With the ever-rising volume worldwide of visual content on computers and communication networks, it becomes increasingly important to understand visual processing, to model and evaluate image formation, and to attempt to interpret image content.

Numerical Geometry of Images presents an authoritative examination of new computational methods and algorithms in image processing and analysis. In addition to providing the requisite vocabulary for formulating problems, the book describes and utilizes tools from mathematical morphology, differential geometry, numerical analysis, and calculus of variations. Many applications, such as shape reconstruction, color-image enhancement and segmentation, edge integration, path planning, and calculation invariant signatures are explored.

Topics and features:

• Introduces new concepts in geometric image modeling and image interpretation (computer vision)

• Provides the requisite theoretical basis and progresses to using key tools

• Offers a solution to the face-recognition problem by generalizing principles from texture-mapping methods in computer graphics

• Contains numerous helpful exercises and solutions to facilitate learning

• Presents a new perspective on solving classic problems, as well as classic approaches to solving new problems

• Uses industry-proven variational geometric methods and numerical schemes

  With its well-organized structure, clarity of presentation, and intuitive style, this new text/reference expedites a solid grasp of the technical material. Only a good background in geometry, linear algebra, and basic calculus is required. Graduate students and professionals with interests in computational geometry, computer vision, image processing, computer graphics, and algorithms will find the book an invaluable and highly practical learning resource.

  Klappentext

  Numerical Geometry of Images examines computational methods and algorithms in image processing. It explores applications like shape from shading, color-image enhancement and segmentation, edge integration, offset curve computation, symmetry axis computation, path planning, minimal geodesic computation, and invariant signature calculation. In addition, it describes and utilizes tools from mathematical morphology, differential geometry, numerical analysis, and calculus of variations. Graduate students, professionals, and researchers with interests in computational geometry, image processing, computer graphics, and algorithms will find this new text / reference an indispensable source of insight of instruction.

  Inhalt

  • Short introduction to calculus of variations Short introduction to differential geometry Curve evolution theory and invariant signatures The Osher-Sethian level-set method The level-set method: numerical considerations Mathematical morphology Distance maps and skeletons Fast marching methods 2D and 3D image segmentation * Geometric framework in image processing