WO2015154601A1 - 一种基于无特征提取的紧致sfm三维重建方法 - Google Patents
一种基于无特征提取的紧致sfm三维重建方法 Download PDFInfo
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- H04N13/10—Processing, recording or transmission of stereoscopic or multi-view image signals
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- G06T7/55—Depth or shape recovery from multiple images
- G06T7/579—Depth or shape recovery from multiple images from motion
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
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- G06T7/593—Depth or shape recovery from multiple images from stereo images
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- G06T2207/20016—Hierarchical, coarse-to-fine, multiscale or multiresolution image processing; Pyramid transform
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- G06T2207/30244—Camera pose
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
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- H04N13/00—Stereoscopic video systems; Multi-view video systems; Details thereof
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Definitions
- the present invention relates to the field of image three-dimensional reconstruction, and more particularly to a compact SFM three-dimensional reconstruction method without feature extraction.
- 3D reconstruction based on computer vision refers to the use of digital cameras or cameras to acquire images, construct algorithms to estimate the three-dimensional information of the captured scene or target, and achieve the purpose of expressing three-dimensional objective world, including robot navigation, auto or assisted driving, Virtual reality, digital media creation, computer animation, image-based rendering, and preservation of cultural heritage.
- Motion from Motion is a commonly used three-dimensional reconstruction method that estimates three-dimensional information of a scene or a target from two or more images or videos.
- the technical means for realizing SFM three-dimensional reconstruction has the following characteristics: feature point-based, sparse and two-step completion.
- the existing SFM 3D reconstruction is completed in two steps: firstly, the feature points with scale or affine invariance are detected and matched from the image, including Harris feature points, Kanade-Lukas-Tomasi (KLT) features and Lowe scales.
- KLT Kanade-Lukas-Tomasi
- a scale invariant feature transform SIFT is then used to estimate the three-dimensional information of the detected feature quantity and the pose of the camera (including position and angle).
- the existing SFM 3D reconstruction algorithm is completed in two steps, and can not really achieve the optimization effect. Since the two-dimensional coordinates of the feature points are detected from the image, there is no optimization result in the global sense even if the three-dimensional information is reconstructed by the optimization algorithm. Since the matching accuracy of feature points is usually low, it is inevitable to cause low-precision three-dimensional reconstruction.
- the three-dimensional reconstruction effect is sparse; since only the three-dimensional information of the extracted feature points is estimated, the dense three-dimensional reconstruction cannot be realized, that is, the three-dimensional information of all the pixel points cannot be estimated.
- the dense three-dimensional reconstruction cannot be realized, that is, the three-dimensional information of all the pixel points cannot be estimated.
- For a 300,000-pixel 480*640 image only 200 to 300 or less feature points can be detected under the premise of ensuring a correct matching rate.
- the feature point is very Sparse, most pixels do not directly estimate their three-dimensional information.
- the present invention proposes a compact SFM three-dimensional reconstruction method without feature extraction.
- the SFM three-dimensional reconstruction method does not require feature point detection and matching, and one-step optimization can achieve compact three-dimensional reconstruction.
- a compact SFM three-dimensional reconstruction method without feature extraction comprising the following steps:
- the depth of the three-dimensional scene refers to the depth q of the three-dimensional space point corresponding to the pixel point of the first image
- the camera projection matrix refers to other (n-1) a 3 ⁇ 4 matrix P i of the image, 2 ⁇ i ⁇ n;
- an iterative algorithm is designed to optimize the objective function in a continuous domain or a discrete domain, and output a depth representing the three-dimensional information of the scene and a camera projection matrix representing the relative pose information of the camera;
- a compact projective, similar or Euclidean reconstruction is achieved based on the depth of the three-dimensional information representing the scene.
- the method can complete the SFM three-dimensional reconstruction in one step. Because the three-dimensional information is estimated by one-step optimization, and the objective function value is used as an index, the optimal solution can be obtained, at least the local optimal solution, which is greatly improved than the existing method. Initially obtained experimental verification.
- the above camera refers to a camera corresponding to a certain image.
- the camera corresponding to the first image of the scene is the first camera, and the coordinate system of the first camera is consistent with the world coordinate system; each image corresponds to A 3 x 4 camera projection matrix.
- the world coordinate system is established by using this type of method for the convenience of calculation.
- the world coordinate system can be arbitrarily established.
- the parameters to be estimated include n camera projection matrices, and each three-dimensional image is depicted. The point requires three coordinate parameters.
- the scheme for arbitrarily establishing a world coordinate system is the same as the above-described scheme for establishing a world coordinate system.
- the parameterization is firstly set.
- the parameterization is specifically as follows: while establishing the world coordinate system, the camera projection matrix of the first camera is [I 3 0] ⁇ R 3,4 , where I 3 is a 3 ⁇ 3 unit matrix, 0 is a 3 ⁇ 1 zero vector; other camera projection matrices P i ⁇ R 3,4 , 2 ⁇ i ⁇ n, as to be estimated Unknown parameter; the three-dimensional structure of the scene is determined by the depth of the three-dimensional scene defined on the first sub-image: the depth of the three-dimensional scene of the three-dimensional space point corresponding to the first image pixel (x, y) is q x, y , the three-dimensional coordinates of the three-dimensional point are
- the camera projection matrix P i and the depth q x, y of the three-dimensional scene are taken as undetermined parameters to be estimated.
- the subscript x, y is omitted without causing misunderstanding.
- the objective function on the constructed continuous domain is specifically:
- the description of the above objective function is as follows: (a) For the gradient operator, a Laplacian; (b) the objective function is divided into three parts, a data item f data , an offset smoothing term f smooth_uv and a depth smoothing term f smooth_depth , wherein ⁇ , ⁇ , ⁇ 1 and ⁇ 2 are non-negative weights; (c) The image has k color components a color I component value representing the position (x, y) of the first image, correspondingly, The value of the color I component at the position (u i , v i ) of the i-th image; (d) the introduction of the robust function ⁇ is to overcome the influence of the drastic change of the depth, and the robust function ⁇ is the Charbonnier function.
- P i,j is the jth row vector of the i-th camera projection matrix P i ; for the sake of concise expression, without causing misunderstanding, with The subscript x, y is omitted in the middle;
- the iterative optimization algorithm designed on the continuous domain is specifically: because the depth of the three-dimensional scene is a continuous function defined on the first image domain, the Euler-Lagrange equation must be satisfied at the extreme point; meanwhile, at the extreme value
- the partial derivative of the point-to-camera projection matrix parameter is 0; on the discrete grid points of the image, the Euler-Lagrangian equation and the two types of equations with partial derivatives of the camera projection matrix are 0, and are expressed in increments.
- the vector ⁇ is constructed in order from the camera projection matrix P i 2 ⁇ i ⁇ n and the depth q of the three-dimensional scene; thus, each iteration is reduced to solving
- n images initialize the depth q of the 3D scene and the camera projection matrix P i , 2 ⁇ i ⁇ n;
- the above color image can be represented by common RGB or HSV. Taking the RGB format as an example, the image has three components, namely red (R), green (G) and blue (B) components; the color components can be in different formats. Combination, such as Four components of R, G, B, and H are used. There are many options for the above robust functions and are not limited to the functions listed above.
- the basis of the objective function f(P, q) constructed in the above formula (1) is similar to the optical flow calculation to some extent, that is, the gradation invariant assumption and the smoothing of the pixel offsets u i -x and v i -y Assume that each corresponds to the first part of the objective function And the second part That is, data items and smoothing items.
- the third part of the formula (1) A smoothing assumption for the depth.
- the discrete objective function (11) and its variant iterative optimization algorithm are as follows:
- the discrete form of the objective function (11) is essentially a nonlinear least squares problem, which can adopt the conventional Levenberg-Marquardt algorithm or Gauss-Newton algorithm. Each iteration process comes down to solving a linear system of equations (15):
- H is the Hessian matrix or Gauss-Newton Hessian matrix
- b is the gradient vector
- u is a non-negative number, depending on the Levenberg-Marquardt algorithm or the Gauss-Newton algorithm, to determine the corresponding increments ⁇ P i and ⁇ q; Updating the parameters P i and q, P i ⁇ P i +P i , q ⁇ q+q until convergence;
- Input multiple images, and initialization of the camera projection matrix P i and the depth q of the three-dimensional scene, 2 ⁇ i ⁇ n;
- Interpolation of depths of three-dimensional scenes between different precision layers is implemented by bilinear interpolation, bicubic interpolation or other similar interpolation methods;
- the pixel ratio of the adjacent two-level precision in the x and y directions is s 1 and s 2 , s 1 , s 2 ⁇ 1, and the image is estimated in the lower precision image.
- the camera projection matrix of a camera is P (k+1) , where the superscript (k+1) represents the k+1th layer of the image pyramid structure, then the camera projection matrix corresponding to the k-th layer image is
- the depth q (k+1) of the estimated three-dimensional scene of the above layer is used as a reference, and the interpolation method is used to calculate the depth q (k) of the three-dimensional scene of the layer as the initialization of the depth of the three-dimensional scene;
- Camera projection matrix estimated using the previous image Calculate the camera projection matrix of this layer according to equation (16) Using it as the initialization of the camera projection matrix;
- the parameterization is specifically as follows:
- the camera projection matrix is described by the camera internal parameters and camera external parameters:
- the external parameters of the camera are determined by a 3 ⁇ 3 rotation matrix R and a 3 ⁇ 1 translation vector t, which is determined by three angle parameters, namely rotation angles ⁇ x , ⁇ y and respectively around the x-axis, the y-axis and the z-axis.
- ⁇ z :
- the internal parameters ⁇ x , ⁇ y , s, p x , p y , translation vector t, rotation angles ⁇ x , ⁇ y and ⁇ z and the depth q of the three-dimensional scene are Estimated undetermined parameters to achieve similar three-dimensional reconstruction;
- the translation vector t, the rotation angles ⁇ x , ⁇ y and ⁇ z and the depth q of the three-dimensional scene are undetermined parameters to be estimated, achieving similar three-dimensional reconstruction;
- the depth q of the three-dimensional scene is an undetermined parameter to be estimated.
- the large baseline situation means that the relative motion between the cameras is relatively large, resulting in significant differences between the images.
- SFM 3D reconstruction is divided into three steps:
- features are extracted from the image and matched, and the extracted features are: Harris feature, SIFT feature or KLT feature;
- the second step based on the extracted features, estimating the three-dimensional information of the feature points and the camera projection matrix of the camera;
- algorithm 3 is used to implement compact SFM three-dimensional reconstruction
- the camera projection matrix estimated in the second step is used as the initial value of the camera projection matrix of the third step, and the depth of the three-dimensional scene estimated in the second step is interpolated as the depth initial value of the third-dimensional scene of the third step.
- the invention has the beneficial effects that the present invention proposes a compact SFM three-dimensional reconstruction scheme without feature extraction, which can complete the compact SFM three-dimensional reconstruction in one step compared with the existing SFM three-dimensional reconstruction method. Since the estimation of three-dimensional information is realized by one-step optimization, and the objective function value is used as an index, the optimal solution, at least the local optimal solution, can be obtained, which is much improved compared with the existing methods, and has been experimentally verified.
- FIG. 1 is a flow chart of implementing a three-dimensional reconstruction of the present invention.
- the depth of the three-dimensional scene refers to the depth q of the three-dimensional space point corresponding to the pixel point of the first image
- the camera projection matrix refers to other (n-1) a 3 ⁇ 4 matrix P i of the image, 2 ⁇ i ⁇ n;
- an iterative algorithm is designed to optimize the objective function in a continuous domain or a discrete domain, and output a depth representing the three-dimensional information of the scene and a camera projection matrix representing the relative pose information of the camera;
- a compact projective, similar or Euclidean reconstruction is achieved based on the depth of the three-dimensional information representing the scene.
- the core model of the present invention is described in detail: projective three-dimensional reconstruction from two grayscale images on a continuous domain.
- the first and second images are I 1 and I 2 respectively (the superscript indicates the image number), and the gray value of the first image at the position (x, y) is Correspondingly, the gray value of the second image at position (u, v)
- the images obtained at present are mostly digital images, that is, the images are defined on discrete lattices
- a numerical optimization algorithm is used to implement three-dimensional reconstruction.
- the world coordinate system is established as follows: its origin, x-axis, and y-axis coincide with the camera center of the first camera, the x-axis and the y-axis of the first camera imaging plane, and the z-axis An imaging plane that points vertically to the first camera.
- the camera projection matrix of the first camera is [I 3 0] ⁇ R 3,4 , where I 3 is a 3 ⁇ 3 unit matrix, and 0 is a 3 ⁇ 1 zero vector;
- the camera projection matrix of the two cameras is a 3 x 4 matrix P ⁇ R 3,4 .
- the three-dimensional point corresponding to the first image pixel (x, y) has a depth q x, y , ie its z coordinate is q x, y ; accordingly, the three-dimensional coordinates of the point are
- the three-dimensional structure of the captured scene or object is described by the depth q x, y defined on the first image; at the same time, the camera projection matrix P of the second camera describes the relative motion information between the two cameras.
- the purpose of the projective three-dimensional reconstruction is to estimate the depth information q x,y of the scene (under the condition that the depth information q x,y can be calculated, the corresponding three-dimensional coordinates can be calculated by the equation (1)) and the camera projection matrix P.
- the imaging position (u x, y , v x, y ) of the three-dimensional point corresponding to the first image pixel (x, y) in the second image is as follows:
- u and v are functions defined on the image domain with the camera projection matrix P and depth q as parameters: u(P, q) and v(P, q).
- the first part of the objective function (3) is based on the gray value constancy assumption in the optical flow calculation, that is, the same three-dimensional space point has the same gray value in different images. If there is only a gray-scale invariant assumption, the optimization problem is a morbid problem. To this end, a second part is introduced in the objective function (3), assuming that the imaging in the two images has smooth offsets ux and vy, which are assumed by the second part of the objective function (3).
- the two parts of the objective function (3) are called data items and smoothing items, respectively, corresponding to the data items and smoothing items in the optical flow calculation.
- the invention adopts an iterative algorithm to realize the optimization of the objective function (3), and the core idea is the Euler-Lagrange equation in the variational method.
- the integral quantity L in the optimization objective function (3) is defined as follows (temporarily ignore the camera projection matrix parameter P, only the depth parameter q is considered):
- the objective function (3) must satisfy the extreme value:
- each iterative process is to solve the increments ⁇ P and ⁇ q of P and q, and update the parameters as follows.
- the 12 variables of the camera projection matrix P and the n variables of the depth q form a vector ⁇ having a dimension n+12.
- the incremental forms of (6) and (7) can be expressed as the following linear equations.
- the following algorithm can be used to implement SFM projective three-dimensional reconstruction.
- a pyramid method from coarse to fine is used. That is, the 3D reconstruction is first implemented in the lower resolution image; then the estimated depth is interpolated and the camera projection matrix is corrected as the initial solution for the next layer of higher resolution 3D reconstruction; up to the highest resolution.
- the depth interpolation can be implemented by bilinear interpolation, bicubic interpolation or other similar interpolation methods.
- the second camera projection matrix estimated in the lower precision layer is P (i+1). ) (where i + 1-i + 1 layer superscript representative image pyramid structure), the corresponding i-th layer image, the second camera projection matrix
- the estimated depth q (i+1) of the above layer is used as a reference, and the interpolation depth is used to calculate the depth q (i) at the current layer as the initialization of the depth;
- the objective function (12) is essentially a nonlinear least squares problem, which can be iteratively optimized using the Gauss-Newton algorithm (or other similar algorithms such as Levenberg Marquardt, LM algorithm).
- Gauss-Newton algorithm or other similar algorithms such as Levenberg Marquardt, LM algorithm.
- u and v are variables.
- the Gauss-Newton approximation method can be used to obtain the relevant Gauss-Newton Hessian matrix H data and gradient vector b data :
- the first derivative is used instead of the partial derivative.
- the partial derivative is used instead of the partial derivative.
- the smoothing term in the objective function (12) can be expressed as:
- ⁇ x, y [ ⁇ u x-1, y ⁇ u x, y ⁇ u x, y-1 ⁇ v x-1, y ⁇ v x, y ⁇ v x, y-1 ] T ,
- the final parameters are the camera projection matrix P and the depth q.
- a parameter vector ⁇ including the camera projection matrix P and the depth q is established for the concise expression.
- the increment ⁇ is:
- a discrete form of 3D reconstruction can be implemented using a coarse to fine pyramid method, the basic framework of which is the same as Algorithm 2 .
- algorithm 2 is used to realize the three-dimensional reconstruction of each layer.
- the three-dimensional reconstruction discrete algorithm from coarse to fine pyramid is omitted here.
- RGB Red Green Blue
- HSV Human Saturation Value
- HSL Human Saturation Lightness
- HSI Human Saturation Intensity
- the optimization algorithm of the objective function (19) is identical to the objective function (12) and is omitted here.
- the three-dimensional reconstruction of the color image on the continuous domain can also be realized, and the implementation algorithm is similar to the three-dimensional reconstruction of the continuous domain grayscale image.
- the basic algorithm is the same as the three-dimensional reconstruction based on two images, constructing an objective function like (3) or (12), including data items and smoothing items.
- the world coordinate system can be set to the coordinate system of the first camera, so that the projection matrix of the first camera is [I 3 0] ⁇ R 3,4 , other n-1 cameras
- the projection matrix and depth q are the parameters to be estimated.
- the first construction of the data item is as follows
- the gray-scale invariant assumption in equation (20), it is very similar to the data items of the two images (12), that is, the gray-scale invariant assumption, assuming that the same point has the same gray value in all images.
- the gray-scale invariant assumption is slightly changed, and only the gray-scale invariant assumption between adjacent images is considered.
- the second scheme is more suitable for 3D reconstruction based on video sequences.
- the offset is based on the first image, and the offset between adjacent images is considered in (23).
- the three-dimensional reconstruction algorithm based on multiple images is similar to the three-dimensional reconstruction of two images, and the specific algorithm is omitted.
- the result of the reconstruction is a projective three-dimensional structure, which is not a common Euclidean three-dimensional structure.
- This section proposes a similarity three-dimensional reconstruction and a Euclidean three-dimensional reconstruction scheme.
- the camera's projection matrix can be described by camera internal parameters and camera external parameters:
- the camera external parameters are determined by the rotation matrix R and the translation vector t, where R depicts the rotational transformation of the world coordinate system to the camera coordinate system.
- the world coordinate system is the same as the coordinate system of the first camera, so that the motion information between the cameras is completely described by the external parameters of the second camera.
- both cameras have the same internal parameters.
- the second camera format is accordingly set to
- the depth parameter q describing the scene or target is the same as the projective three-dimensional reconstruction.
- the scheme for achieving similar three-dimensional reconstruction is similar to projective reconstruction, ie optimizing the objective function (3) or (12), with the difference that the second camera projects the form of the matrix P (27).
- the second camera projects the form of the matrix P (27).
- only discrete implementations of similar three-dimensional reconstructions are given.
- the rotation matrix R is determined by three angular parameters, namely the rotation angles ⁇ x , ⁇ y and ⁇ z around the x-axis, the y-axis and the z-axis, respectively:
- the first 12 quantities of the n+12-dimensional parameter vector ⁇ in the projective three-dimensional reconstruction are camera projection matrix parameters, and the rest are n depth parameters.
- ⁇ x , ⁇ y, s, p x and p y form an 11-dimensional vector ⁇ ′′ followed by n depth parameters.
- H, J and b are H, J and b of the formula (18).
- the similar three-dimensional reconstruction described above can also be achieved when the partial parameters of the camera are known, such as when the camera is calibrated, ie the camera internal parameters are known.
- Euclidean 3D reconstruction can be achieved when both the camera's internal and external parameters are known.
- large baseline means that the relative motion between the cameras is relatively large, causing significant differences between the images. The reason may be that the angle of rotation or the translation between the cameras is too large. Probably because the focal length between the cameras is too different.
- SFM 3D reconstruction is divided into three steps. The first step is to extract features from the image and match them, such as Harris features, SIFT features or KLT features. In the second step, based on the extracted features, estimate the three-dimensional information of the feature points.
- the camera projection matrix of the camera; the third step based on the previous two steps, using the method proposed above to achieve compact SFM three-dimensional reconstruction.
- the camera projection matrix estimated in the second step is used as the initial value of the camera projection matrix of the third step, and the depth of the three-dimensional scene estimated in the second step is interpolated as the depth initial value of the third-dimensional scene of the third step.
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Abstract
Description
Claims (8)
- 一种无特征提取的紧致SFM三维重建方法,其特征在于,包括以下步骤:S1.输入关于某场景的n幅图像,n≥2;S2.建立与某个相机坐标系相一致的世界坐标系,设世界坐标系与第一相机的坐标系相一致,即世界坐标系的原点、x轴和y轴与第一相机的相机中心、第一相机成像平面的x轴和y轴重合,其z轴垂直指向第一相机的成像平面;S3.以三维场景的深度和相机投影矩阵作为变量,所述三维场景的深度是指第1幅图像像素点对应的三维空间点具有的深度q;所述相机投影矩阵是指其它(n-1)幅图像的3×4矩阵Pi,2≤i≤n;S4.构造类似光流估计的目标函数,所述目标函数是连续域上的变分目标函数或其离散形式的目标函数;S5.采用由粗到细的金字塔方法,在连续域或者离散域上设计迭代算法对目标函数进行优化,输出表示场景三维信息的深度和代表相机相对位姿信息的相机投影矩阵;S6.根据表示场景三维信息的深度,实现紧致的射影、相似或者欧几里德重建。
- 根据权利要求1所述的无特征提取的紧致SFM三维重建方法,其特征在于,在实现射影三维重建中,参数化具体为:在建立世界坐标系的同时,其第一相机的相机投影矩阵为(qx,y×x,qx,y×y,qx,y) (1)在射影三维重建中,相机投影矩阵Pi和三维场景的深度qx,y作为待估计的未定参数,为了表达式的简练,在不造成误解的情况下,省略下标x,y。
- 根据权利要求2所述的无特征提取的紧致SFM三维重建方法,其特征在于,实现连续域上射影三维重建的具体实现过程为:构造的连续域上的目标函数具体为:f(P2,…,Pn,q)=fdata+fsmooth_uv+fsmooth_depth (2)其中对上述目标函数的说明如下:(a)为梯度算子,为拉普拉斯算子;(b)目标函数分为三部分,数据项fdata,偏移平滑项fsmooth_uv和深度平滑项fsmooth_depth,其中α、β、τ1和τ2是非负权重;(c)图像有k个色彩分量C1,…,Ck,代表第一幅图像在位置(x,y)的色彩I分量值,相应地,为第i幅图像在位置(ui,vi)的色彩I分量值;(d)鲁棒函数ρ的引入是为了克服深度发生剧变带来的影响,鲁棒函数ρ为Charbonnier函数其中∈是一个足够小的的正数,ε<10-6;或者为Lorentzian函数 σ为某个常数;当不引入鲁棒函数,则ρ(x)=x;(e)ui和vi是定义在图像域上、以相机投影矩阵Pi和深度q为参数的函数:和代表与第一幅图像像素(x,y)相对应的三维点在第i幅图像的成像位置在连续域上设计的迭代优化算法具体为:因为三维场景的深度是定义在第一幅图像上的连续函数,在极值点必须满足欧拉-拉格朗日方程;同时,在极值点对相机投影矩阵参数的偏导数为0;在图像的离散格点上,联合欧拉-拉格朗日方程和对相机投影矩阵参数偏导数为0的两类方程,并采用增量方式表示形式,能够把求解相机投影矩阵和三维场景深度增量的迭代过程转化为求解如下线性方程组Hδθ+b=0 (6)其中向量θ由相机投影矩阵Pi2≤i≤n和三维场景的深度q按次序构造而成;这样,每次迭代归结为求解δθ=-H-1b (7),从而确定相应的增量δPi和δq;根据所求解的增量更新参数Pi和q,Pi←δPi+Pi,q←δq+q,直到收敛;即算法1的具体过程为:输入:n幅图像,初始化三维场景的深度q和相机投影矩阵Pi,2≤i≤n;输出:相机投影矩阵Pi(2≤i≤ni)、三维场景的深度q和场景的三维表示;1、迭代1)、由欧拉-拉格朗日方程和目标函数对相机投影矩阵参数的偏导数为0确定式子(7)中的H和b;2)、由式子(7)计算增量δθ,并确定相应的增量δPi和δq;3)、更新参数Pi,2≤i≤n和q:Pi←δPi+Pi,q←δq+q;直到收敛2、根据收敛后的三维场景的深度q,由式子(1)计算场景的三维表示。
- 根据权利要求2所述的无特征提取的紧致SFM三维重建方法,其特征在于,构造离散形式的目标函数具体为:f(P2,…,Pn,q)=fdata+fsmooth_uv+fsmooth_depth (11)其中离散目标函数(11)及其变化形式的迭代优化算法具体为:离散形式的目标函数(11)在本质上是一个非线性最小二乘问题,能够采用常规的Levenberg-Marquardt算法或高斯-牛顿算法,每次迭代过程归结为求解一个线性方程组(15):δθ=-(H+μI)-1b (15),其中H是海森矩阵或者高斯-牛顿海森矩阵,b是梯度向量,μ是非负数,取决于采用Levenberg-Marquardt算法或高斯-牛顿算法,从而确定相应的增量δPi和δq;根据增量更新参数Pi和q,Pi←δPi+Pi,q←δq+q,直到收敛;算法2具体实现过程:输入:n幅图像,以及相机投影矩阵Pi和三维场景的深度q的初始化,2≤i≤n;输出:相机投影矩阵Pi(2≤i≤ni)、三维场景的深度q和场景的三维表示;1、迭代1)、计算式子(15)中的高斯-牛顿海森矩阵H和梯度向量b;2)、由式子(15)计算增量δθ,并分别确定相应的增量δPi和δq;3)、更新参数Pi和q:Pi←δPi+Pi,q←δq+q,2≤i≤n;直到收敛;2、根据收敛后的三维场景的深度q,由式子(1)计算场景的三维表示。
- 根据权利要求1所述的无特征提取的紧致SFM三维重建方法,其特征在于,由粗到细的金字塔方法步骤具体为:计算图像的n层金字塔表示;在最粗图像层,初始化n-1个相机投影矩阵为关于不同精度层之间三维场景的深度的插值,采用双线性插值或双三次插值方法实现;关于不同精度层之间相机投影矩阵的修正,设相邻两级精度的图像在x和y方向的像素比为s1和s2,s1,s2<1,在较低精度图像层估计得到某个相机的相机投影矩阵为P(k+1),其中上标(k+1)代表图像金字塔结构的第k+1层,那么对应第k层图像的相机投影矩阵为由粗到细金字塔方法的具体迭代算法如下:即算法3的具体过程为:输入:n幅图像;输出:相机投影矩阵Pi(2≤i≤ni)、三维场景的深度q和场景的三维表示;1、计算图像的m层金字塔表示;2、迭代:图像层k从第m层依次到第1层(1)如果k≠m以上一层估计的三维场景的深度q(k+1)为基准,采用插值方法计算在本层的三维场景的深度q(k),以其作为三维场景的深度的初始化;利用上一层图像估计的相机投影矩阵Pi (k+1),2≤i≤n,根据式子(16)计算本层的相机投影矩阵Pi (k),以其作为相机投影矩阵的初始化;否则,在第m层图像结束(2)采用算法1或者算法2估计该层相机投影矩阵Pi (k),2≤i≤n和三维场景的深度q(k);结束迭代3、输出相机投影矩阵和三维场景的深度:Pi←Pi (1)(2≤i≤n),q←q(1);4、根据三维场景的深度q,由式子(1)计算场景的三维表示。
- 根据权利要求2或6所述的无特征提取的紧致SFM三维重建方法,其特征在于,实现相似三维重建或者欧几里德三维重建的具体过程为:参数化具体为:相机投影矩阵由相机内部参数和相机外部参数描述:P=K[R t]当相机内部参数和外部参数都是未知的,内部参数αx、αy、s、px、py、平移向量t、旋转角度γx、γy和γz和三维场景的深度q为待估计的未定参数,实现相似三维重建;当相机内部参数是已知的,而外部参数是未知的,平移向量t、旋转角度γx、γy和γz和三维场景的深度q为待估计的未定参数,实现相似三维重建;当相机的内部参数和外部参数都已知的条件下,实现欧几里德三维重建中,在这种情形中,三维场景的深度q为待估计的未定参数。
- 根据权利要求6所述的无特征提取的紧致SFM三维重建方法,其特征在于,所述无特征提取的紧致SFM三维重建方法还能够推广到大基线情形,具体步骤为:在射影几何中,大基线情形是指相机之间的相对运动比较大,造成图像之间有显著的区别,在大基线情形中,具体来说,SFM三维重建分为三步:第一步,从图像提取特征并匹配,提取的特征为:Harris特征、SIFT特征或KLT特征;第二步,在所提取特征的基础上,估计特征点的三维信息和相机投影矩阵;第三步,在前面两步的基础上,利用算法3实现紧致SFM三维重建;其中,以第二步估计得到的相机投影矩阵作为第三步的相机投影矩阵初始值,对第二步估计得到的三维场景的深度进行插值,作为第三步的三维场景的深度初始值。
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