WO2022088510A1 - 一种随机矸石块体三维形状参数自动获取方法 - Google Patents

一种随机矸石块体三维形状参数自动获取方法 Download PDF

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WO2022088510A1
WO2022088510A1 PCT/CN2021/071068 CN2021071068W WO2022088510A1 WO 2022088510 A1 WO2022088510 A1 WO 2022088510A1 CN 2021071068 W CN2021071068 W CN 2021071068W WO 2022088510 A1 WO2022088510 A1 WO 2022088510A1
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gangue
random
block
cuboid
model
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PCT/CN2021/071068
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French (fr)
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黄艳利
郭亚超
李英顺
李俊孟
欧阳神央
吴来伟
张伟光
高华东
常治国
杨长德
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中国矿业大学
新疆工程学院
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T5/00—Image enhancement or restoration
    • G06T5/70—Denoising; Smoothing
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T19/00—Manipulating 3D models or images for computer graphics
    • G06T19/20—Editing of 3D images, e.g. changing shapes or colours, aligning objects or positioning parts
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/0002—Inspection of images, e.g. flaw detection
    • G06T7/0004—Industrial image inspection
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/20—Special algorithmic details
    • G06T2207/20024—Filtering details
    • G06T2207/20032—Median filtering
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/30—Subject of image; Context of image processing
    • G06T2207/30108—Industrial image inspection
    • G06T2207/30132—Masonry; Concrete
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2219/00—Indexing scheme for manipulating 3D models or images for computer graphics
    • G06T2219/20—Indexing scheme for editing of 3D models
    • G06T2219/2021—Shape modification

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  • the invention relates to an automatic acquisition method for three-dimensional shape parameters of random gangue blocks, in particular to random gangue blocks with extremely irregular external shapes.
  • the traditional test of basic shape parameters of gangue blocks mainly measures five items of long-axis size, sub-long-axis size, short-axis size, volume and surface area.
  • the above five basic shape parameters are mainly obtained by manual measurement, and The measurement results are highly subjective, the accuracy is not high, and it will consume a lot of manpower and material resources.
  • a digital 3D model reading program for random gangue blocks which can automatically calculate and store the major axis size, sub-major axis size, minor axis size, volume and surface area, is designed and developed to reduce the measurement cost and improve the measurement accuracy. Realizing the automatic acquisition of the three-dimensional shape index of the block has become a technical problem that needs to be solved.
  • the purpose of the present invention is to make up for the gaps in the prior art, and to propose an automatic acquisition method for the three-dimensional shape parameters of random gangue blocks, which solves the difficulty in acquiring the basic shape parameters of random gangue blocks, the subjectivity of measurement accuracy, and the high measurement cost. question.
  • the method for automatically acquiring the three-dimensional shape parameters of random gangue blocks of the present invention includes the following steps:
  • the three-dimensional shape feature of the gangue block is an important parameter to characterize the gangue block, and there is still no unified quantitative index.
  • the method of the present invention selects needle, flatness and sphericity as the quantitative index to characterize the irregular block shape.
  • Step 1 CT scan to obtain two-dimensional slice images of random gangue blocks
  • the gangue blocks are firstly pretreated to clean up the debris on the surface and in the gaps; Adjust the technical parameters such as rate and HU scale range; place the processed random gangue block in a CT scanner for scanning, and obtain a two-dimensional slice image (original CT slice image) of the random gangue block.
  • Step 2 The original CT slice image is binarized and denoised
  • the optimal threshold value of the CT image of the sample is obtained by the Ojin algorithm, and the original CT slice image is binarized based on the optimal threshold value to eliminate the interference of the diversity of gangue mineral components, and make the digital model of the random gangue sample obtained by three-dimensional reconstruction. Only two phases of gangue matrix and voids are included; then the processed binarized image is denoised by using a three-dimensional median filtering algorithm to eliminate isolated noise points and convert them into a single phase that can clearly characterize the fabric of the gangue block sample. Series of 2D slice plots.
  • Step 3 Reconstruct the digital 3D model of random gangue blocks
  • the MIMICS 3D reconstruction software is used to superimpose the binarized and denoised CT slices - 3D reconstruction calculation - smoothing - grid optimization and other operations, and finally reconstruct the real shape random gangue block digital 3D model.
  • Step 4 Obtain the surface area of the digital 3D model of random gangue blocks
  • the outline of the block reconstruction model is composed of tens of thousands of triangular pieces. First, traverse and calculate the area of all the triangular pieces, then accumulate them, and use the accumulated result as the surface area of the irregular gangue block.
  • the calculation formula is as follows:
  • S i is the area of the i-th triangular patch in the block reconstruction model
  • n is the total number of triangular patches constituting the outline of the random gangue block reconstruction model.
  • Step 5 Obtain the digital 3D model volume of random gangue blocks
  • Vi is the volume of the area that is skipped by the projection of the i -th triangular piece to the reference plane.
  • V i has positive and negative points.
  • the direction of the model perpendicular to the reference plane is taken as the positive direction of the z-axis of the coordinate. If the z-axis component of the normal phase vector of the triangular slice (pointing to the inside of the model) is the proof, then V i is positive, otherwise it is negative.
  • Step 6 Obtain the digital 3D model of the random gangue block to contain the cuboid:
  • the digital three-dimensional model of the block firstly generate the initial containing cuboid V 0 ( ⁇ 0 , ⁇ 0 , ⁇ 0 ) of the block.
  • the coordinates of any vertex of the random gangue block be A 1 A 2 . 2, 3, 4..., n, rotate the block A 1 A 2 ... A n around the x-axis, y-axis, and z-axis by angles ⁇ , ⁇ , ⁇ , respectively, to obtain the rotated block A' 1 A' 2 ... A' n
  • the relationship between A′ i (x′ i ,y′ i ,z′ i ) and A i (x i ,y i ,z i ) is as follows:
  • the frontmost, last, leftmost, rightmost, topmost and bottommost vertices of the rotated blocks A' 1 A' 2 ...A' n are respectively made into 6 planes parallel to the coordinate plane, and the 6 planes are surrounded by
  • the cuboid is the containing cuboid of the block.
  • V( ⁇ , ⁇ , ⁇ ) is the volume of the cuboid containing the block after rotation; It is the maximum value of the x-axis coordinates of all the triangular slice vertices on the polyhedron surface, that is, the x-axis coordinate of the position of the right side of the smallest inclusive cuboid. It is the minimum value of the x-axis coordinates of all the triangular slice vertices on the surface of the polyhedron, that is, the x-axis coordinate of the position of the left side of the smallest inclusive cuboid.
  • Step 7 Obtain the shape index of the digital 3D model of the random gangue block
  • the major axis dimension L, secondary major axis dimension W, and minor axis dimension T of the block reconstruction model can be obtained by finding its minimum accommodating cuboid, and the length of the minimum enveloping cuboid is used as the long axis. size, width is taken as the secondary major dimension, and thickness is taken as the minor axis dimension, where L ⁇ W ⁇ T.
  • Step 8 Obtain the three-dimensional shape features of the digital three-dimensional model of the random gangue block: needle degree e, flatness f, sphericity ⁇ .
  • the needle degree e is used to describe the slenderness of the gangue block, and the calculation formula is Among them: L is the long axis dimension of the gangue block, the unit is mm; W is the secondary long axis size of the gangue block, the unit is mm.
  • the flatness f is used to describe the flatness of the gangue block, and the calculation formula is Where f is the flatness; T is the short axis of the gangue block, size, in mm.
  • the sphericity ⁇ is used to describe the roughness and shape symmetry of the gangue block, that is, the ratio of the surface area of the irregular particle to the actual surface area of the particle.
  • S is the actual surface area of the gangue block, the unit is mm 2 ;
  • V is the actual volume of the gangue block, the unit is mm 3 .
  • the method of the invention adopts CT slice, binarization processing, noise reduction, and reconstructs the digital three-dimensional model of the random gangue block, thereby obtaining the three-dimensional shape parameters that characterize the random gangue block, thereby solving the difficulty in obtaining the basic shape parameters of the random gangue block.
  • the measurement accuracy is highly subjective and the measurement cost is high.
  • the measurement results are highly accurate.
  • Figure 1 is a diagram showing the effect of three-dimensional median filtering noise reduction processing of a CT slice binarized image of a random gangue block.
  • Figure a is the original CT image;
  • Figure b is the binarized image;
  • Figure c is the binarized image after noise reduction.
  • Figure 2 is a schematic diagram of a digital three-dimensional model for reconstructing random gangue blocks.
  • Figure 3 is a schematic diagram of the area calculation principle of the random gangue block reconstruction model.
  • Figure 4 is a schematic diagram of the volume calculation of the random gangue block reconstruction model.
  • Figure 5 is a schematic diagram of the spatial position and containing cuboid of random gangue blocks.
  • Figure 6 shows the minimum accommodating cuboid and main size parameters of random gangue blocks.
  • Step 1 CT scan to obtain two-dimensional slice images of random gangue blocks
  • the gangue block is firstly pretreated to clean up the debris on the surface and in the gap;
  • Technical parameters such as matrix, density resolution, and HU scale range can be adjusted.
  • the processed random gangue block is placed in a CT scanner for scanning processing, and a two-dimensional slice image (original CT slice image) of the random gangue block is obtained, as shown in FIG. 1 .
  • Step 2 The original CT slice image is binarized and denoised
  • the optimal threshold value of the CT image of the sample is obtained by the Ojin algorithm, and the original CT slice image is binarized based on the optimal threshold value to eliminate the interference of the diversity of gangue mineral components, and make the digital model of the random gangue sample obtained by three-dimensional reconstruction. Only two phases of gangue matrix and voids are included; then the processed binarized image is denoised by using a three-dimensional median filtering algorithm to eliminate isolated noise points and convert them into a single phase that can clearly characterize the fabric of the gangue block sample. Series of 2D slice plots.
  • Step 3 Reconstruct the digital 3D model of random gangue blocks
  • Step 4 Obtain the surface area of the digital 3D model of random gangue blocks
  • a single block is selected as an example to obtain parameters (the gangue is used as an example for subsequent parameter acquisitions).
  • the obtained parameters are shown in Table 2.
  • the outline of the block reconstruction model is composed of tens of thousands of triangular pieces. First, the area of all the triangular pieces is traversed and calculated, and then they are accumulated, and the accumulated result is taken as the surface area of the irregular gangue block (see Figure 3). Calculated as follows:
  • S i is the area of the i-th triangular patch in the block reconstruction model
  • n is the total number of triangular patches constituting the outline of the random gangue block reconstruction model.
  • Step 5 Obtain the digital 3D model volume of random gangue blocks
  • Vi is the volume of the area that is skipped by the projection of the i -th triangular piece to the reference plane.
  • V i has positive and negative points.
  • the direction of the model perpendicular to the reference plane is taken as the positive direction of the z-axis of the coordinate. If the z-axis component of the normal phase vector of the triangular slice (pointing to the inside of the model) is the proof, then V i is positive, otherwise it is negative.
  • Table 2 The obtained parameters are shown in Table 2.
  • Step 6 Obtain the digital 3D model of the random gangue block to contain the cuboid:
  • the digital three-dimensional model of the block firstly generate the initial containing cuboid V 0 ( ⁇ 0 , ⁇ 0 , ⁇ 0 ) of the block.
  • the coordinates of any vertex of the random gangue block be A 1 A 2 . 2, 3, 4..., n, rotate the block A 1 A 2 ... A n around the x-axis, y-axis, and z-axis by angles ⁇ , ⁇ , ⁇ , respectively, to obtain the rotated block A' 1 A' 2 ... A' n
  • the relationship between A′ i (x′ i ,y′ i ,z′ i ) and A i (x i ,y i ,z i ) is as follows:
  • the frontmost, last, leftmost, rightmost, topmost and bottommost vertices of the rotated blocks A' 1 A' 2 ...A' n are respectively made into 6 planes parallel to the coordinate plane, and the 6 planes are surrounded by
  • the cuboid is the containing cuboid of the block.
  • V( ⁇ , ⁇ , ⁇ ) is the volume of the cuboid containing the block after rotation; It is the maximum value of the x-axis coordinates of all the triangular slice vertices on the polyhedron surface, that is, the x-axis coordinate of the position of the right side of the smallest inclusive cuboid. It is the minimum value of the x-axis coordinates of all the triangular slice vertices on the surface of the polyhedron, that is, the x-axis coordinate of the position of the left side of the smallest inclusive cuboid.
  • Step 7 Obtain the shape index of the digital 3D model of the random gangue block
  • the major axis dimension L, secondary major axis dimension W, and minor axis dimension T of the block reconstruction model can be obtained by finding its minimum accommodating cuboid, and the length of the minimum enveloping cuboid is used as the long axis. Size, width is taken as the secondary major axis dimension, and thickness is taken as the minor axis dimension, where L ⁇ W ⁇ T, and the acquired parameters are shown in Table 2.
  • Step 8 Obtain the three-dimensional shape features of the digital three-dimensional model of the random gangue block: needle degree e, flatness f, sphericity ⁇ , the acquired parameters are shown in Table 2.
  • the needle degree e is used to describe the slenderness of the gangue block, and the calculation formula is Among them: L is the long axis dimension of the gangue block, the unit is mm; W is the secondary long axis size of the gangue block, the unit is mm.
  • the flatness f is used to describe the flatness of the gangue block, and the calculation formula is Where f is the flatness; T is the short axis of the gangue block, size, in mm.
  • the sphericity ⁇ is used to describe the roughness and shape symmetry of the gangue block, that is, the ratio of the surface area of the irregular particle to the actual surface area of the particle.
  • S is the actual surface area of the gangue block, the unit is mm 2 ;
  • V is the actual volume of the gangue block, the unit is mm 3 .
  • the method of the invention adopts CT slice, binarization processing, noise reduction, and reconstructs the digital three-dimensional model of the random gangue block, thereby obtaining the three-dimensional shape parameters that characterize the random gangue block, thereby solving the difficulty in obtaining the basic shape parameters of the random gangue block.
  • the measurement accuracy is highly subjective and the measurement cost is high.
  • the measurement results are highly accurate.

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Abstract

一种随机矸石块体三维形状参数自动获取方法，通过CT扫描获取随机矸石块体的二维切片图像，然后进行二值化处理并降噪，进而重构随机矸石块体数字化三维模型。获取随机矸石块体数字化三维模型表面积、模型体积、模型包容长方体，获取随机矸石块体数字化三维模型形状指标和模型的三维形状特征：针度e，扁平度f，球形度ψ。采用CT切片并二值化处理、降噪，重构随机矸石块体数字化三维模型，由此获取表征随机矸石块体三维形状的参数，从而解决了随机矸石块体基本形状参数获取困难、测量精度主观性大、测量成本高的问题。实现了随机矸石块体三维形状参数自动获取，测量结果精度高。

Description

一种随机矸石块体三维形状参数自动获取方法 技术领域
本发明涉及一种随机矸石块体三维形状参数的自动获取方法，尤其是针对外表形状极其不规则的随机矸石块体。
背景技术
传统的矸石块体基本形状参数测试主要测量长轴尺寸、次长轴尺寸、短轴尺寸、体积和表面积五项，目前的相关研究中主要通过人工测量的方式获取以上五个基本形状参数，且测量结果具有较大的主观性，精度不高，并且会耗费大量人力、物力。针对这一现状，设计研发一种能够自动计算、存储长轴尺寸、次长轴尺寸、短轴尺寸、体积和表面积的随机矸石块体数字化三维模型读取程序，降低测量成本，提高测量精度，实现块体三维形状指标的自动获取，成为需要解决技术问题。
发明内容
本发明的目的在于，弥补现有技术存在的空白，提出了一种随机矸石块体三维形状参数自动获取方法，解决了随机矸石块体基本形状参数获取困难、测量精度主观性大、测量成本高等问题。
本发明随机矸石块体三维形状参数自动获取方法，其步骤如下：
矸石块体的三维形状特征作为表征矸石块体重要参量，目前仍没有统一的量化指标，针对该现状本发明方法选取针度、扁平度、球形度作为表征不规则块体形状的量化指标。
步骤1.CT扫描，获取随机矸石块体的二维切片图像
为提高成像质量，确保获得清晰的原始CT切片，首先对矸石块体进行预处理，清理表面及缝隙内的杂物；然后对CT扫描设备的扫描层厚、旋转时间、图像重建矩阵、密度分辨率、HU标度范围等技术参数进行调整；将处理后的随机矸石块体放置到CT扫描机中进行扫描处理，获取随机矸石块体的二维切片图像(原始CT切片图像)。
步骤2.原始CT切片图像进行二值化处理并降噪
采用大津算法获得试样CT图像的最优阈值，基于最优阈值对原始CT切片图像进行二值化处理，排除矸石矿物组分多样性的干扰，使三维重构得到的随机矸石试样数字化模型只包括矸石基质与空隙两相；然后对处理后的二值化图片采用三维中值滤波算法进行降噪处理，消除孤立噪声点，将其转化为能够清晰表征矸石块体试样组构的一系列二维切片图。
步骤3.重构随机矸石块体数字化三维模型
采用MIMICS三维重构软件对经二值化和降噪处理后的CT切片进行叠加—3D重构计算 —平滑处理—网格优化等操作，最终重构真实形状随机矸石块体数字化三维模型。
步骤4.获取随机矸石块体数字化三维模型表面积
块体重构模型的轮廓是由数万个三角片组成的，首先遍历并计算所有三角片的面积，然后将其进行累加，将累加结果作为不规则矸石块体的表面积，计算公式如下：
Figure PCTCN2021071068-appb-000001
其中，S i为块体重构模型中第i个三角片的面积，n为构成随机矸石块体重构模型轮廓的三角片总数。
步骤5.获取随机矸石块体数字化三维模型体积
在模型外指定一基准面，遍历所有三角片并向投影面做垂直投影，计算所有三角片做投影所略过区域的体积并累加，计算公式如下：
Figure PCTCN2021071068-appb-000002
其中，V i为第i个三角片向基准面做投影所略过区域的体积。V i有正负之分，以模型垂直指向基准面的方向作为坐标z轴正方向，若三角片法相向量(指向模型内部)的z轴分量为证，则V i为正，否则为负。
步骤6.获取随机矸石块体数字化三维模型包容长方体：
根据块体数字化三维模型首先生成块体的初始包容长方体V 0(α 0,β 0,γ 0)。设随机矸石块体的任意顶点坐标为A 1A 2…A n，首先以A 1为坐标原点建立空间坐标系，顶点坐标为A i(x i,y i,z i)，i＝1，2，3，4……,n，将块体A 1A 2…A n绕x轴，y轴，z轴分别旋转角度α，β，γ，得到旋转后块体A′ 1A′ 2…A′ n，顶点坐标变为A′ i(x′ i,y′ i,z′ i)，i＝1，2，3，4……,n。A′ i(x′ i,y′ i,z′ i)与A i(x i,y i,z i)关系如下：
Figure PCTCN2021071068-appb-000003
分别过旋转后的块体A′ 1A′ 2…A′ n的最前、最后、最左、最右、最上和最下的顶点做平行于坐标面的6个平面，6个平面所围成的长方体即块体的包容长方体。包容长方体的体积公式：
Figure PCTCN2021071068-appb-000004
V(α,β,γ)为旋转后块体包容长方体体积；
Figure PCTCN2021071068-appb-000005
为多面体表面所有三角片顶点x轴坐标中的最大值，即最小包容长方体右面所在位置的x轴坐标。
Figure PCTCN2021071068-appb-000006
为多面体表面所有三角片顶点x轴坐标中的最小值，即最小包容长方体左面所在位置的x轴坐标。
Figure PCTCN2021071068-appb-000007
Figure PCTCN2021071068-appb-000008
分别为最小包容长方体前面和后面所在位置的y轴坐标，
Figure PCTCN2021071068-appb-000009
分别为最小包容长方体顶面和底面所在位置的z轴坐标。可见以上取值均与多面体旋转的角度有关，必然存在一组(α，β，γ)使函数V(α,β,γ)最小，即通过求取函数V(α,β,γ)最小值过程即获取最小包容长方体的过程。
步骤7.获取随机矸石块体数字化三维模型形状指标
块体的最小包容长方体建立后，块体重构模型的长轴尺寸L、次长轴尺寸W、短轴尺寸T即可通过求其最小包容长方体的方式获得，最小包容长方体的长作为长轴尺寸，宽作为次长轴尺寸，厚作为短轴尺寸，此处L≥W≥T。
步骤8.获取随机矸石块体数字化三维模型的三维形状特征：针度e，扁平度f，球形度ψ。
所述针度e，用于描述矸石块体的细长程度，计算公式为
Figure PCTCN2021071068-appb-000010
其中：L为矸石块体的长轴尺寸，单位mm；W为矸石块体的次长轴尺寸，单位mm。
所述扁平度f，用于描述矸石块体的扁平程度，计算公式为
Figure PCTCN2021071068-appb-000011
其中f为扁平度；T为矸石块体的短轴，尺寸，单位mm。
所述球形度ψ，用于描述矸石块体的粗糙度与形状对称性，即不规则颗粒同体积球的表面积与颗粒实际表面积的比值，计算公式为
Figure PCTCN2021071068-appb-000012
其中S为矸石块体实际表面积，单位mm 2；V为矸石块体实际体积，单位mm 3。
本发明方法采用CT切片并二值化处理、降噪，重构随机矸石块体数字化三维模型，由此获取表征随机矸石块体三维形状参数，从而解决了随机矸石块体基本形状参数获取困难、测量精度主观性大、测量成本高等问题。测量结果精度高。
附图说明
图1是随机矸石块体CT切片二值化图像三维中值滤波降噪处理效果图。其中图a是原始CT图片；图b是二值化图片；图c是降噪处理后二值化图片。
图2是重建随机矸石块体数字化三维模型示意图。
图3是随机矸石块体重构模型面积计算原理图。
图4是随机矸石块体重构模型体积计算原理图。
图5是随机矸石块体的空间位置与包容长方体示意图。
图6是随机矸石块体的最小包容长方体与主要尺寸参数。
具体实施方式
下面结合实施例和附图，对本发明方法作进一步详细说明。
步骤1.CT扫描，获取随机矸石块体的二维切片图像
为提高成像质量，确保获得清晰的原始CT切片，首先对矸石块体进行预处理，清理表面及缝隙内的杂物；根据矸石的理化特性对CT扫描设备的扫描层厚、旋转时间、图像重建矩阵、密度分辨率、HU标度范围等技术参数进行调整。
表1矸石块体CT扫描试验主要参数设置
主要参数 数值设置
工作电压 140kV
电流 105mA
扫描层厚 0.67mm
旋转时间 0.33sec
mAs 45mAs/Slice
视野 500.0mm
图像重建矩阵 768×768
密度分辨率 0.3％
HU标度范围 -1024～+3071
将处理后的随机矸石块体放置到CT扫描机中进行扫描处理，获取随机矸石块体的二维切片图像(原始CT切片图像)，如图1所示。
步骤2.原始CT切片图像进行二值化处理并降噪
采用大津算法获得试样CT图像的最优阈值，基于最优阈值对原始CT切片图像进行二值化处理，排除矸石矿物组分多样性的干扰，使三维重构得到的随机矸石试样数字化模型只包括矸石基质与空隙两相；然后对处理后的二值化图片采用三维中值滤波算法进行降噪处理，消除孤立噪声点，将其转化为能够清晰表征矸石块体试样组构的一系列二维切片图。
步骤3.重构随机矸石块体数字化三维模型
采用MIMICS三维重构软件对经二值化和降噪处理后的CT切片进行叠加—3D重构计算—平滑处理—网格优化等操作，最终重构真实形状随机矸石块体数字化三维模型,以部分20～25mm尺寸的矸石为例(见图2)。
步骤4.获取随机矸石块体数字化三维模型表面积
从20～25mm尺寸的矸石的重构模型中选取单一块体为例进行参数的获取(后续参数的获取都以该矸石为例)，获取后的参数见表2。块体重构模型的轮廓是由数万个三角片组成的，首先遍历并计算所有三角片的面积，然后将其进行累加，将累加结果作为不规则矸石块体的 表面积(见图3)，计算公式如下：
Figure PCTCN2021071068-appb-000013
其中，S i为块体重构模型中第i个三角片的面积，n为构成随机矸石块体重构模型轮廓的三角片总数。
步骤5.获取随机矸石块体数字化三维模型体积
在模型外指定一基准面，遍历所有三角片并向投影面做垂直投影，计算所有三角片做投影所略过区域的体积并累加，计算公式如下：
Figure PCTCN2021071068-appb-000014
其中，V i为第i个三角片向基准面做投影所略过区域的体积。V i有正负之分，以模型垂直指向基准面的方向作为坐标z轴正方向，若三角片法相向量(指向模型内部)的z轴分量为证，则V i为正，否则为负，获取后的参数见表2。
步骤6.获取随机矸石块体数字化三维模型包容长方体：
根据块体数字化三维模型首先生成块体的初始包容长方体V 0(α 0,β 0,γ 0)。设随机矸石块体的任意顶点坐标为A 1A 2…A n，首先以A 1为坐标原点建立空间坐标系，顶点坐标为A i(x i,y i,z i)，i＝1，2，3，4……,n，将块体A 1A 2…A n绕x轴，y轴，z轴分别旋转角度α，β，γ，得到旋转后块体A′ 1A′ 2…A′ n，顶点坐标变为A′ i(x′ i,y′ i,z′ i)，i＝1，2，3，4……,n。A′ i(x′ i,y′ i,z′ i)与A i(x i,y i,z i)关系如下：
Figure PCTCN2021071068-appb-000015
分别过旋转后的块体A′ 1A′ 2…A′ n的最前、最后、最左、最右、最上和最下的顶点做平行于坐标面的6个平面，6个平面所围成的长方体即块体的包容长方体。包容长方体的体积公式：
Figure PCTCN2021071068-appb-000016
V(α,β,γ)为旋转后块体包容长方体体积；
Figure PCTCN2021071068-appb-000017
为多面体表面所有三角片顶点x轴坐标中的最大值，即最小包容长方体右面所在位置的x轴坐标。
Figure PCTCN2021071068-appb-000018
为多面体表面所有三角片顶点x轴坐标中的最小值，即最小包容长方体左面所在位置的x轴坐标。
Figure PCTCN2021071068-appb-000019
Figure PCTCN2021071068-appb-000020
分别为最小包容长方体前面和后面所在位置的y轴坐标，
Figure PCTCN2021071068-appb-000021
分别为最小包容长方体顶面和底面所在位置的z轴坐标。可见以上取值均与多面体旋转的角度有关，必然存在一组(α，β，γ)使函数V(α,β,γ)最小，即通过求取函数V(α,β,γ)最小值过程即获取最小包容长方体的过程。
步骤7.获取随机矸石块体数字化三维模型形状指标
块体的最小包容长方体建立后，块体重构模型的长轴尺寸L、次长轴尺寸W、短轴尺寸T即可通过求其最小包容长方体的方式获得，最小包容长方体的长作为长轴尺寸，宽作为次长轴尺寸，厚作为短轴尺寸，此处L≥W≥T，获取后的参数见表2。
步骤8.获取随机矸石块体数字化三维模型的三维形状特征：针度e，扁平度f，球形度ψ，获取后的参数见表2。
所述针度e，用于描述矸石块体的细长程度，计算公式为
Figure PCTCN2021071068-appb-000022
其中：L为矸石块体的长轴尺寸，单位mm；W为矸石块体的次长轴尺寸，单位mm。
所述扁平度f，用于描述矸石块体的扁平程度，计算公式为
Figure PCTCN2021071068-appb-000023
其中f为扁平度；T为矸石块体的短轴，尺寸，单位mm。
所述球形度ψ，用于描述矸石块体的粗糙度与形状对称性，即不规则颗粒同体积球的表面积与颗粒实际表面积的比值，计算公式为
Figure PCTCN2021071068-appb-000024
其中S为矸石块体实际表面积，单位mm 2；V为矸石块体实际体积，单位mm 3。
表2示例矸石具体参数表
长/mm 宽/mm 高/mm 表面积/mm 2 体积/mm 3 针度 扁平度 球形度
62.394 42.552 35.862 7490.137 43840.108 1.466 0.843 0.805
本发明方法采用CT切片并二值化处理、降噪，重构随机矸石块体数字化三维模型，由此获取表征随机矸石块体三维形状参数，从而解决了随机矸石块体基本形状参数获取困难、测量精度主观性大、测量成本高等问题。测量结果精度高。

Claims (7)

  1. 一种随机矸石块体三维形状参数自动获取方法，其步骤如下：
    步骤1.CT扫描，获取随机矸石块体的二维切片图像；
    步骤2.原始CT切片图像进行二值化处理并降噪；
    步骤3.重构随机矸石块体数字化三维模型；
    步骤4.获取随机矸石块体数字化三维模型表面积；
    步骤5.获取随机矸石块体数字化三维模型体积；
    步骤6.获取随机矸石块体数字化三维模型包容长方体；
    步骤7.获取随机矸石块体数字化三维模型形状指标
    块体的最小包容长方体建立后，块体重构模型的长轴尺寸L、次长轴尺寸W、短轴尺寸T,通过求其最小包容长方体的方式获得，最小包容长方体的长作为长轴尺寸，宽作为次长轴尺寸，厚作为短轴尺寸，此处L≥W≥T；
    步骤8.获取随机矸石块体数字化三维模型的三维形状特征：针度e，扁平度f，球形度ψ；
    所述针度e，用于描述矸石块体的细长程度，计算公式为
    Figure PCTCN2021071068-appb-100001
    其中：L为矸石块体的长轴尺寸，单位mm；W为矸石块体的次长轴尺寸，单位mm；
    所述扁平度f，用于描述矸石块体的扁平程度，计算公式为
    Figure PCTCN2021071068-appb-100002
    其中f为扁平度；T为矸石块体的短轴，尺寸，单位mm；
    所述球形度ψ，用于描述矸石块体的粗糙度与形状对称性，即不规则颗粒同体积球的表面积与颗粒实际表面积的比值，计算公式为
    Figure PCTCN2021071068-appb-100003
    其中S为矸石块体实际表面积，单位mm 2；V为矸石块体实际体积，单位mm 3。
  2. 根据权利要求1所述随机矸石块体三维形状参数自动获取方法，其特征是：
    所述步骤1，首先对矸石块体进行预处理，清理表面及缝隙内的杂物；然后对CT扫描设备的扫描层厚、旋转时间、图像重建矩阵、密度分辨率、HU标度范围进行调整；将处理后的随机矸石块体放置到CT扫描机中进行扫描处理，获取随机矸石块体的二维切片图像。
  3. 根据权利要求1所述随机矸石块体三维形状参数自动获取方法，其特征是：
    所述步骤2，采用大津算法获得试样CT图像的最优阈值，基于最优阈值对原始CT切片图像进行二值化处理，使三维重构得到的随机矸石试样数字化模型只包括矸石基质与空隙两相；然后对处理后的二值化图片采用三维中值滤波算法进行降噪处理，消除孤立噪声点，得到二值化和降噪处理后的CT切片。
  4. 根据权利要求1所述随机矸石块体三维形状参数自动获取方法，其特征是：
    所述步骤3，采用MIMICS三维重构软件对经二值化和降噪处理后的CT切片进行叠加—3D重构计算—平滑处理—网格优化操作，最终重构随机矸石块体数字化三维模型。
  5. 根据权利要求1所述随机矸石块体三维形状参数自动获取方法，其特征是：
    所述步骤4，随机矸石块体重构模型的轮廓是由数万个三角片组成的，首先遍历并计算所有三角片的面积，然后将其进行累加，将累加结果作为不规则矸石块体的表面积，计算公式如下：
    Figure PCTCN2021071068-appb-100004
    其中，S i为块体重构模型中第i个三角片的面积，n为构成随机矸石块体重构模型轮廓的三角片总数。
  6. 根据权利要求1所述随机矸石块体三维形状参数自动获取方法，其特征是：
    所述步骤5，在模型外指定一基准面，遍历所有三角片并向投影面做垂直投影，计算所有三角片做投影所略过区域的体积并累加，计算公式如下：
    Figure PCTCN2021071068-appb-100005
    其中，V i为第i个三角片向基准面做投影所略过区域的体积；V i有正负之分，以模型垂直指向基准面的方向作为坐标z轴正方向，若三角片法相向量的z轴分量为证，则V i为正，否则为负。
  7. 根据权利要求1所述随机矸石块体三维形状参数自动获取方法，其特征是：
    所述步骤6.获取随机矸石块体数字化三维模型包容长方体，其步骤如下：
    根据块体数字化三维模型首先生成块体的初始包容长方体V 0(α 0,β 0,γ 0)；设随机矸石块体的任意顶点坐标为A 1A 2…A n，首先以A 1为坐标原点建立空间坐标系，顶点坐标为A i(x i,y i,z i)，i＝1，2，3，4……,n，将块体A 1A 2…A n绕x轴，y轴，z轴分别旋转角度α，β，γ，得到旋转后块体A′ 1A′ 2…A′ n，顶点坐标变为A′ i(x′ i,y′ i,z′ i)，i＝1，2，3，4……,n；A′ i(x′ i,y′ i,z′ i)与A i(x i,y i,z i)关系如下：
    Figure PCTCN2021071068-appb-100006
    分别过旋转后的块体A′ 1A′ 2…A′ n的最前、最后、最左、最右、最上和最下的顶点做平行于 坐标面的6个平面，6个平面所围成的长方体即块体的包容长方体；包容长方体的体积公式：
    Figure PCTCN2021071068-appb-100007
    V(α,β,γ)为旋转后块体包容长方体体积；
    Figure PCTCN2021071068-appb-100008
    为多面体表面所有三角片顶点x轴坐标中的最大值，即最小包容长方体右面所在位置的x轴坐标；
    Figure PCTCN2021071068-appb-100009
    为多面体表面所有三角片顶点x轴坐标中的最小值，即最小包容长方体左面所在位置的x轴坐标；
    Figure PCTCN2021071068-appb-100010
    Figure PCTCN2021071068-appb-100011
    分别为最小包容长方体前面和后面所在位置的y轴坐标，
    Figure PCTCN2021071068-appb-100012
    分别为最小包容长方体顶面和底面所在位置的z轴坐标；可见以上取值均与多面体旋转的角度有关，必然存在一组(α，β，γ)使函数V(α,β,γ)最小，即通过求取函数V(α,β,γ)最小值过程即获取最小包容长方体的过程。
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