Advances in Imaging and Electron Physics

1. Auflage 2015
ISBN: 978-0-12-802521-5
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, Band Volume 187, 150 Seiten

Reihe: Advances in Imaging and Electron Physics

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

Autoren/Hrsg.

Inhaltsverzeichnis

1;Front Cover;1
2;Advances in IMAGING AND ELECTRON PHYSICS
;4
3;Copyright
;5
4;Contents;6
5;Preface;8
6;Future Contributions;10
7;Contributors;14
8;Homeomorphic Manifold Analysis (HMA): Untangling Complex Manifolds;16
8.1;1. Introduction;17
8.2;2. Motivating Scenarios;21
8.2.1;2.1 Case Example I: Modeling the View-Object Manifold;21
8.2.2;2.2 Case Example II: Modeling the Visual Manifold of Biological Motion;23
8.2.3;2.3 Biological Motivation;26
8.3;3. Framework Overview;28
8.4;4. Manifold Factorization;31
8.4.1;4.1 Style Setting;31
8.4.2;4.2 Manifold Parameterization;32
8.4.3;4.3 Style Factorization;33
8.4.3.1;4.3.1 One-Style-Factor Model;33
8.4.3.2;4.3.2 Multifactor Model;34
8.4.4;4.4 Content Manifold Embedding;36
8.4.4.1;4.4.1 Nonlinear Dimensionality Reduction from Visual Data;37
8.4.4.2;4.4.2 Topological Conceptual Manifold Embedding;39
8.5;5. Inference;40
8.5.1;5.1 Solving for One Style Factor;41
8.5.1.1;5.1.1 Iterative Solution;41
8.5.1.1.1;5.1.1.1 Closed-Form Linear Approximation for the Coordinate on the Manifold;41
8.5.1.1.2;5.1.1.2 Solving for Discrete Styles;42
8.5.1.2;5.1.2 Sampling-based Solution;43
8.5.2;5.2 Solving for Multiple Style Factors Given a Whole Sequence;43
8.5.3;5.3 Solving for Body Configuration and Style Factors from a Single Image;44
8.6;6. Applications of Homomorphism on 1-D Manifolds;45
8.6.1;6.1 A Single-Style-Factor Model for Gait;46
8.6.1.1;6.1.1 Style-Dependent Shape Interpolation;47
8.6.1.2;6.1.2 Style-Preserving Posture-Preserving Reconstruction;48
8.6.1.3;6.1.3 Shape and Gait Synthesis;49
8.6.2;6.2 A Multifactor Model for Gait;52
8.6.3;6.3 A Multifactor Model for Facial Expression Analysis;56
8.6.3.1;6.3.1 Facial Expression Synthesis and Recognition;57
8.7;7. Applications of Homomorphism on 2-D Manifolds;59
8.7.1;7.1 The Topology of the Joint Configuration-viewpoint Manifold;61
8.7.2;7.2 Graphical Model;64
8.7.3;7.3 Torus Manifold Geometry;65
8.7.4;7.4 Embedding Points on the Torus;65
8.7.5;7.5 Generalization to the Full-View Sphere;66
8.7.6;7.6 Deforming the Torus;67
8.7.6.1;7.6.1 Torus to Visual Manifold;67
8.7.6.2;7.6.2 Torus to Kinematic Manifold;68
8.7.6.3;7.6.3 Modeling Shape Style Variations;68
8.7.7;7.7 Bayesian Tracking on the Torus;69
8.7.7.1;7.7.1 Dynamic Model;70
8.7.8;7.8 Experimental Results;71
8.8;8. Applications to Complex Motion Manifolds;74
8.8.1;8.1 Learning Configuration-viewpoint, and Shape Manifolds;77
8.8.2;8.2 Parameterizing the View Manifold;79
8.8.2.1;8.2.1 Parameterizing the Configuration Manifold;79
8.8.2.2;8.2.2 Parameterizing the Shape Space;80
8.8.3;8.3 Simultaneous Tracking on the Three Manifolds Using Particle Filtering;80
8.8.4;8.4 Examples: Pose and View Estimation from General Motion Manifolds;81
8.8.4.1;8.4.1 Catch/Throw Motion;81
8.8.4.2;8.4.2 Ballet Motion;82
8.8.4.3;8.4.3 Aerobic Dancing Sequence;84
8.9;9. Bibliographical Notices;84
8.9.1;9.1 Factorized Models: Linear, Bilinear, and Multilinear Models;84
8.9.2;9.2 Manifold Learning;87
8.9.3;9.3 Manifold-based Models of Human Motion;89
8.10;10. Conclusions;90
8.11;Acknowledgments;92
8.12;References;92
9;Spin-Polarized Scanning Electron Microscopy;98
9.1;1. Introduction;99
9.2;2. Principles;101
9.2.1;2.1 Principle of Magnetic Domain Observation;101
9.2.2;2.2 Principle of Spin-Polarization Detection;103
9.2.2.1;2.2.1 Mott Polarimeter;103
9.2.2.2;2.2.2 Detection of All Three Spin-Polarization Components;107
9.3;3. Device Configuration and Sample Preparation;111
9.3.1;3.1 Chamber Configuration;111
9.3.2;3.2 Sample Preparation;113
9.3.3;3.3 Electron Gun;114
9.3.4;3.4 Secondary Electron Optics;115
9.3.5;3.5 Spin Detectors;116
9.3.5.1;3.5.1 Classical Mott Detector;116
9.3.5.2;3.5.2 Compact Mott Detector;119
9.3.5.3;3.5.3 Diffuse Scattering Detector;119
9.3.5.4;3.5.4 LEED Detector;120
9.3.6;3.6 Signal-Analyzing System;120
9.4;4. Examples of Spin-SEM Measurements;121
9.4.1;4.1 Co Single Crystal;121
9.4.2;4.2 HDD Recorded Bits;123
9.4.3;4.3 Nd2Fe14B Magnet;128
9.4.3.1;4.3.1 Magnetization in Boundary Phase of Sintered Magnet;128
9.4.3.2;4.3.2 Magnetization Process in the Fine Powders of NdFeB Magnet;130
9.4.4;4.4 Other Examples of Spin-SEM Measurements;135
9.5;5. Conclusions;136
9.6;Acknowledgments;137
9.7;References;137
10;Contents of Volumes 151-186
;142
10.1;Volume 151
;142
10.2;Volume 152;142
10.3;Volume 153;142
10.4;Volume 154;143
10.5;Volume 155;143
10.6;Volume 156;143
10.7;Volume 157;143
10.8;Volume 158;143
10.9;Volume 159;143
10.10;Volume 160;143
10.11;Volume 161;144
10.12;Volume 162;144
10.13;Volume 163;144
10.14;Volume 164;144
10.15;Volume 165;144
10.16;Volume 166;144
10.17;Volume 167;145
10.18;Volume 168;145
10.19;Volume 169;145
10.20;Volume 170;145
10.21;Volume 171;145
10.22;Volume 172;146
10.23;Volume 173;146
10.24;Volume 174;146
10.25;Volume 175;146
10.26;Volume 176;146
10.27;Volume 177;146
10.28;Volume 178;146
10.29;Volume 179;147
10.30;Volume 180;147
10.31;Volume 181;147
10.32;Volume 182;147
10.33;Volume 183;147
10.34;Volume 184;147
10.35;Volume 185;147
10.36;Volume 186;147
11;Index;148
12;Color Plates;152

Leseproben

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...