Advances in Imaging and Electron Physics (eBook)

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2015 | 1. Auflage
150 Seiten
Elsevier Science (Verlag)
978-0-12-802521-5 (ISBN)

Advances in Imaging and Electron Physics merges two long-running serials-Advances in Electronics and Electron Physics and Advances in Optical and Electron Microscopy. The series features extended articles on the physics of electron devices (especially semiconductor devices), particle optics at high and low energies, microlithography, image science and digital image processing, electromagnetic wave propagation, electron microscopy, and the computing methods used in all these domains.

Contributions from leading authorities
Informs and updates on all the latest developments in the field

Advances in Imaging and Electron Physics merges two long-running serials-Advances in Electronics and Electron Physics and Advances in Optical and Electron Microscopy. The series features extended articles on the physics of electron devices (especially semiconductor devices), particle optics at high and low energies, microlithography, image science and digital image processing, electromagnetic wave propagation, electron microscopy, and the computing methods used in all these domains. Contributions from leading authorities Informs and updates on all the latest developments in the field

Front Cover 1
Advances in IMAGING AND ELECTRON PHYSICS
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Copyright
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Contents 6
Preface 8
Future Contributions 10
Contributors 14
Homeomorphic Manifold Analysis (HMA): Untangling Complex Manifolds 16
1. Introduction 17
2. Motivating Scenarios 21
2.1 Case Example I: Modeling the View-Object Manifold 21
2.2 Case Example II: Modeling the Visual Manifold of Biological Motion 23
2.3 Biological Motivation 26
3. Framework Overview 28
4. Manifold Factorization 31
4.1 Style Setting 31
4.2 Manifold Parameterization 32
4.3 Style Factorization 33
4.3.1 One-Style-Factor Model 33
4.3.2 Multifactor Model 34
4.4 Content Manifold Embedding 36
4.4.1 Nonlinear Dimensionality Reduction from Visual Data 37
4.4.2 Topological Conceptual Manifold Embedding 39
5. Inference 40
5.1 Solving for One Style Factor 41
5.1.1 Iterative Solution 41
5.1.1.1 Closed-Form Linear Approximation for the Coordinate on the Manifold 41
5.1.1.2 Solving for Discrete Styles 42
5.1.2 Sampling-based Solution 43
5.2 Solving for Multiple Style Factors Given a Whole Sequence 43
5.3 Solving for Body Configuration and Style Factors from a Single Image 44
6. Applications of Homomorphism on 1-D Manifolds 45
6.1 A Single-Style-Factor Model for Gait 46
6.1.1 Style-Dependent Shape Interpolation 47
6.1.2 Style-Preserving Posture-Preserving Reconstruction 48
6.1.3 Shape and Gait Synthesis 49
6.2 A Multifactor Model for Gait 52
6.3 A Multifactor Model for Facial Expression Analysis 56
6.3.1 Facial Expression Synthesis and Recognition 57
7. Applications of Homomorphism on 2-D Manifolds 59
7.1 The Topology of the Joint Configuration-viewpoint Manifold 61
7.2 Graphical Model 64
7.3 Torus Manifold Geometry 65
7.4 Embedding Points on the Torus 65
7.5 Generalization to the Full-View Sphere 66
7.6 Deforming the Torus 67
7.6.1 Torus to Visual Manifold 67
7.6.2 Torus to Kinematic Manifold 68
7.6.3 Modeling Shape Style Variations 68
7.7 Bayesian Tracking on the Torus 69
7.7.1 Dynamic Model 70
7.8 Experimental Results 71
8. Applications to Complex Motion Manifolds 74
8.1 Learning Configuration-viewpoint, and Shape Manifolds 77
8.2 Parameterizing the View Manifold 79
8.2.1 Parameterizing the Configuration Manifold 79
8.2.2 Parameterizing the Shape Space 80
8.3 Simultaneous Tracking on the Three Manifolds Using Particle Filtering 80
8.4 Examples: Pose and View Estimation from General Motion Manifolds 81
8.4.1 Catch/Throw Motion 81
8.4.2 Ballet Motion 82
8.4.3 Aerobic Dancing Sequence 84
9. Bibliographical Notices 84
9.1 Factorized Models: Linear, Bilinear, and Multilinear Models 84
9.2 Manifold Learning 87
9.3 Manifold-based Models of Human Motion 89
10. Conclusions 90
Acknowledgments 92
References 92
Spin-Polarized Scanning Electron Microscopy 98
1. Introduction 99
2. Principles 101
2.1 Principle of Magnetic Domain Observation 101
2.2 Principle of Spin-Polarization Detection 103
2.2.1 Mott Polarimeter 103
2.2.2 Detection of All Three Spin-Polarization Components 107
3. Device Configuration and Sample Preparation 111
3.1 Chamber Configuration 111
3.2 Sample Preparation 113
3.3 Electron Gun 114
3.4 Secondary Electron Optics 115
3.5 Spin Detectors 116
3.5.1 Classical Mott Detector 116
3.5.2 Compact Mott Detector 119
3.5.3 Diffuse Scattering Detector 119
3.5.4 LEED Detector 120
3.6 Signal-Analyzing System 120
4. Examples of Spin-SEM Measurements 121
4.1 Co Single Crystal 121
4.2 HDD Recorded Bits 123
4.3 Nd2Fe14B Magnet 128
4.3.1 Magnetization in Boundary Phase of Sintered Magnet 128
4.3.2 Magnetization Process in the Fine Powders of NdFeB Magnet 130
4.4 Other Examples of Spin-SEM Measurements 135
5. Conclusions 136
Acknowledgments 137
References 137
Contents of Volumes 151-186
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Volume 151
142
Volume 152 142
Volume 153 142
Volume 154 143
Volume 155 143
Volume 156 143
Volume 157 143
Volume 158 143
Volume 159 143
Volume 160 143
Volume 161 144
Volume 162 144
Volume 163 144
Volume 164 144
Volume 165 144
Volume 166 144
Volume 167 145
Volume 168 145
Volume 169 145
Volume 170 145
Volume 171 145
Volume 172 146
Volume 173 146
Volume 174 146
Volume 175 146
Volume 176 146
Volume 177 146
Volume 178 146
Volume 179 147
Volume 180 147
Volume 181 147
Volume 182 147
Volume 183 147
Volume 184 147
Volume 185 147
Volume 186 147
Index 148
Color Plates 152

2. Motivating Scenarios

2.1. Case Example I: Modeling the View-Object Manifold

Consider collections of images from any of the following cases or combinations of them: (1) instances of different object classes; (2) instances of an object class (within-class variations); (3) different views of an object. The shape and appearance of an object in a given image is a function of its category, style within category, viewpoint, and several other factors. The visual manifold given all these variables collectively is impossible to model. Let us first simplify the problem. Let us assume that the object is detected in the training images (so there is no 2-D translation or in the plane rotation manifold). Let us also assume that we are dealing with rigid objects, and ignore the illumination variations (using an illumination invariant feature representation). Basically, we are left with variations due to category, within category, and viewpoint; i.e., we are dealing with a combined view-object manifold. We will set aside some of these assumptions later in the discussion

The aim here is to learn a factorized model (or class of models) that can parameterize each of these factors of variability independently. The shape and appearance of an object instance in an image is considered to be function of several latent parameterizing variables: category, style within class, and, object viewpoint. Given a test image and the learned model(s), such a model is supposed to be used to make simultaneous inferences about the different latent variables. Obviously, learning a latent variable model and using it in inference is not a novel idea. It is quite challenging to make inferences in a high-dimensional parameter space, and even more challenging to do so in multiple spaces. Therefore, it is essential that the learned model would represent each latent variable in a separate low-dimensional representation, invariant of other factors (untangled), to facilitate efficient inference. Moreover, the model should explicitly exploit the manifold structure of each latent variable.

The underlying principle in this framework is that multiple views of an object lie on an intrinsically low-dimensional manifold (view manifold) in the input space. The view manifolds of different objects are distributed in that input space. To recover the category and pose of a test image, we need to know which manifold this image belongs to and what the intrinsic coordinate of that image is within that manifold. This basic view of object recognition and pose estimation is not new; it was used in the seminal work of Murase and Nayar (1995). In that work, PCA (Jolliffe, 1986) was used to achieve linear dimensionality reduction of the visual data, and the manifolds of different objects were represented as parameterized curves in the embedding space. However, dimensionality reduction techniques, whether linear or nonlinear, will only project the data to a lower dimension and will not be able to achieve the desired untangled representation.

The main challenge is how to achieve an untangled representation of the visual manifold. The key is to utilize the low-dimensionality and known topology of the view manifold of individual objects. To explain the point, let us consider the simple case where the different views are obtained from a viewing circle (e.g., a camera looking at an object on a turntable). The view manifold of each object in this case is a 1-D closed manifold embedded in the input space. However, that simple closed curve deforms on the input space as a function of the object geometry and appearance. The visual manifold can be degenerate-- for example, imaging a textureless sphere from different views result in the same image; i.e., the view manifold in this case is degenerate to a single-point.

Ignoring degeneracy, the view manifolds of all objects share the same topology but differ in geometry, and they are all homeomorphic to each other. Therefore, capturing and parameterizing the deformation of a given object’s view manifold gives fundamental information about the object category and within category. The deformation space of these view manifolds captures a view-invariant signature of objects, and analyzing such space provides a novel way to tackle the categorization and within-class parameterization. Therefore, a fundamental aspect to untangle the complex object-view manifold is to use view-manifold deformation as an invariant for categorization and modeling the within-class variations. If the views are obtained from a full or part of the view-sphere around the object, the resulting visual manifold should be a deformed sphere as well. In general, the dimensionality of the view manifold of an object is bounded by the dimensionality of viewing manifold (degrees of freedom imposed by the camera-object relative pose). Figure 1 illustrates the framework for untangling the object-view manifold by factorizing the deformation of individual object’s view manifolds in a view-invariant space, which can be the basis for recognition (Zhang et al., 2013; Bakry & Elgammal, 2014).

2.2. Case Example II: Modeling the Visual Manifold of Biological Motion

Let us consider the case of a biological motion: human motion. Concerning an articulated motion observed from a camera (stationary or moving), such a motion can be represented as a kinematic sequence 1:T=z1,…,zT and observed as an observation sequence 1:T=y1,…,yT. With an accurate 3-D body model, camera calibration, and geometric transformation information, 1:T can be explained as a projection of an articulated model. However, in this chapter, I am interested in a different interpretation of the relation between the observations and the kinematics that does not involve any body model.

Figure 1 Framework for untangling the view-object manifold. The nondegenerate view manifolds of different objects are topologically equivalent. Factorizing the deformation space of these manifolds leads to an view-invariant representation. (See color plate)

For illustration, let us consider the observed motion, in the form of shape, for a gait motion. The silhouette (occluding contour) of a human walking or performing a gesture is an example of a dynamic shape, where the shape deforms over time based on the action being performed. These deformations are restricted by the physical body and the temporal constraints posed by the action being performed. Given the spatial and temporal constraints, these silhouettes, as points in a high-dimensional visual input space, are expected to lie on a low-dimensional manifold. Intuitively, the gait is a 1-D manifold that is embedded in a high-dimensional visual space. Such a manifold twists in the high-dimensional visual space. Figure 2(a) shows an embedding of the visual gait manifold in a three-dimensional (3-D) embedding space (Elgammal & Lee, 2004a). Similarly, the appearance of a face with expressions is an example of a dynamic appearance that lies on a low-dimensional manifold in the visual input space.

Figure 2 Homeomorphism of gait manifolds (Elgammal & Lee, 2004a). Visualization of gait manifolds from different viewpoints of a walker obtained using LLE embedding. (a) Embedded gait manifold for a side view of the walker. Sample frames from a walking cycle along the manifold with the frame numbers shown to indicate the order. A total of 10 walking cycles are shown (300 frames). (b) Embedded gait manifold from kinematic data (joint angle position through the walking cycles (c) Embedded gait manifolds from five different viewpoints of the walker (Elgammal & Lee, 2004a, © IEEE). (See color plate)

In general, not only for the case of periodic motions such as gait, despite the high dimensionality of the body configuration space, many human motions intrinsically lie on low-dimensional manifolds. This is true for the kinematics of the body (the kinematic manifold), as well as for the observed motion through image sequences (the visual manifold). Therefore, the dynamic sequence 1:T lies on a manifold called the kinematic manifold. The kinematic manifold is the manifold of body configuration changes in the kinematic space. In addition, the observations lie on a manifold, known as the visual manifold. Although the intrinsic body configuration manifold might be very low in dimensionality, the resulting visual manifold (in terms of shape, appearance, or both) is challenging to model, given the various aspects that affect the appearance. Examples of such aspects include the body type (slim, big, tall, etc.) of the person performing the motion, clothing, viewpoint, and illumination. Such variability makes the task of learning a visual manifold very challenging because we are dealing with data points that lie on multiple manifolds at the same time: body configuration manifold, viewpoint manifold, body shape manifold, illumination manifold, etc. However, the underlying body configuration manifold, invariant to all other factors, is low in dimensionality. In contrast, we do not know the dimensionality of the shape manifold of all people, while we know that gait is a 1-D manifold motion. Therefore, the body configuration manifold can be explicitly modeled, while all the other factors can model deformations to this intrinsic manifold.

Consequently, a key property that we will use to model complex...

Erscheint lt. Verlag	31.1.2015
Mitarbeit	Herausgeber (Serie): Peter W. Hawkes
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Naturwissenschaften ► Physik / Astronomie ► Atom- / Kern- / Molekularphysik
	Naturwissenschaften ► Physik / Astronomie ► Elektrodynamik
	Naturwissenschaften ► Physik / Astronomie ► Hochenergiephysik / Teilchenphysik
	Naturwissenschaften ► Physik / Astronomie ► Optik
	Technik ► Elektrotechnik / Energietechnik
ISBN-10	0-12-802521-2 / 0128025212
ISBN-13	978-0-12-802521-5 / 9780128025215

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