Image Processing with Cellular Topology [electronic resource] /

Chapter 1. Introduction -- Chapter 2. Boundary Presentation Using Abstract Cell Complexes -- Chapter 3. Boundary Tracing in Binary Images Using Cell Complexes -- Chapter 4. Boundary Tracing and Encoding in Color Images -- Chapter 5. Boundary Polygonization -- Chapter 6. Edge Detection in 2D Images -- Chapter 7. Surface Traversing and Encoding in 3D Images -- Chapter 8. Edge Detection in 3D Images -- Chapter 9. Discussion.

This book explains why the finite topological space known as abstract cell complex is important for successful image processing and presents image processing methods based on abstract cell complex, especially for tracing and encoding of boundaries of homogeneous regions. Many examples are provided in the book, some teach you how to trace and encode boundaries in binary, indexed and colour images. Other examples explain how to encode a boundary as a sequence of straight-line segments which is important for shape recognition. A new method of edge detection in two- and three-dimensional images is suggested. Also, a discussion problem is included in the book: A derivative is defined as the limit of the relation of the increment of the function to the increment of the argument as the latter tends to zero. Is it not better to estimate derivatives as the relation of the increment of the function to the optimal increment of the argument instead of taking exceedingly small increment whichleads to errors? This book addresses all above questions and provide the answers.