outside the river channel is blurred, and the calculation amount of graph cuts cannot be effectively reduced. Therefore, we set the number K of supervoxels to 150, the segmented supervoxels can fit the edge of the channel well, and the homogeneity of the geological supervoxels is also better. Of course, K can also be set to other values.
步骤3,通过k-means聚类方法,建立目标区域和非目标区域的高斯混合 模型,构建网络图和能量函数,基于最小割准则对地质数据进行分割,得到二 值化的分割结果,并通过提取等值面的方法得到河道地质体的三维模型。Step 3, through the k-means clustering method, establish the Gaussian mixture model of the target area and the non-target area, construct the network graph and energy function, and segment the geological data based on the minimum cut criterion to obtain the binarized segmentation result, and pass The method of extracting the isosurface can obtain the three-dimensional model of the channel geological body.
本实施例中,由于地质超体素是一个小的区域,区域存在着隐藏的纹理特 征。因此在传统图割算法的基础上,通过融合超体素的属性值和纹理特征代替 灰度属性来代表每个超体素的特性,首次将基于超体素的图割算法应用在河道 地质体的分割上。与传统图割算法相比,本发明用高斯混合模型(GMM)替 代属性直方图,来精确表达概率模型。高斯混合模型是多个高斯模型的线性叠 加。GMM的核心在于求得每个高斯分量的均值、方差,以及权重比。首先对 GMM中每一个高斯分量的参数进行随机初始化,计算其密度函数、后验概率以及高斯分量参数的最大似然估计。最后通过不断重复迭代,直至似然函数收 敛,得到河道地质体的高斯混合模型,请参阅图5,具体通过以下流程实现:In this embodiment, since the geological supervoxel is a small area, there are hidden texture features in the area. Therefore, on the basis of the traditional graph-cut algorithm, the characteristics of each super-voxel are represented by fusing the attribute values and texture features of super-voxels instead of gray-scale attributes. on the division. Compared with the traditional graph cut algorithm, the present invention replaces the attribute histogram with a Gaussian mixture model (GMM) to accurately express the probability model. A Gaussian mixture model is a linear superposition of multiple Gaussian models. The core of GMM is to obtain the mean, variance, and weight ratio of each Gaussian component. Firstly, the parameters of each Gaussian component in the GMM are randomly initialized, and its density function, posterior probability and maximum likelihood estimation of the Gaussian component parameters are calculated. Finally, through repeated iterations until the likelihood function converges, the Gaussian mixture model of the channel geological body is obtained, as shown in Figure 5, which is implemented through the following process:
步骤31,通过k-means聚类方法,建立目标区域和非目标区域的高斯混合 模型;Step 31, by k-means clustering method, sets up the Gaussian mixture model of target area and non-target area;
标记属于河道的超体素αi=1,其余超体素αi=0;Mark the supervoxel α i = 1 that belongs to the channel, and the remaining supervoxels α i = 0;
设定K=5,通过GLCM四个属性作为特征对地质超体素进行k-means聚 类;Set K=5, and perform k-means clustering on the geological supervoxels by using the four attributes of GLCM as features;
根据聚类结果,随机初始化高斯混合模型中每一个高斯分量的参数,权重 ωk,样本均值uk和协方差∑k,高斯混合模型的密度函数为According to the clustering results, randomly initialize the parameters of each Gaussian component in the Gaussian mixture model, the weight ω k , the sample mean u k and the covariance Σ k , the density function of the Gaussian mixture model is
其中, in,
计算后验概率Calculate the posterior probability
计算高斯分量参数的最大似然估计Compute maximum likelihood estimates of Gaussian component parameters
通过迭代至似然函数收敛,得到河道高斯混合模型和非河道高斯混合模型;By iterating until the likelihood function converges, the channel Gaussian mixture model and the non-channel Gaussian mixture model are obtained;
步骤32,构建网格图和能量函数;Step 32, constructing a grid diagram and an energy function;
采用灰度共生矩阵来计算每个超地质体素的纹理属性。GLCM是图像中两 个灰度值的联合概率分布,选取GLCM的熵、相异性、能量三种属性作为超 体素的特征值,融合了地质超体素区域信息和边缘信息的能量函数为The gray-scale co-occurrence matrix is used to calculate the texture properties of each metageological voxel. GLCM is the joint probability distribution of two gray values in the image. The entropy, dissimilarity, and energy of GLCM are selected as the eigenvalues of the supervoxel. The energy function that combines the geological supervoxel region information and edge information is:
其中,C为网格图的分割;Er为区域项,代表网格图汇总t-link边的权值, 反映了地质超体素的区域信息;Eb为边界项,代表了网络图中n-link边的权值, 体现出分割的边界属性;通过构建能量函数,将河道的分割转换成能量函数最 小化问题;Among them, C is the division of the grid map; E r is the regional item, which represents the weights of the t-link edges in the grid map summary, reflecting the regional information of the geological supervoxel; E b is the boundary term, representing the network map. The weight of the n-link edge reflects the boundary attribute of the segmentation; by constructing an energy function, the segmentation of the river channel is converted into an energy function minimization problem;
步骤33,基于最小割准则对地质数据进行分割,并更新高斯混合模型中的 地震数据点和数据点标记αi,迭代结束后输出分割结果,得到河道地质体的二 值化分割结果,通过提取等值面的方法得到河道地质体的三维模型。Step 33: Segment the geological data based on the minimum cut criterion, update the seismic data points and the data point markers α i in the Gaussian mixture model, and output the segmentation results after the iteration to obtain the binarized segmentation results of the channel geological body. The method of isosurface obtains the three-dimensional model of the channel geological body.
本领域的普通技术人员将会意识到,这里所述的实施例是为了帮助读者理 解本发明的原理,应被理解为本发明的保护范围并不局限于这样的特别陈述和 实施例。本领域的普通技术人员可以根据本发明公开的这些技术启示做出各种 不脱离本发明实质的其它各种具体变形和组合,这些变形和组合仍然在本发明 的保护范围内。Those of ordinary skill in the art will appreciate that the embodiments described herein are for the purpose of assisting the reader in understanding the principles of the present invention, and it should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific modifications and combinations without departing from the essence of the present invention according to these technical teachings disclosed in the present invention, and these modifications and combinations still fall within the protection scope of the present invention.
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