Ebook: Statistics and Analysis of Shapes

The subject of pattern analysis and recognition pervades many aspects of our daily lives, including user authentication in banking, object retrieval from databases in the consumer sector, and the omnipresent surveillance and security measures around sensitive areas. Shape analysis, a fundamental building block in many approaches to these applications, is also used in statistics, biomedical applications (Magnetic Resonance Imaging), and many other related disciplines.

With contributions from some of the leading experts and pioneers in the field, this self-contained, unified volume is the first comprehensive treatment of theory, methods, and algorithms, available in a single resource, without the typical quagmire of vast information scattered over a wide body of literature. Developments are discussed from a rapidly increasing number of research papers in diverse fields, including the mathematical and physical sciences, engineering, and medicine.

The initial chapters explore the statistical modeling of landmarks while subsequent chapters address the probabilistic modeling of entire shapes. The latter part of the book, with the exception of the last two chapters, concentrates on case studies as well as implementational and practical challenges in real systems. Extensive illustrations throughout help readers overcome the sometimes terse technical details of the geometric and probabilistic formalism. Knowledge of advanced calculus and basic statistics and probability theory are the only prerequisites for the reader.

Statistics and Analysis of Shapes will be an essential learning kit for statistical researchers, engineers, scientists, medical researchers, and students seeking a rapid introduction to the field. It may be used as a textbook for a graduate-level special topics course in statistics and signal/image analysis, or for an intensive short course on shape analysis and modeling. The state-of-the-art techniques presented will also be useful for experienced researchers and practitioners in academia and industry.

---

The subject of pattern analysis and recognition pervades many aspects of our daily lives, including user authentication in banking, object retrieval from databases in the consumer sector, and the omnipresent surveillance and security measures around sensitive areas. Shape analysis, a fundamental building block in many approaches to these applications, is also used in statistics, biomedical applications (Magnetic Resonance Imaging), and many other related disciplines.

 

With contributions from some of the leading experts and pioneers in the field, this self-contained, unified volume is the first comprehensive treatment of theory, methods, and algorithms, available in a single resource, without the typical quagmire of vast information scattered over a wide body of literature. Developments are discussed from a rapidly increasing number of research papers in diverse fields, including the mathematical and physical sciences, engineering, and medicine.

 

The initial chapters explore the statistical modeling of landmarks while subsequent chapters address the probabilistic modeling of entire shapes. The latter part of the book, with the exception of the last two chapters, concentrates on case studies as well as implementational and practical challenges in real systems. Extensive illustrations throughout help readers overcome the sometimes terse technical details of the geometric and probabilistic formalism. Knowledge of advanced calculus and basic statistics and probability theory are the only prerequisites for the reader.

 

Statistics and Analysis of Shapes will be an essential learning kit for statistical researchers, engineers, scientists, medical researchers, and students seeking a rapid introduction to the field. It may be used as a textbook for a graduate-level special topics course in statistics and signal/image analysis, or for an intensive short course on shape analysis and modeling. The state-of-the-art techniques presented will also be useful for experienced researchers and practitioners in academia and industry.

---

The subject of pattern analysis and recognition pervades many aspects of our daily lives, including user authentication in banking, object retrieval from databases in the consumer sector, and the omnipresent surveillance and security measures around sensitive areas. Shape analysis, a fundamental building block in many approaches to these applications, is also used in statistics, biomedical applications (Magnetic Resonance Imaging), and many other related disciplines.

 

With contributions from some of the leading experts and pioneers in the field, this self-contained, unified volume is the first comprehensive treatment of theory, methods, and algorithms, available in a single resource, without the typical quagmire of vast information scattered over a wide body of literature. Developments are discussed from a rapidly increasing number of research papers in diverse fields, including the mathematical and physical sciences, engineering, and medicine.

 

The initial chapters explore the statistical modeling of landmarks while subsequent chapters address the probabilistic modeling of entire shapes. The latter part of the book, with the exception of the last two chapters, concentrates on case studies as well as implementational and practical challenges in real systems. Extensive illustrations throughout help readers overcome the sometimes terse technical details of the geometric and probabilistic formalism. Knowledge of advanced calculus and basic statistics and probability theory are the only prerequisites for the reader.

 

Statistics and Analysis of Shapes will be an essential learning kit for statistical researchers, engineers, scientists, medical researchers, and students seeking a rapid introduction to the field. It may be used as a textbook for a graduate-level special topics course in statistics and signal/image analysis, or for an intensive short course on shape analysis and modeling. The state-of-the-art techniques presented will also be useful for experienced researchers and practitioners in academia and industry.

Content:
Front Matter....Pages i-xi
Medial Axis Computation and Evolution....Pages 1-28
Shape Variation of Medial Axis Representations via Principal Geodesic Analysis on Symmetric Spaces....Pages 29-59
2D Shape Modeling using Skeletal Graphs in a Morse Theoretic Framework....Pages 61-80
Matching with Shape Contexts....Pages 81-105
Shape Recognition Based on an a Contrario Methodology....Pages 107-136
Integral Invariants and Shape Matching....Pages 137-166
On the Representation of Shapes Using Implicit Functions....Pages 167-199
Computing with Point Cloud Data....Pages 201-229
Determining Intrinsic Dimension and Entropy of High-Dimensional Shape Spaces....Pages 231-252
Object-Image Metrics for Generalized Weak Perspective Projection....Pages 253-279
Wulff Shapes at Zero Temperature for Some Models Used in Image Processing....Pages 281-301
Curve Shortening and Interacting Particle Systems....Pages 303-311
Riemannian Structures on Shape Spaces: A Framework for Statistical Inferences....Pages 313-333
Modeling Planar Shape Variation via Hamiltonian Flows of Curves....Pages 335-361
Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics....Pages 363-395

---

The subject of pattern analysis and recognition pervades many aspects of our daily lives, including user authentication in banking, object retrieval from databases in the consumer sector, and the omnipresent surveillance and security measures around sensitive areas. Shape analysis, a fundamental building block in many approaches to these applications, is also used in statistics, biomedical applications (Magnetic Resonance Imaging), and many other related disciplines.

 

With contributions from some of the leading experts and pioneers in the field, this self-contained, unified volume is the first comprehensive treatment of theory, methods, and algorithms, available in a single resource, without the typical quagmire of vast information scattered over a wide body of literature. Developments are discussed from a rapidly increasing number of research papers in diverse fields, including the mathematical and physical sciences, engineering, and medicine.

 

The initial chapters explore the statistical modeling of landmarks while subsequent chapters address the probabilistic modeling of entire shapes. The latter part of the book, with the exception of the last two chapters, concentrates on case studies as well as implementational and practical challenges in real systems. Extensive illustrations throughout help readers overcome the sometimes terse technical details of the geometric and probabilistic formalism. Knowledge of advanced calculus and basic statistics and probability theory are the only prerequisites for the reader.

 

Statistics and Analysis of Shapes will be an essential learning kit for statistical researchers, engineers, scientists, medical researchers, and students seeking a rapid introduction to the field. It may be used as a textbook for a graduate-level special topics course in statistics and signal/image analysis, or for an intensive short course on shape analysis and modeling. The state-of-the-art techniques presented will also be useful for experienced researchers and practitioners in academia and industry.

Content:
Front Matter....Pages i-xi
Medial Axis Computation and Evolution....Pages 1-28
Shape Variation of Medial Axis Representations via Principal Geodesic Analysis on Symmetric Spaces....Pages 29-59
2D Shape Modeling using Skeletal Graphs in a Morse Theoretic Framework....Pages 61-80
Matching with Shape Contexts....Pages 81-105
Shape Recognition Based on an a Contrario Methodology....Pages 107-136
Integral Invariants and Shape Matching....Pages 137-166
On the Representation of Shapes Using Implicit Functions....Pages 167-199
Computing with Point Cloud Data....Pages 201-229
Determining Intrinsic Dimension and Entropy of High-Dimensional Shape Spaces....Pages 231-252
Object-Image Metrics for Generalized Weak Perspective Projection....Pages 253-279
Wulff Shapes at Zero Temperature for Some Models Used in Image Processing....Pages 281-301
Curve Shortening and Interacting Particle Systems....Pages 303-311
Riemannian Structures on Shape Spaces: A Framework for Statistical Inferences....Pages 313-333
Modeling Planar Shape Variation via Hamiltonian Flows of Curves....Pages 335-361
Approximations of Shape Metrics and Application to Shape Warping and Empirical Shape Statistics....Pages 363-395
....