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出处：nvzhuang.ping-jia.net &&更新日期：Patent CNB - 一种基于压缩感知的点云数据稀疏表示方法 Sparse indicates data compression ... - Google PatentsCN BGrantCN Feb 15, 2017Jan 9, 2014Jan 9, 2014.3, CN
B, CN B, CN , CN-B-, CN B, CNB, CN, CN.3, , , , , ,
一种基于压缩感知的点云数据稀疏表示方法 Sparse indicates data compression method based on cloud-aware translated from CN
B 本申请公开一种基于压缩感知的点云数据稀疏表示方法，其在保证一定精度的前提下对海量点云数据进行压缩，使得点云数据的稀疏度大幅提高，为基于压缩感知的点云数据压缩与重建奠定良好基础。 The present application discloses a method based on the sparse representation point cloud data compression-aware, which was guaranteed under the premise of mass accuracy of point cloud data compression, so that the point cloud data sparsity substantial increase in the point cloud data based on the compressed sensing compression lay a good foundation and reconstruction. 包括步骤：（1）点云数据规格化；（2）基于K-SVD算法的过完备字典稀疏表示；（3）规格化点云数据观测，传输并存储；（4）基于l1范数最小化的点云数据重建；（5）规格化点云数据恢复。 Comprising the steps of: (1) point clou (2) a sparse representation based on over-complete dictionary K-SVD and (3) normalizing the observation point cloud data, tran (4) based on the l1 norm minimization the point cloud (5) normalized point cloud data recovery.
1. 一种基于压缩感知的点云数据稀疏表示方法，其特征在于:包括以下步骤： (1) 点云数据规格化； (2) 基于K-SVD算法的过完备字典稀疏表示； (3) 规格化点云数据观测，传输并存储； (4) 基于11范数最小化的点云数据重建； (5) 规格化点云数据恢复； 步骤（1)中采用最小二乘算法对片元进行平面方程拟合，用平面法向对片元法向进行估计，以便后续的点云数据规格化;对片元中的点云进行几何变换，使得具有相似几何特性的片元在数值上同样具有一定的相似性； 通过公式（1)、（ 2)计算点云数据的片元： 点云集合为户；fPi丨i ,片元质心为 A sparse representation based on the compression-aware point cloud data, characterized in that: comprising the steps of: (1) point clou (2) based on over-complete dictionary K-SVD (3) normalized observation point cloud data, tran (4) 11 based on the norm minimization point cloud (5) normalized point step (1) in the least square algorithm for fragments fit plane equation, the fragment of a plane normal to estimate method, so that subsequent point clou point cloud fragments of geometric transformation, such sheet element having a similar geometric properties with the same values in by the equation (1), fragments (2) calculation point cloud data: the point clo FPI Shu i, the fragment centroid
，点Pj的Κ近邻分片Sj为： , The point Pj Κ neighboring slice Sj is:
(1) 由质心p指向K近邻片元的中心点的方向向量为胃与拟合平面的夹角为β，胃与拟合出的法向??夹角为a，FI与Η的内积为屮=JI·两，当Ρ&〇时，表示拟合出的法向η指向模型外部，不对拟合出的法向进行调整，当&0时，表示拟合出的法向η指向模型内部，对法向η进行调整，对法向玨进行取反操作； 点云数据片元的规则化变换矩阵为： normMatj = Tj*Rj (2) 其中L为根据质心坐标构建平移变换矩阵，心为旋转矩阵； 步骤(2)包括以下分步骤： (1) 设1)?1^'3^1^，$妒，1^{3^|11,:|；=_；^1，其中，〇为原过完备原子库， 7 表示训练信号，X为训练信号的稀疏表示系数向量，Y为Μ个训练信号集合，X为Y的解向量集合，Rn表示η维信号集，通过公式(3)计算： Direction vector (1) by the centroid K p at the center of the nearest neighbor tile-fit plane for the stomach and the angle of β, the stomach and the fitted normal ?? angle is a, the volume of the FI and Η Che = JI · two, when Ρ& square indicates the fitted model of normal η directed outward, not fitted to the adjustment method, when a &0, represents the normal internal fitting point to the model η of method to η adjustment of method negate operation to J point cloud data fragment regularization transformation matrix: normMatj = Tj * Rj (2) where L is a construct translation transformation matrix according centroid coordinates, the hear step (2) comprises the following substeps: (1) provided 1) ? 1 ^ '3 ^ 1 ^, $ jealous, 1 ^ {3 ^ | 11,: |; = _; ^ 1, wherein the square original through the complete dictionary, 7 denotes a training signal, X is the sparse representation coefficient vector of the training signal, Y is Μ training set of signals, X is the solution vector Y is set, Rn represents η-dimensional signal set by the formula (3) calculation:
⑶ 其中，To为稀疏表示系数中非零分量个数的上限； (2) 对D进行迭代训练，设dk为要更新的原子库D的第k列向量，此时信号集的分解形式为公式(4): ⑶ wherein, To represents the upper limit of the number of coefficients in a sparse non- (2) the D training iteration, dk is set to update the k-th column vector library atom D, in which case the set of signals in exploded form of the formula (4):
(!) 通过奇异值分解，逐列更新字典，产生新的字典5 ,然后根据新的字典I得出新的稀疏系数，并迭代更新，直到收敛； 步骤(5)通过公式(9)、（ 10)重建点云数据： (!) By singular value decomposition, the dictionary is updated by the column, a new dictionary 5, then I obtained according to the new dictionary new sparse coefficients, and iteratively updat Step (5) by the equation (9), ( 10) reconstruction point cloud data:
其中f为规格化点云数据在字典D下的稀疏系数重建结果， 然后对重建的规格化点云数据F做反变换来获得重建的点云数据梦。 Wherein f is normalized point cloud data reconstruction results in a sparse coefficient dictionary D, F and point cloud data normalized to inverse transform the reconstructed done to obtain point cloud data reconstructed dream.
一种基于压缩感知的点云数据稀疏表示方法 Sparse indicates data compression method based on cloud-aware
技术领域 FIELD
[0001]本发明属于三维点云数据压缩编码的技术领域，具体地涉及一种基于压缩感知的点云数据稀疏表示方法。 [0001] The present invention belongs to the three-dimensional point cloud data compression techniques in the field of coding, particularly to a point cloud data based on the compressed sensing sparse representation.
背景技术 Background technique
[0002] 随着三维扫描技术迅速发展，点云数据渐渐成为多媒体数据中非常重要的一类数据。 [0002] With the rapid development of 3D scanning technology, point cloud data multimedia data gradually become a very important class of data. 如今的扫描设备能够高效获得离散的、散乱分布的海量点云数据来表示物体，因此点云数据高效压缩、编码逐渐成为研究热点之一。 Today scanning equipment can be efficiently obtained discrete, randomly distributed massive point cloud data to represent the object, point cloud data and therefore efficient compression coding is becoming one of the hotspots. 点云数据压缩的主要研究目标是在尽可能保留原有模型几何特征的情况下，降低数据文件的大小，使得点云数据在有限带宽下能够更加快速的存储和传播。 Point cloud data compression main objective in the case of geometric features of the original model to retain as much as possible, reduce the size of data files, make the point cloud data can be more quickly stored and disseminated in a limited bandwidth. 虽然许多学者都致力于复杂点云数据的压缩与重建，如何在不降低点云模型几何特征的情况下，对点云数据进行压缩是一项更具挑战性的工作。 Although many scholars dedicated to compression and reconstruction complex point cloud data, how in the case of point clouds without reducing the geometric features of the model point cloud data compression is a more challenging task.
[0003] 目前散乱点云数据压缩方法主要有两种:基于网格的压缩方法和基于点的压缩方法。 [0003] It Scattered Data compression method are mainly two: grid-based compression method and compression method based on points. 前者要先建立点云数据的三角网格，然后将相同顶点的三角面片的最大法矢夹角、压缩后点数和最大边界误差等，与相应的自定义阈值相比较，进行取舍，对网格进行简化。 The former must first establish a triangular mesh point cloud data, then the maximum angle vector method triangular facets same vertex, and the compressed count maximum boundary errors, compared to the corresponding custom threshold, trade-offs, the mesh simplified grid. 基于网格的压缩方法压缩效果比较好，但是构建网格，尤其是构建海量数据网格是一项复杂耗时的工作，效率低，而且没有固定的阈值选取准则，压缩效果具有一定的随意性。 Grid-based compression method is better compression, but to build a grid, in particular mass data grid work to build a complex and time-consuming, inefficient, and there is no fixed threshold selection criterion, with a certain arbitrariness compression . 基于点的压缩方法是根据点云的空间拓扑关系计算对应的离散几何信息，如平均点距值、包围盒点数、均匀网格中心、曲率等，根据信息量对点云进行精简处理。 Calculates the corresponding compression method is based on the spatial point of the point cloud topological relations discrete geometric information, such as the average value of the pitch, points bounding box, uniform grid center, the curvature and the like, to streamline the processing of information in accordance with the point cloud. 基于点的压缩方法直接简化点云，效率较高，但是压缩数据在细节和特征上的损失难以避免甚至难以控制。 Direct compression methods to simplify point based cloud point, high efficiency, but the loss in data compression characteristics and details difficult to avoid even difficult to control.
[0004] 近年来Donoho、Candgs等人提出了一种新的信息获取指导理论，即压缩感知(Compressive Sensing，CS)，该理论指出：对于变换域下稀疏的信号，可以利用优化方法由与变换基非一致关系的观测矩阵生成少量的数据来精确重建。 [0004] In recent years Donoho, Candgs et al proposed a new information for guidance theory that compressed sensing (Compressive Sensing, CS), the theory states that: For the sparse signal in the transform domain, you can use optimization method by a transformation observation matrix based non-uniform relationship to the amount of data generated exact reconstruction. 该理论利用信号的稀疏特性将基于Shannon/Nyquist定理的采样过程转化为观测矩阵的观测过程，从而数据的采样速率不取决于信号带宽，而是信号的结构和内容，而信号稀疏性的好坏是利用压缩感知对信号进行压缩重构质量优劣的关键因素之一。 The theory of using the signal conversion characteristic based on sparse sampling process Shannon / Nyquist theorem is observed during the observation matrix, thus is not dependent on the sampling rate of the data signal bandwidth, but the structure and content of the signal quality of the signal sparsity is the use of compressed sensing the signal is a key factor in the quality of the merits of compression reconstruction. 因此，该理论为点云数据的压缩提供了一种崭新的思路和方向。 Therefore, the point cloud data compression provides a new idea and direction of the theory.
[0005] 考虑到点云数据离散分布的特性，基于过完备字典的稀疏表示方法可以使得散乱点云数据在一定程度上可以稀疏化。 [0005] Consider characteristic cloud point data discretely distributed, based on over-complete dictionary sparse representation can be made in the scattered point cloud data can be thinned out to some extent. 基于过完备字典的信号稀疏表示理论可以认为是在尽可能重构原始信号的条件下，利用过完备冗余基来取代传统的正交基，这个过完备冗余函数集合通常用学习的方法来选取。 Overcomplete dictionary based on the sparse representation of the signal can be considered in theory under reconstruction of the original signal as possible, using the redundancy group over a complete orthogonal basis to replace the traditional, fully redundant function over the set of methods commonly used to study select. 因此，信号的稀疏表示主要涵盖两方面内容，一个是信号的稀疏编码，另一个是过完备字典的训练。 Therefore, the sparse representation of the signal mainly covers two aspects, one is sparse coding signal, and the other is over-complete dictionary of training.
[0006] 如何寻找一个合适的字典D是近年来在在基于过完备字典进行稀疏表示的热门研究问题。 [0006] how to find a suitable dictionary D in recent years in the over-complete dictionary based on popular research questions sparse representation. 关于过完备字典的选取也有多种方案：一种是直接利用已经构造好的字典，比如steerable小波，curve lets小波等。 Select on over-complete dictionary also has a variety of programs: one is the direct use of already constructed a good dictionary, such as steerable wavelet, curve lets wavelets and so on. 另一种方法是选择可通过参数调整的字典，即在参数约束下生成字典. Another method is to select the parameter adjustment by the dictionary, the dictionary that is generated in the parameter constraints.
[0007] 字典训练方法作为一种字典设计的方法出现较晚，学习字典带来的主要好处在于经过训练的字典能够在训练过程中自适应许多实际的信号，并且国内外学者也已经提出许多比较有效的字典训练算法。 [0007] dictionary training method appeared later as a method of dictionary design, the main benefit is the ability to bring the dictionary to learn many practical adaptive signal through the dictionary in the training process of training, and domestic and foreign scholars have proposed many compare effective dictionary training algorithm. Engan等人在2000年提出的最优方向法（MOD, Method of Optimal Direct ions)最早用于稀疏表示，MOD算法的主要贡献在于其简单的字典更新策略。 Optimal direction method (MOD, Method of Optimal Direct ions) Engan, who proposed in 2000, the first for the sparse representation algorithm MOD main contribution lies in its simple dictionary update policy. 一般情况下，MOD只需要少量次数的迭代就可以收敛，总体上比较有效，但是这种方法在求解过程中需要计算矩阵的逆，其复杂度比较高，因此，之后的学者的研究主要目的是为了减少时间复杂度引入了一些更加实用的方法。 Under normal circumstances, MOD requires only a small number of iterations to converge, on the whole more effective, but this method requires computing the inverse matrix in the solution process, its high complexity, therefore, the main purpose of research scholars is after in order to reduce the time complexity introduces some of the more practical approach.
[0008] 在K-Means算法的基础上，Michal Aharon等人又提出了K-SVD过完备字典训练算法，K-SVD算法非常灵活，可以和常见的稀疏分解的最优原子搜索算法，如MP，0ΜΡ，BP， F0CUSS，结合使用，并且其作为一个字典训练算法，收敛性是其获得新能优良字典的保证。 [0008] On the basis of K-Means algorithms, Michal Aharon, who proposed the K-SVD over-complete dictionary training algorithm, K-SVD algorithm is very flexible, and the common search algorithm optimized atomic sparse decomposition, such as MP , 0ΜΡ, BP, F0CUSS, used in combination, as a dictionary and its training algorithm, convergence is guaranteed access to new energy good dictionary. K-SVD算法通过不断的训练更新得到最适合于样本集合的冗余字典，由于是通过训练更新自适应得到的，信号在冗余字典上可以根据自己特优的结构特征进行分解，即训练更新得到的冗余字典可以更好的发掘信号的稀疏性。 K-SVD algorithm is best suited for sample collection through continuous training redundant dictionary updated, as is, the signal can be decomposed according to their structural features privileged updating the adaptive obtained by training on a redundant dictionary, i.e., updated training sparsity redundant dictionary can get better explore signals. 因此本方法采取K-SVD算法来进行对点云数据进行稀疏表示，从而达到压缩感知的先验条件。 This method thus adopted K-SVD algorithm for sparse point cloud data, said compressed to achieve priori perception.
发明内容 SUMMARY
[0009] 本发明的技术解决问题是：克服现有技术的不足，提供一种基于压缩感知的点云数据稀疏表示方法，其在保证一定精度的前提下对海量点云数据进行压缩、使得点云数据的稀疏度大幅提高、为基于压缩感知的点云数据压缩与重建奠定的良好基础。 [0009] The techniques of the present invention is to solve the problem: to overcome the deficiencies of the prior art, to provide a point cloud data based on sparse representation compressed sensing, which compresses the mass at point cloud data guaranteed accuracy of the premise, such that the point sparsity cloud data significantly improved, point cloud data based on compression-aware compression and reconstruction laid a good foundation.
[0010] 本发明的技术解决方案是:这种基于压缩感知的点云数据稀疏表示方法，包括以下步骤： [0010] The technical solution of the invention is: This point cloud data based on the compression-aware sparse representation method, comprising the steps of:
[0011] (1)点云数据规格化； [0011] (1) point clou
[0012] (2)基于K-SVD算法的过完备字典稀疏表示； [0012] (2) a sparse representation based on over-complete dictionary K-SVD
[0013] (3)规格化点云数据观测，传输并存储； [0013] (3) normalizing the observation point cloud data, tran
[0014] (4)基于11范数最小化的点云数据重建； [0014] (4) 11 based on the norm minimization point cloud
[0015] (5)规格化点云数据恢复。 [0015] (5) normalized point cloud data recovery.
[0016]由于本方法在对点云数据做稀疏求解之前，先对点云数据做预处理操作，即点云数据的规格化，而基于稀疏表示的过完备字典训练方法，与传统的完备字典(如FFT、DCT、小波、Gabor字典)相比是自适应地根据训练信号提取其特征，因而具有更强的稀疏表示能力， 从而在保证一定精度的前提下对海量点云数据进行压缩、使得点云数据的稀疏度大幅提高、为基于压缩感知的点云数据压缩与重建奠定的良好基础。 [0016] Since the present method before making solving sparse point cloud data, the point cloud data to preprocessing operations, i.e., the point cloud data normalization, and overcomplete dictionary training method based on sparse representation, the conventional complete dictionary (e.g., FFT, DCT, wavelet, Gabor dictionary) is compared to the training signal extracting adaptively further, thus having sparse representation stronger capability to compress the data in the point cloud mass guaranteed accuracy of the premise, such that point cloud data sparsity substantial increase in the point cloud data based on compression-aware compression and reconstruction laid a good foundation.
具体实施方式 detailed description
[0017] 这种基于压缩感知的点云数据稀疏表示方法，包括以下步骤： [0017] This method is based on sparse representation compression-aware point cloud data, comprising the steps of:
[0018] (1)点云数据规格化； [0018] (1) point clou
[0019] (2)基于K-SVD算法的过完备字典稀疏表示； [0019] (2) a sparse representation based on over-complete dictionary K-SVD
[0020] (3)规格化点云数据观测，传输并存储； [0020] (3) normalizing the observation point cloud data, tran
[0021] (4)基于11范数最小化的点云数据重建； [0021] (4) 11 based on the norm minimization point cloud
[0022] (5)规格化点云数据恢复。 [0022] (5) normalized point cloud data recovery.
[0023]由于本方法在对点云数据做稀疏求解之前，先对点云数据做预处理操作，即点云数据的规格化，而基于稀疏表示的过完备字典训练方法，与传统的完备字典(如FFT、DCT、小波、Gabor字典)相比是自适应地根据训练信号提取其特征，因而具有更强的稀疏表示能力， 从而在保证一定精度的前提下对海量点云数据进行压缩、使得点云数据的稀疏度大幅提高、为基于压缩感知的点云数据压缩与重建奠定的良好基础。 [0023] Since the present method before making solving sparse point cloud data, the point cloud data to preprocessing operations, i.e., the point cloud data normalization, and overcomplete dictionary training method based on sparse representation, the conventional complete dictionary (e.g., FFT, DCT, wavelet, Gabor dictionary) is compared to the training signal extracting adaptively further, thus having sparse representation stronger capability to compress the mass point cloud data in a guaranteed accuracy of the premise, such that point cloud data sparsity substantial increase in the point cloud data based on compression-aware compression and reconstruction laid a good foundation.
[0024]步骤（1)中采用最小二乘算法对片元进行平面方程拟合，用平面法向对片元法向进行估计，以便后续的点云数据规格化;对片元中的点云进行几何变换，使得具有相似几何特性的片元在数值上同样具有一定的相似性。 [0024] Step (1) of the sheet in the least square method to fit equation planar element, the element normal to the sheet plane method for estimation, in order to normalize the subsequ point cloud of the fragment geometric transformation, such sheet element having a similar geometric features also have certain similarities in value.
[0025]通过公式（1)、（2)计算点云数据的片元： [0025] by the equation (1), (2) the point cloud data calculated sheet element:
[0026] 点云集合为 [0026] Cloud point is set
点Pj的K近邻分片Sj为： K nearest neighbor peers Pj slice Sj is:
[0027] [0027]
[0028] 由质心P指向K近邻片元的中心点的方向向量为胃，胃与拟合平面的夹角为β， Ρ尺与拟合出的法向??夹角为α，PR与η的内积为： [0028] from the center of the centroid direction vector P K nearest neighbor points to the fragment of the stomach, gastric planar angle of β with the fitting, [rho] Size and fitted to the law ?? angle α, the PR and η the inner product is:
[0029] ρ _二当Ρ&0时，表示拟合出的法向η指向模型外部，不对拟合出的法向进行调整，当& 〇时，表示拟合出的法向η指向模型内部，对法向η进行调整，对法向Η进行取反操作； [0029] ρ _ when two Ρ& 0, indicates the fitted model of normal η directed outward, not fitted to the adjustment method, when &square, the internal fitting point to the normal model η , [eta] of the adjustment method, method of [eta]
[0030] 点云数据片元的规则化变换矩阵为： [0030] point cloud data fragment regularization transformation matrix:
[0031] normMatj=Tj*Rj (2) [0031] normMatj = Tj * Rj (2)
[0032] 其中L为根据质心坐标构建平移变换矩阵，吣为旋转矩阵。 [0032] wherein L is a translational transformation matrix construct according centroid coordinates, Qin is the rotation matrix.
[0033]优选地，步骤(4)包括以下分步骤： [0033] Preferably, step (4) comprises the following substeps:
[0034] (lH5DeRnXK，yeRn，xeRK [0034] (lH5DeRnXK, yeRn, xeRK
其中，D为原过完备原子库，y表示训练信号，X为训练信号的稀疏表示系数向量，Y为Μ个训练信号集合，X为Y的解向量集合，Rn表示η维信号集，通过公式(3)计算： Wherein, D is the original over-complete dictionary, y denotes a training signal, X is the sparse representation coefficient vector of the training signal, Y is Μ training set of signals, X is the solution vector Y is set, Rn represents η-dimensional signal set by the formula (3) calculated:
[0035] [0035]
[0036] 其中，To为稀疏表示系数中非零分量个数的上限； [0036] where, To represents the upper limit of the number of coefficients in a sparse non-
[0037] (2)对D进行迭代训练，设dk为要更新的原子库D的第k列向量，此时信号集的分解形式为公式(4): [0037] (2) D training iteration, dk is set to update the k-th column vector D library atoms, in which case the set of signals in exploded form of equation (4):
[0038] ⑷ [0038] ⑷
[0039] 通过奇异值分解，逐列更新字典，产生新的字典方，然后根据新的字典0得出新的稀疏系数，并迭代更新，直到收敛。 [0039] by the singular value decomposition, the dictionary is updated by the column, a new dictionary square, then the new sparse coefficients derived based on the new dictionary 0, and iteratively updated until convergence.
[0040] 优选地，步骤(5)通过公式(9)、（10)重建点云数据： [0040] Preferably, the step (5) by the equation (9), (10) the reconstruction point cloud data:
[0041] [0041]
[0042] p = 〇? (10) [0042] p = square ? (10)
[0043] 其中交为规格化点云数据在字典D下的稀疏系数重建结果， [0043] wherein the cross point cloud data is normalized reconstruction results in a sparse coefficient dictionary D,
[0044] 然后对重建的规格化点云数据：故反变换来获得重建的点云数据P。 [0044] The point cloud data was then normalized to the reconstruction: it is the inverse transform to obtain point cloud data reconstructed P.
[0045] 下面详细说明本发明的实施方案。 [0045] The following detailed description of embodiments of the present invention.
[0046] 1)点云数据规格化方法 [0046] 1) point cloud data normalization method
[0047]点云数据由于其空间散落分布的特性，并不具备明显的稀疏性，并不能直接利用压缩感知相关理论来进行压缩、重建。 [0047] Due to its point cloud data of the spatial distribution of scattered properties, does not have obvious sparseness, the compression can not be directly related to sensing compression theory, reconstruction. 因此，本发明利用K-SVD过完备字典的方法对点云数据进行稀疏表示。 Accordingly, the present invention is the point cloud data using the sparse representation method K-SVD overcomplete dictionary. 但是，原始的散乱点云数据并不具备良好的相似性，直接利用K-SVD过完备字典训练算法并不能得到良好的稀疏表示结果。 However, the original scattered point cloud data does not have good similarity, the direct use of K-SVD algorithm over-complete dictionary and can not get good training sparse representation of results. 因此，为了使点云数据在过完备字典下能有更好的稀疏度，本发明首先对散乱点云数据进行规格化处理，使得不同部位，但具有相似几何性质的点云数据能够在数值上具有更高的相似度，从而达到提高点云数据内部相似性的目的，进而提高点云数据的稀疏表示效果。 Accordingly, in order to make the point cloud data in a complete dictionary could have had a better degree of thinning, the present invention firstly Scattered Data is normalized, so that the different parts, but having a similar geometric properties of value in the point cloud data can be It has a higher degree of similarity, similarity to achieve the purpose of improving internal point cloud data, thereby improving the sparse point cloud data representation of the effect.
[0048]通过K近邻聚类，使得每块的点的数量能够一致，但是不能保证具有几何相似性的片元在数值上也具有相似性。 [0048] nearest neighbor clustering by K, so that the number of dots of each block can be the same, but can not guarantee a fragment similar geometric similarity also numerically.
[0049] 为了解决上述问题，考虑到K近邻聚类算法是将具有相似几何特性的散乱点云进行聚类，根据点云K近邻聚类结果的性质，片元内部点的法向具有极高相似性，因此本发明采用最小二乘算法对片元进行平面方程拟合，用平面法向对片元法向进行估计，以便后续的点云数据规格化。 [0049] To solve the above problem, a clustering algorithm is the K-nearest neighbor having a similar geometric properties scattered point cloud cluster, depending on the nature of the point cloud neighbor clustering result K, fragment interior point method to a very high similarity, the present invention is therefore the least square method to equation planar sheet element fitted to the plate element normal to a plane estimating method, so that subsequent point cloud data normalization.
[0050] 设散乱点集 [0050] provided unorganized points
分割后的散乱点集可以表示为 Scattered points after division can be expressed as
S」为第j个子集，集合中的元素都是根据元素与聚类中心的距离有序分类。 S &as the j-th set of elements of the collection are classified according to the distance elements and orderly cluster center. 对于子集&中的法向n，通过最小二乘求得的法向会因为具体的数值不同导致朝向不同。 For a subset of the normal & n, obtained by the least squares method to a specific value because of the different results in different orientations. 对于同一个模型，相邻片元的法向不一致会导致曲面梯度变化在法向方向投影的不一致，因此，需要对点云法向的方向进行一致性调整，使得相邻片元间的法向朝向能够相同。 For the same model, the normal adjacent sheets element inconsistency can lead to inconsistencies in the surface gradient in the direction of projection method, therefore, it is necessary to adjust the consistency of the direction of the point cloud method, a method such that the element between adjacent sheets It can be the same orientation.
[0051] 通常没有数学方法能解决法线的正负向问题，通过主成分分析法来计算法向方向也具有二义性，无法对整个点云数据集的法线方向进行一致性调整。 [0051] Generally there is no negative mathematical method to solve the problem of normal, calculated by principal component analysis also normal direction is ambiguous, you can not adjust the consistency of normal direction of the entire point cloud data set. 本发明采用一种针对质心在点云数据内部的点云法向调整方法。 The present invention employs a method for adjusting the point cloud centroid method cloud point internal data.
[0052] 设点云集合为尸二fejf，贝lj，片元质心为 [0052] Cloud point set is set dead two fejf, shellfish lj, the fragment centroid
点仍的K近邻分片Sj为： K-nearest neighbor still point Sj is fragmented:
[0053] [0053]
[0054] 设由质心卩指向K近邻片元的中心点的方向向量为胃，设P巧与拟合平面的夹角为β，两与拟合出的法向η夹角为α，记两与η的内积为：P二w·两。 [0054] Jie provided by the centroid point of the center point K nearest neighbor direction vector fragment stomach, and clever set-fit plane P is angle beta], fitted with two of the normal angle is η [alpha], referred to two and η inner product is: P w · two two. 由于质心P在点云模型内部，方向向量始终指向模型外部，且质心Ρ与拟合平面的夹角β范围在〇&β& 180°，因此，当Ρ&0时，表示拟合出的法向η指向模型外部，无需对拟合出的法向进行调整， 当Ρ&〇时，表示拟合出的法向η指向模型内部，则需要对法向η进行调整，对法向Η进行取反操作。 Since the center of mass within the P point cloud model, a direction vector always points outside the model, and [rho] and fit plane centroid angle in the range of billion beta] &β &180 °, and therefore, when Ρ& 0, represented by the fitted Method [eta] point to the external model, without the need for the fitted normal adjustment, when Ρ &square indicates the fitted model to the interior point method [eta], it is necessary to adjust the method of [eta], of the orientation method η anti operation.
[0055]对片元进行法向估计之后，本发明对片元中的点云进行几何变换，使得具有相似几何特性的片元在数值上同样具有一定的相似性，为后续的点云数据稀疏表示做准备。 [0055] After the fragments were method to estimate, according to the present invention, the point cloud fragments of geometric transformation, such sheet element having a similar geometric properties also has a certain similarity in the value of the subsequent point cloud data sparse He represents preparation. [0056]首先根据质心坐标构建平移变换矩阵乃，通过平移变换矩阵将片元&的点移至坐标原点附近。 [0056] The first construct translational transformation matrix is the barycentric coordinates, the point moves & fragment near the coordinate origin by translation transformation matrix. 通过上述操作，点云数据中相邻若干片元的数据相似性会有所提高，对于均匀的点云模型，甚至会出现所有数据点完全重合的情况，这会使得在进行稀疏表示时极大的提高数据之间的相似性。 When the above operation, a plurality of fragment data point cloud adjacent the similarity will be increased, even to the point cloud model, all the data may even be completely coincident points, which makes carrying extremely sparse representation increase the similarity between the data. 事实上，仅通过平移操作并不能最大化片元之间数值的相似性，由于相距较远的片元法向朝向的不同，导致虽然具有相似的几何特性，但是在具体的数据值上存在较大差异，因此为了消除这方面的差异，在通过平移变换后，K近邻片元&的质心g位于坐标原点，其近似估计的法向η，为了使每个Κ近邻片元的朝向相同，对片元做旋转变换使得所有片元的朝向均与ζ轴同向，设旋转矩阵分别为心，则点云数据片元的规则化变换矩阵为： In fact, only by the similarity value between the panning operation does not maximize the fragment, since the farther apart the different orientation of the sheet element method, while resulting in similar geometric properties, but the presence of the specific data values than large differences, and therefore in order to eliminate the difference in this regard, after passing through translation transformation, K nearest neighbor fragment & centroid g at the origin, which approximated the normal [eta], in order to make toward each Κ neighbor fragment of same, of fragments for rotational transform so that all fragments are facing the same direction with the ζ-axis, rotation matrix are provided for the heart, the point cloud data fragment regularization transformation matrix:
[0057] normMatj=Tj*Rj (2) [0057] normMatj = Tj * Rj (2)
[0058] 通过上述变换矩阵可以使得K近邻分片结果的所有片元分布在坐标原点附近，并且每个分片的法向均朝向z轴，这将使得在几何特征上具有相似性的片元能够在点云坐标数值上也具有一定的相似性，这为后续的点云数据稀疏化表示提供了良好的基础。 [0058] can be made by the above transformation matrix K neighbors all pieces of slice result of the coordinate origin in the vicinity of the distribution element, and each slice to process both the z-axis direction, which will make a sheet having a similarity in the characteristic element geometry possible to have a certain similarity coordinate values at a point cloud, which provides a good basis for the subsequent sparse point cloud data representation.
[0059 ] 2)点云数据的稀疏表示方法 Sparse Representation [0059] 2) point cloud data
[年，Michal Aharon等人在总结K均值聚类算法的基础上提出了K-SVD算法。 [0060] In 2006, Michal Aharon and others On the basis of K-means clustering algorithm on the proposed K-SVD algorithm. 它通过迭代过程中实现原有过完备字典在样本下的训练，通过稀疏分解系数不断调整原子库中的原子，最终获得更加能有效反应信号特征的过完备原子库。 It implements original over-complete dictionary of training at the sample through an iterative process by constantly adjusting coefficient sparse decomposition atomic library, finally won complete dictionary more effective response signal characteristics. K-SVD算法通过不断的训练更新得到最适合于样本集合的冗余字典，由于是通过训练更新自适应得到的，信号在冗余字典上可以根据自己特优的结构特征进行分解可以更好的发掘信号的稀疏性。 K-SVD algorithm is best suited for sample sets redundant dictionary updated by the continuous training, because it is obtained by updating the adaptive training, signal decomposition can be better on a redundant dictionary according to their structural features of the privileged explore the sparsity of the signal. 信号在冗余字典上可以根据自己特优的结构特征进行分解，即训练更新得到的冗余字典可以更好的发掘信号的稀疏性。 Signal can be decomposed according to the structural characteristics of their own privileged on a redundant dictionary that training can be updated redundancy Dictionary get better explore the signal sparsity.
[0061] 对于本发明所解决的问题是对规格化的点云数据求得其过完备字典，从而得到其稀疏表示。 [0061] For the problem addressed by the present invention is a point cloud data which is obtained through the normalization of the complete dictionary to obtain their sparse representation. 通过1)中所述的点云数据规格化算法，已经使得点云数据分片均匀，并且每一片的维度均相同，并且具有相似的几何特性。 1) in the point cloud data normalization algorithm, that has a uniform point cloud data piece, and a dimension of each are the same and have similar geometric properties.
[0062] 设散乱点集 [0062] provided unorganized points
规格化点云数据为P'，分割后的散乱点集可以表示为 Point cloud data is normalized P ', scattered points after division can be expressed as
, 3/4 为第j个子集，集合中的元素都是根据元素与聚类中心的距离有序分类，通过规格化之后，使得在几何上具有相似性的片元能够在数值上具有极高的相似性，因此将规格化后的点云数据集合S作为过完备字典的训练集来训练更新得到冗余字典，从而更好的挖掘点云数据的稀疏性，也为基于压缩感知的点云数据压缩奠定了基础。 ,
j for the first subset, the set of ordered elements are classified according to the distance to the cluster center element, then normalized by that of a similar sheet element having geometrically can have a high value of the similarity , and therefore the point cloud data set S after normalization through a complete dictionary update the training set to get redundant training dictionary to better sparsity mining point cloud data, but also based on the point cloud data compression-aware compression Foundation.
[0063]基于K-SVD的点云数据过完备字典训练算法可分两步来实现。 [0063] Based on Point Cloud Data K-SVD complete dictionary of over-training algorithm can be implemented in two steps. 首先，设DeRnXK，ye Rn，xeRK， First, set up DeRnXK, ye Rn, xeRK,
其中，D为原过完备原子库，y表示训练信号，x为训练信号的稀疏表示系数向量，Y为Μ个训练信号集合，X为Y的解向量集合，Rn表示η维信号集。 Wherein, D is the original through the complete dictionary, y denotes a training signal, x represents a sparse coefficient vector of the training signal, Y is set Μ training signal, X is the solution vector set Y, Rn represents η-dimensional signal set. K-SVD算法的第一步要达到的目标是： The first step of K-SVD algorithm to achieve the objectives are:
[0064] [0064]
[0065] 其中，To为稀疏表示系数中非零分量个数的上限，接下来对原子库D进行迭代训练。 [0065] wherein, To represents the upper limit for the number of sparse coefficients non-zero components, the next iteration of training atoms D library. 设dk为要更新的原子库D的第k列向量，此时信号集的分解形式可以表示为： Dk is set to update the k-th column vector library atom D, in which case the signal set exploded form can be expressed as:
[0066] [0066]
[0067]通过奇异值分解，逐列更新字典，最终产生新的字典0,然后根据新的字典J得出新的稀疏系数，并迭代更新，直到收敛。 [0067] The singular value decomposition, the dictionary is updated by the column, eventually produce new dictionary 0, then the new sparse coefficients derived based on the new dictionary J, and iteratively updated until convergence.
[0068] 3)点云数据稀疏表不的应用 [0068] 3) the sparse point cloud data table is not in use
[0069]考虑到原始散乱点云数据P在数值上几乎不具备任何稀疏性，采用本发明所述方法，对原始点云P进行规格化得到其规格化后的结果P'，对于点云数据本发明获得了点云数据的过完备字典，信号稀疏表示的理论指出，自然信号可以通过某种变换来进行稀疏表示， 因此，点云数据可以在过完备变换基下进行稀疏表示，即P ' =Dx，X为该信号在过完备字典变换域下的稀疏表示，考虑到测量公式y= Φ P '，并且P '是可以稀疏表示的，即P ' =Dx，则有 [0069] Taking into account the original Scattered Data on the P value hardly have any sparsity, using the method of the invention, P original point cloud normalizes the normalized result obtained P ', the point cloud data for the present invention achieves the point cloud data through the complete dictionary signal indicates sparse representation theory, the natural thinning signal may be represented by a transformation, therefore, the sparse point cloud data can be converted in a group represented by over-complete, i.e., P ' = Dx, X for the signal is sparse in the transform domain over-complete dictionary, taking into account the measurement equation y = Φ P ', and P' is sparse representation, i.e., P '= Dx, there
[0070] [0070]
[0071] 其中φ = Φ/)为MXN的矩阵，被称为传感矩阵，y可以看作是稀疏信号X关于测量矩阵Φ的测量值。 [0071] wherein φ = Φ /) of MXN matrix, the matrix is referred to as the sensing, y can be regarded as sparse signal X [Phi] measurements on the measurement matrix. 这时如果Φ满足约束等距条件，可以通过求解最小10范数问题(5-4)来重构稀疏信号X。 Then if Φ satisfies the constraint condition equidistant, sparse signal can be reconstructed by solving the problem of the minimum norm 10 (5-4) X. 对于点云数据的压缩重建，实际上是对如下问题的求解： For the reconstruction of point cloud data compression is actually solving the following problems:
[0072] [0072]
[0073] 其中，f二φ/?，测量矩阵Φ利用高斯随机矩阵来进行观测，通过对⑴问题的求解可以得到点云数据P'的稀疏表示无，可以进一步由过完备字典D通过下式精确重构原始点云F 二.D.5L Sparse [0073] wherein, f two φ / ?, using a Gaussian random measurement matrix Φ observation matrix can be obtained by solving P point cloud data ⑴ problem of 'no representation, through a complete dictionary may further by the following formula D accurate reconstruction of the original point cloud F = .D.5L
[0074]但是，对于(7)的问题求解本质上是一个NP-hard问题，需要穷举X中非零值的所有种排列可能，因而无法求解[9]。 [0074] However, for (7) is essentially a problem solving NP-hard problem, we need to be exhaustive of all permutations of possible non-zero values in the X, and therefore can not be solved [9]. 鉴于此，研究人员对于该问题的求解提出了求得次最优解的算法，主要是指h范数最小化，通常的解法是利用1:范数替代1〇范数。 In view of this, researchers for solving this problem is proposed to obtain sub-optimal solution algorithms, mainly refers to h norm minimization, the usual solution is to use 1: Alternative 1〇 norm norm. 因此本发明对于(7)问题的求解转为如下问题的求解： Accordingly the present invention for solving (7) into the problem of solving the following problems:
[0075] [0075]
[0076] 考虑到重构误差，最终将上述问题转换为如下最小li范数问题的求解： [0076] Considering the reconstruction error, eventually converting the problem to solve the following problems of the minimum norm li:
[0077] [0077]
[0078] 通过对问题(9)的求解，可以获得规格化点云数据在字典D下的稀疏系数重建结果交，因此重建的规格化点云数据可由下式获得： [0078] By solving the problem of (9) can be obtained in the sparse point cloud data normalization coefficient dictionary D cross reconstruction results, thus normalizing the reconstructed point cloud data obtained by the following formula:
[0079] P! = Βχ (10) [0079] P! = Βχ (10)
[0080] 由于本发明的规格化方法引入了几何变换，因此对于重建的规格化点云数据p 需要做反变换来获得重建的点云数据p [0080] Since the normalization process of the present invention introduces a geometric transformation, and therefore for the reconstruction of point cloud data p normalized inverse transform needs to be done to obtain a reconstructed point cloud data p
[0081]考虑到基于欧氏距离的K近邻聚类算法在聚类后期会因为周围未聚类点数量稀少，导致产生一些半径过大的片元，因此，我们忽略K近邻聚结果中部分半径过大的片元，以避免此类片元对结果的影响。 [0081] Considering the K-nearest neighbor clustering algorithm based on Euclidean distance in the late clustering because clustering is not scarce around the point number, resulting in some of the radius is too large fragment, therefore, we ignore a K-poly result in part of the radius too large fragment, in order to avoid the effects of such a fragment of the results. 在后续工作中，我们会对点云数据的聚类算法做相关优化，避免产生类似片元。 In subsequent work, we would point cloud clustering algorithms make data related to optimization, to avoid similar fragments.
[0082]本发明的方法使得压缩感知理论能够应用到点云数据的压缩与重建过程当中，并且具有良好的重建结果。 [0082] The method of the invention makes it possible to apply compressive sensing point cloud data among the compression and reconstruction process, and has good reconstruction results.
[0083]以上所述，仅是本发明的较佳实施例，并非对本发明作任何形式上的限制，凡是依据本发明的技术实质对以上实施例所作的任何简单修改、等同变化与修饰，均仍属本发明技术方案的保护范围。 [0083] The above, only the preferred embodiment of the present invention is not limited in the present invention of any form, all according to the technical essence any simple modification of the above embodiment of the present invention is made of embodiments, modifications and equivalent, are the present invention is still in the scope of the technical solution.
*中国科学院深圳先进技术研究院Device and method for point cloud optimization *北京大学Mode recognition method based on inner product maintaining dimension reduction technology *US Title not availableInternational Classification, C06PublicationC10Entry into substantive examinationC14Grant of patent or utility modelRotate