实例介绍
【实例简介】
三维重建，将不同视角的多张图片处理成物体三维信息的方法，简明易懂。。。
Contents 1 Introduction to 3D Acquisition 7 1.1 A Tax y of mcthods 1.2T 1.2.1 (Passive)Stereo 8 1. 3 Active Triangulation 10 1. 4 Other methods 1.4.1 Time-of-Flight 13 1.4.2 Shape-from-Shading and Photometric Stereo 1.4.3 Shape-from-Texture and Shape-from-Contour 1.4.1 Shape-from-Defocus 17 1.4.5 Shape-from-Silhouettes 17 1.4.6 Hybrid techniques 18 1.5 Challenges 1. 6 Conclusions 2 Image Formation and Camera models 23 1 Introdu 2.2 The Linear camera model 2.2.1 The Pinhole carnera 2.2.2 A Camera-Centered Reference Frame and the Associated projection Equations 24 2.2.3 A Matrix Exprcssion for the Projcction Equations Associatcd with a Camera Centered reference frame 2.2.4 The General Linear Camera model 2.2.5 Non-Linear Distorti 29 2.3 Calera calibration 2.3. 1 Internal Calibration 31 2.3.2 External calibration 3 Principles of Passive 3D Reconstruction 37 3.1 Introduction 37 3.2 The 3d Reconstruction Problem 37 3.3 The Epipolar Relation Between Two Images of a Static Scene 39 3.4 3D Reconstruction Equations Up-Close 42 3. 4.1 Euclidean 3d reconstruction 3.4.2 Metric 3D Reconstruction 3.4.3 Affine 3d reconstruction 3.4.4 Projective 3D Reconstruction 3.4.5 Taking Stock-Stratification 18 3.4.6 From Projective to Metric C sing More Than Iwo Images 3.5 Soine Inportant Special Cases 55 3.5. 1 Camera Translation and Stereo Ri 55 CONTENTS 3.5.2 Pure Rotation around the Camera Center 58 4 Epipolar geometry inl Practice 61 4.1 Finding seed correspondences 61 4.1.1 Interest points 4.1.2 Other seed features 63 4.2 Epipolar geometry -implementation 4.2.1 Pairs of epipolar lines 64 4.2.2 Computation of the Fundamental matrix 4.2.3 RANSAC 5 Relations betweell Multiple views 73 5.1 The Trifocal Relations Between Three Images of a Static Scene 5.1.1 The Fundamcntal Trifocal Rclation bctwccn Thrcc Images .74 5.1.2 The Trifocal Relation bet ween Corresponding tines 5.1.3 The Trifocal Relations between Corresponding Image Points 5.1.4 The Trifocal Constraints as Incidence relations 81 5.1.5 The Trifocal Constraints as a Transfer Princip G Structure and motion 6.1 Computing Projection Matrices and a Projective Reconstruction 6.1.1 Initialization Step 6.1.2 Projective Pose Estimation 6.13 lating structure 90 6.1. 4 Global minimization 6.2 The Projective Aillbiguity 91 6.3 Scene Constraints 6.4 Self-Calibration 6.4.1 Conics and Quadrics 6.4.2 The Absolute Conic 6.4.3 Practical C 99 6.4. 4 Coupled self- Calibration 100 7 Model selection 103 7. 1 Introduction 103 7.2 Problcms with Planar Scones .,,103 7.3 Detecting Planar Scenes 104 7.3.1 Occam's Razor 104 7.3.2 GRIC 7.4 More GRICs 106 7.5 Long Vidco Scqucnccs 108 7.5.1 Video frame 110 7.5.2 Long Sequences and Subsequences 112 7.5.31 116 7.5.1 Blurry Frames 116 8 Essential matrices 121 8.1 Essential Matrices 121 8.1.1 Normalized coordinates 121 8.1.2 Thc Essential Matrix 121 1.3P1 of the essential matrix 8.1.4 Cameras from the ssential Matrix 123 8.2C tation of the Essential matri 8.2. 1 8 and 7 Point algorithm 124 CONTENTS 8.2.2 6 Point Algo 125 8.2.3 5 Point Alge 126 8.2.4 Planar Degeneracy 9 Bundle Adjustment 129 9.1 Introduction 9.2 Levenberg- Marquardt algorithm 93S Bundle adjustment 1:1 10 Dense Matching 137 10.1 Introducti 17 10.2 Rectification 137 10.2.1 Planar rectification 137 10.2.2 Pular Rectification 10.3 Stereo Matching 140 10.3.1 Constraint 10.3.2 Matching matrix 144 10.3.3 Cost Function 144 10.3. 4 Hierarchical Stereo , 146 10.3.5 Post Processing 147 10.4 Linking Stereo Pairs ..148 10.5 Fast Matching on the gpu 150 0.5.1 Why gPl 10.3.2 Basic Setup and Conventions 151 10.5.3 Hierarchical Plane-Sweep algorithm 151 10.5.4 The Connectivity Constraint 152 10.5.5 Retrieval of Fine structures 153 10.5.6 Smoothness Penalty 154 10. 6 Bay nIti-View m 155 11 3D Webservic 159 11.1 Introduction 159 I1. 1. 1 3D Technologies in the cultural Heritage Field 159 11.1.2L BD Reconstruction 159 11.1.3 Chapter Overview 159 11.2 System Overview 11.2.1 Upload Tool 162 11.2.2 Modelviewer Tool 162 11.3 Automatic reconst ruction pi 163 11.3.1 Pipeline Overview 163 11.3.2 Opportunistic Pipeline 167 11.3.3 Hierarchical Pipeline 垂 167 11.3. Parallel pipeline 167 11.4 Global Image Comparison ,167 11.5 Self-calibration 168 11.5.1 Classical SaM techniques 168 11.5.2 Triplet matching 170 11.5.3 Coupled self-calibration 171 11.5. 4 Statistical Coupled Sclf-calibration 171 11. 6 Reconstruction 172 11.6.1 Upscaling the Result 11.6.2 Robust Euclidean Bundle Adjustment 174 11.7 Dense matching 176 11.7.1 Linked Pairwise Stereo .176 6 CONTENTS 11.7.2 Multi-View Stereo 177 11.8 Rcsults 178 11.9 Conclusion Chapter 1 Introduction to 3D Acquisition diffe ng the 3-dimensional shape of surfaces and, ill sOine cases, also the distance of the object to the 3d device. Sucl distance is often referred to as range. The chapter aills at positioning the inethods discussed in this text within this more global context. This will make clear that alternative methods may actually be better suited for some applications that need 3D. This said, the discussion will also show that the approach described here is onc of the morc attractivc and powerful oncs The reader will be able to experiment with the described techniques through the ARC3d Webservice. As we will explain at the end of the tutorial. this is a free service (for non-commercia use)which lets users upload images to a central server, and then applies the described techniques to extract depth maps for each uploaded image. As a by-product, also the spatial arrangement of thecamerapositionsissuppliedThiswebservicecanbevisitedatwww.arc3d.be 1.1 a Taxonomy of Methods a 3-D acquisition taxonomy is given in Figure 1.1 A first distinction is between active and passive methods. With active techniques the light sources are specially controlled. as part of the strategy to arrive at the 3D information. Active lighting incorporates some form of temporal or spatial modulation of the illumination. With pas sive tcchniqucs, on the othcr hand, light is not controlled or only with respect to image quality Typically they work with whatever ambient light that is available From a computational viewpoint, active methods tend to be less demanding as the special illu mination is used to simplify some of the steps in the 3D capturing process. Their applicability is restricted to environments where the special illumination techniques can be applied A second distinction is between the number of vantage points from where the scene is observed and or illuminatcd. With singlc-vantage methods the systcm works from a single vantage point In case there are multiple viewing or illumination components, these are positioned close to each other, and ideally they would coincide. The latter can sometimes be realised virtually, through op tical means like semi-transparent mirrors. With ma. age sy stem. s, several viewpoints and or controlled illumination source positions are involved. For multi-vantage systems to work well, the different components often have to be positioned far eNough froll each othler. One says that the baseline' between the components has to be wide enough Single-vantage methods have as advantages that they can be made compact and that they suffer less from occlusion problcms with parts of the sccnc not visible from all vantage points The met hods mentioned in the taxonomy will now be discussed in a bit more detail. In the remaining chapters, we then continue with the more detailed discussion of passive, multi-vantage Structure-froIl-Motioll(SiM techniques, the actual subject of this tutorial. As this overview o 3D acquisition methods is not intended to be in-depth nor exhaustive, we dont include references in this part CHAPTER 1. INTRODUCTION TO 3D ACQUISITION Range extraction Passive Active Single vantage point Mu tiple vantage points Single vantage point Multiple vantage points Shape-from-texture Passive stereo Time-of-flight Structured light Shape-from-occlusion Shape-from-silhouettes Shape-from-shading Active stereo Time to-contact Photometric stereo Shape-f from-defocus Shape-from-cantcur Figure 1.1: Ta conomy of method s for the ectraction of information on. 3n shape 1.2 Triangulation Several multi-vantage approaches use the principle of triangulation for the extraction of depth information. This also is the key concept exploited by the structure-from-motion(SfM)met, hods described here 1. 2.1(Passive) Stereo Suppose we have two images, taken at the same time and from different viewpoints. Such setting is referred to as stereo. The situation is illustrated in Figure 1. 2. The principle behind stereo-based 3D reconstruction is simple: given the two projections of the same point in the world onto the two iinlages, its 3D position is founld as the intersection of the two projection rays. Repeating such process for several points yields the 3d shape and configuration of the objects in the scene. Note that this construction- rcfcrrcd to as triangulation- rcquires complctc knowledge of the cameras their (relative) positions and orientations, but also their settings like the focal length. These camera parameters will be discussed in chapter 2. The process to determine these parameters is ca lled(camera) calibration. Moreover, in order to perform this triangulation process, one needs ways of solving the corre- spondence problem, i.e. finding the point in the second image that corresponds to a specific point in the first image, or vice versa. Correspondence search actually is the hardest part of stereo and onc would typically have to solvc it for many points. Often the correspondence problcm is solved in two stages. First, correspondences are sought for those points for which this is easiest Then, correspondences are sought for the remaining points. This will be explained in more detail in subsequent chapters 1.2.2 Structure-from-Motion Passive stereo uses two cameras, usually synchronised. If the scene is static, the two images could also be ta ken by placing the same camera. at, the two positions, and taking t he images in sequence. Clearly, once such strategy is considered, one may just as well take more than two inages, while Inloving the calera. If images are taken over short time intervals, it will be easier to find correspondences, e. g. by tracking feature points over time. Moreover, having more camera. views will yield object models that are more complete. Last but not least, if multiple views are 1. 2. TRIANGULATION Figure 1.2: The principle behind stereo-based 3D reconstruction is very simple: given two ima of a point, the point's position in space is found as the intersection of the two projection rol Es CHAPTER 1. INTRODUCTION TO 3D ACQUISITION Figure 1.3: The triangulation principle used already with stereo, can also be used in an active configuration. The laser projects a ray of light onto the object O. The intersection point P with ihe object is viewed by a cunera and forls the spot P on its inage plane I. This information suffices for the computation of the three-dimensional coordinates of P, assuming that the laser- camera configuration is known vailable, the camera(s)need no longer be calibra.ted beforehand, and a self-calibration procedure may he employed instead. Self-calibration means that, the interna l and externa l camera parameters (see next chapter)are extracted from the images directly. These properties render SfM a very attractive 3D acquisition strategy. A Illore detailed discussion is given in the following chapters 1.3 Active Triangulation Finding corresponding points can be facilitated by replacing one of the cameras in a stereo setup by a projection device. Hence, we combine one illumination source with one camera. For instance OIle call project a spot onto the object surface with a laser. The spot will be easily detectable in the image taken by the camera. If we know the position and orientation of both the laser ray and the camera projcction ray, then the 3D surfacc point is found as thcir intersection. The principlc is illustrated in figure 1.3 The problem is that know ledge about the 3D coordinates of one point, is hardly sufficient in most applications. llence, in the case of the laser. it should be directed at different points on the surface and each tiime an iMage has to be taken. In this way, the 3D coordinates of these points are extracted, one point at a time. Such a'scanning' process requires precise mechanical apparatus (e. g. by steering rotating mirrors that reflect the laser light into controlled directions). If the laser 【实例截图】
【核心代码】
三维重建，将不同视角的多张图片处理成物体三维信息的方法，简明易懂。。。
Contents 1 Introduction to 3D Acquisition 7 1.1 A Tax y of mcthods 1.2T 1.2.1 (Passive)Stereo 8 1. 3 Active Triangulation 10 1. 4 Other methods 1.4.1 Time-of-Flight 13 1.4.2 Shape-from-Shading and Photometric Stereo 1.4.3 Shape-from-Texture and Shape-from-Contour 1.4.1 Shape-from-Defocus 17 1.4.5 Shape-from-Silhouettes 17 1.4.6 Hybrid techniques 18 1.5 Challenges 1. 6 Conclusions 2 Image Formation and Camera models 23 1 Introdu 2.2 The Linear camera model 2.2.1 The Pinhole carnera 2.2.2 A Camera-Centered Reference Frame and the Associated projection Equations 24 2.2.3 A Matrix Exprcssion for the Projcction Equations Associatcd with a Camera Centered reference frame 2.2.4 The General Linear Camera model 2.2.5 Non-Linear Distorti 29 2.3 Calera calibration 2.3. 1 Internal Calibration 31 2.3.2 External calibration 3 Principles of Passive 3D Reconstruction 37 3.1 Introduction 37 3.2 The 3d Reconstruction Problem 37 3.3 The Epipolar Relation Between Two Images of a Static Scene 39 3.4 3D Reconstruction Equations Up-Close 42 3. 4.1 Euclidean 3d reconstruction 3.4.2 Metric 3D Reconstruction 3.4.3 Affine 3d reconstruction 3.4.4 Projective 3D Reconstruction 3.4.5 Taking Stock-Stratification 18 3.4.6 From Projective to Metric C sing More Than Iwo Images 3.5 Soine Inportant Special Cases 55 3.5. 1 Camera Translation and Stereo Ri 55 CONTENTS 3.5.2 Pure Rotation around the Camera Center 58 4 Epipolar geometry inl Practice 61 4.1 Finding seed correspondences 61 4.1.1 Interest points 4.1.2 Other seed features 63 4.2 Epipolar geometry -implementation 4.2.1 Pairs of epipolar lines 64 4.2.2 Computation of the Fundamental matrix 4.2.3 RANSAC 5 Relations betweell Multiple views 73 5.1 The Trifocal Relations Between Three Images of a Static Scene 5.1.1 The Fundamcntal Trifocal Rclation bctwccn Thrcc Images .74 5.1.2 The Trifocal Relation bet ween Corresponding tines 5.1.3 The Trifocal Relations between Corresponding Image Points 5.1.4 The Trifocal Constraints as Incidence relations 81 5.1.5 The Trifocal Constraints as a Transfer Princip G Structure and motion 6.1 Computing Projection Matrices and a Projective Reconstruction 6.1.1 Initialization Step 6.1.2 Projective Pose Estimation 6.13 lating structure 90 6.1. 4 Global minimization 6.2 The Projective Aillbiguity 91 6.3 Scene Constraints 6.4 Self-Calibration 6.4.1 Conics and Quadrics 6.4.2 The Absolute Conic 6.4.3 Practical C 99 6.4. 4 Coupled self- Calibration 100 7 Model selection 103 7. 1 Introduction 103 7.2 Problcms with Planar Scones .,,103 7.3 Detecting Planar Scenes 104 7.3.1 Occam's Razor 104 7.3.2 GRIC 7.4 More GRICs 106 7.5 Long Vidco Scqucnccs 108 7.5.1 Video frame 110 7.5.2 Long Sequences and Subsequences 112 7.5.31 116 7.5.1 Blurry Frames 116 8 Essential matrices 121 8.1 Essential Matrices 121 8.1.1 Normalized coordinates 121 8.1.2 Thc Essential Matrix 121 1.3P1 of the essential matrix 8.1.4 Cameras from the ssential Matrix 123 8.2C tation of the Essential matri 8.2. 1 8 and 7 Point algorithm 124 CONTENTS 8.2.2 6 Point Algo 125 8.2.3 5 Point Alge 126 8.2.4 Planar Degeneracy 9 Bundle Adjustment 129 9.1 Introduction 9.2 Levenberg- Marquardt algorithm 93S Bundle adjustment 1:1 10 Dense Matching 137 10.1 Introducti 17 10.2 Rectification 137 10.2.1 Planar rectification 137 10.2.2 Pular Rectification 10.3 Stereo Matching 140 10.3.1 Constraint 10.3.2 Matching matrix 144 10.3.3 Cost Function 144 10.3. 4 Hierarchical Stereo , 146 10.3.5 Post Processing 147 10.4 Linking Stereo Pairs ..148 10.5 Fast Matching on the gpu 150 0.5.1 Why gPl 10.3.2 Basic Setup and Conventions 151 10.5.3 Hierarchical Plane-Sweep algorithm 151 10.5.4 The Connectivity Constraint 152 10.5.5 Retrieval of Fine structures 153 10.5.6 Smoothness Penalty 154 10. 6 Bay nIti-View m 155 11 3D Webservic 159 11.1 Introduction 159 I1. 1. 1 3D Technologies in the cultural Heritage Field 159 11.1.2L BD Reconstruction 159 11.1.3 Chapter Overview 159 11.2 System Overview 11.2.1 Upload Tool 162 11.2.2 Modelviewer Tool 162 11.3 Automatic reconst ruction pi 163 11.3.1 Pipeline Overview 163 11.3.2 Opportunistic Pipeline 167 11.3.3 Hierarchical Pipeline 垂 167 11.3. Parallel pipeline 167 11.4 Global Image Comparison ,167 11.5 Self-calibration 168 11.5.1 Classical SaM techniques 168 11.5.2 Triplet matching 170 11.5.3 Coupled self-calibration 171 11.5. 4 Statistical Coupled Sclf-calibration 171 11. 6 Reconstruction 172 11.6.1 Upscaling the Result 11.6.2 Robust Euclidean Bundle Adjustment 174 11.7 Dense matching 176 11.7.1 Linked Pairwise Stereo .176 6 CONTENTS 11.7.2 Multi-View Stereo 177 11.8 Rcsults 178 11.9 Conclusion Chapter 1 Introduction to 3D Acquisition diffe ng the 3-dimensional shape of surfaces and, ill sOine cases, also the distance of the object to the 3d device. Sucl distance is often referred to as range. The chapter aills at positioning the inethods discussed in this text within this more global context. This will make clear that alternative methods may actually be better suited for some applications that need 3D. This said, the discussion will also show that the approach described here is onc of the morc attractivc and powerful oncs The reader will be able to experiment with the described techniques through the ARC3d Webservice. As we will explain at the end of the tutorial. this is a free service (for non-commercia use)which lets users upload images to a central server, and then applies the described techniques to extract depth maps for each uploaded image. As a by-product, also the spatial arrangement of thecamerapositionsissuppliedThiswebservicecanbevisitedatwww.arc3d.be 1.1 a Taxonomy of Methods a 3-D acquisition taxonomy is given in Figure 1.1 A first distinction is between active and passive methods. With active techniques the light sources are specially controlled. as part of the strategy to arrive at the 3D information. Active lighting incorporates some form of temporal or spatial modulation of the illumination. With pas sive tcchniqucs, on the othcr hand, light is not controlled or only with respect to image quality Typically they work with whatever ambient light that is available From a computational viewpoint, active methods tend to be less demanding as the special illu mination is used to simplify some of the steps in the 3D capturing process. Their applicability is restricted to environments where the special illumination techniques can be applied A second distinction is between the number of vantage points from where the scene is observed and or illuminatcd. With singlc-vantage methods the systcm works from a single vantage point In case there are multiple viewing or illumination components, these are positioned close to each other, and ideally they would coincide. The latter can sometimes be realised virtually, through op tical means like semi-transparent mirrors. With ma. age sy stem. s, several viewpoints and or controlled illumination source positions are involved. For multi-vantage systems to work well, the different components often have to be positioned far eNough froll each othler. One says that the baseline' between the components has to be wide enough Single-vantage methods have as advantages that they can be made compact and that they suffer less from occlusion problcms with parts of the sccnc not visible from all vantage points The met hods mentioned in the taxonomy will now be discussed in a bit more detail. In the remaining chapters, we then continue with the more detailed discussion of passive, multi-vantage Structure-froIl-Motioll(SiM techniques, the actual subject of this tutorial. As this overview o 3D acquisition methods is not intended to be in-depth nor exhaustive, we dont include references in this part CHAPTER 1. INTRODUCTION TO 3D ACQUISITION Range extraction Passive Active Single vantage point Mu tiple vantage points Single vantage point Multiple vantage points Shape-from-texture Passive stereo Time-of-flight Structured light Shape-from-occlusion Shape-from-silhouettes Shape-from-shading Active stereo Time to-contact Photometric stereo Shape-f from-defocus Shape-from-cantcur Figure 1.1: Ta conomy of method s for the ectraction of information on. 3n shape 1.2 Triangulation Several multi-vantage approaches use the principle of triangulation for the extraction of depth information. This also is the key concept exploited by the structure-from-motion(SfM)met, hods described here 1. 2.1(Passive) Stereo Suppose we have two images, taken at the same time and from different viewpoints. Such setting is referred to as stereo. The situation is illustrated in Figure 1. 2. The principle behind stereo-based 3D reconstruction is simple: given the two projections of the same point in the world onto the two iinlages, its 3D position is founld as the intersection of the two projection rays. Repeating such process for several points yields the 3d shape and configuration of the objects in the scene. Note that this construction- rcfcrrcd to as triangulation- rcquires complctc knowledge of the cameras their (relative) positions and orientations, but also their settings like the focal length. These camera parameters will be discussed in chapter 2. The process to determine these parameters is ca lled(camera) calibration. Moreover, in order to perform this triangulation process, one needs ways of solving the corre- spondence problem, i.e. finding the point in the second image that corresponds to a specific point in the first image, or vice versa. Correspondence search actually is the hardest part of stereo and onc would typically have to solvc it for many points. Often the correspondence problcm is solved in two stages. First, correspondences are sought for those points for which this is easiest Then, correspondences are sought for the remaining points. This will be explained in more detail in subsequent chapters 1.2.2 Structure-from-Motion Passive stereo uses two cameras, usually synchronised. If the scene is static, the two images could also be ta ken by placing the same camera. at, the two positions, and taking t he images in sequence. Clearly, once such strategy is considered, one may just as well take more than two inages, while Inloving the calera. If images are taken over short time intervals, it will be easier to find correspondences, e. g. by tracking feature points over time. Moreover, having more camera. views will yield object models that are more complete. Last but not least, if multiple views are 1. 2. TRIANGULATION Figure 1.2: The principle behind stereo-based 3D reconstruction is very simple: given two ima of a point, the point's position in space is found as the intersection of the two projection rol Es CHAPTER 1. INTRODUCTION TO 3D ACQUISITION Figure 1.3: The triangulation principle used already with stereo, can also be used in an active configuration. The laser projects a ray of light onto the object O. The intersection point P with ihe object is viewed by a cunera and forls the spot P on its inage plane I. This information suffices for the computation of the three-dimensional coordinates of P, assuming that the laser- camera configuration is known vailable, the camera(s)need no longer be calibra.ted beforehand, and a self-calibration procedure may he employed instead. Self-calibration means that, the interna l and externa l camera parameters (see next chapter)are extracted from the images directly. These properties render SfM a very attractive 3D acquisition strategy. A Illore detailed discussion is given in the following chapters 1.3 Active Triangulation Finding corresponding points can be facilitated by replacing one of the cameras in a stereo setup by a projection device. Hence, we combine one illumination source with one camera. For instance OIle call project a spot onto the object surface with a laser. The spot will be easily detectable in the image taken by the camera. If we know the position and orientation of both the laser ray and the camera projcction ray, then the 3D surfacc point is found as thcir intersection. The principlc is illustrated in figure 1.3 The problem is that know ledge about the 3D coordinates of one point, is hardly sufficient in most applications. llence, in the case of the laser. it should be directed at different points on the surface and each tiime an iMage has to be taken. In this way, the 3D coordinates of these points are extracted, one point at a time. Such a'scanning' process requires precise mechanical apparatus (e. g. by steering rotating mirrors that reflect the laser light into controlled directions). If the laser 【实例截图】
【核心代码】
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