This book presents practical optimization techniques used in image processing and computer vision problems. Ill-posed problems are introduced and used as examples to show how each type of problem is related to typical image processing and computer vision problems. Unconstrained optimization gives the best solution based on numerical minimization of a single, scalar-valued objective function or cost function. Unconstrained optimization problems have been intensively studied, and many algorithms and tools have been developed to solve them. Most practical optimization problems, however, arise with a set of constraints. Typical examples of constraints include: (i) pre-specified pixel intensity range, (ii) smoothness or correlation with neighboring information, (iii) existence on a certain contour of lines or curves, and (iv) given statistical or spectral characteristics of the solution. Regularized optimization is a special method used to solve a class of constrained optimization problems. The term regularization refers to the transformation of an objective function with constraints into a different objective function, automatically reflecting constraints in the unconstrained minimization process. Because of its simplicity and efficiency, regularized optimization has many application areas, such as image restoration, image reconstruction, optical flow estimation, etc. Optimization plays a major role in a wide variety of theories for image processing and computer vision. Various optimization techniques are used at different levels for these problems, and this volume summarizes and explains these techniques as applied to image processing and computer vision.

This book presents practical optimization techniques used in image processing and computer vision problems. Ill-posed problems are introduced and used as examples to show how each type of problem is related to typical image processing and computer vision problems. Unconstrained optimization gives the best solution based on numerical minimization of a single, scalar-valued objective function or cost function. Unconstrained optimization problems have been intensively studied, and many algorithms and tools have been developed to solve them. Most practical optimization problems, however, arise with a set of constraints. Typical examples of constraints include: (i) pre-specified pixel intensity range, (ii) smoothness or correlation with neighboring information, (iii) existence on a certain contour of lines or curves, and (iv) given statistical or spectral characteristics of the solution. Regularized optimization is a special method used to solve a class of constrained optimization problems. The term regularization refers to the transformation of an objective function with constraints into a different objective function, automatically reflecting constraints in the unconstrained minimization process. Because of its simplicity and efficiency, regularized optimization has many application areas, such as image restoration, image reconstruction, optical flow estimation, etc. Optimization plays a major role in a wide variety of theories for image processing and computer vision. Various optimization techniques are used at different levels for these problems, and this volume summarizes and explains these techniques as applied to image processing and computer vision.

This book provides ample coverage of theoretical and experimental state-of-the-art work as well as new trends and directions in the biometrics field. It offers students and software engineers a thorough understanding of how some core low-level building blocks of a multi-biometric system are implemented. While this book covers a range of biometric traits, its main emphasis is placed on multi-sensory and multi-modal face biometrics algorithms and systems.

This book provides an ample coverage of theoretical and experimental state-of-the-art work as well as new trends and directions in the biometrics field. It offers students and software engineers a thorough understanding of how some core low-level building blocks of a multi-biometric system are implemented. While this book covers a range of biometric traits including facial geometry, 3D ear form, fingerprints, vein structure, voice, and gait, its main emphasis is placed on multi-sensory and multi-modal face biometrics algorithms and systems. "Multi-sensory" refers to combining data from two or more biometric sensors, such as synchronized reflectance-based and temperature-based face images. "Multi-modal" biometrics means fusing two or more biometric modalities, like face images and voice timber. This practical reference contains four distinctive parts and a brief introduction chapter. The first part addresses new and emerging face biometrics. Emphasis is placed on biometric systems where single sensor and single modality are employed in challenging imaging conditions. The second part on multi-sensory face biometrics deals with the personal identification task in challenging variable illuminations and outdoor operating scenarios by employing visible and thermal sensors. The third part of the book focuses on multi-modal face biometrics by integrating voice, ear, and gait modalities with facial data. The last part presents generic chapters on multi-biometrics fusion methodologies and performance prediction techniques.