Discrete geometry for computer imagery

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The book covers a wide range of topics in digital geometry processing, emphasizing topological guarantees and the relationship between discrete images and the continuous world. It explores weak rational computing, models for distance geometry, and a formal approach to discrete geometry using nonstandard analysis. Key discussions include the generation and recognition of digital planes through multi-dimensional continued fractions, combinatorial views of digital convexity, and the construction of neighborhood operations using linear algebra. The text delves into digitally continuous multivalued functions, continued fractions related to digital lines, and new characterizations of simple points in various discrete spaces. It addresses critical point cancellation in Morse complexes and the detection of toric loops in discrete toric spaces. The book also examines operations for n-dimensional generalized maps and minimal simple pairs in cubic grids, highlighting the NP-completeness of certain simplicial complex problems. Additionally, it presents geometric transforms, medial axis computation, and statistical template matching under geometric transformations. The challenges of digital surface segmentation and curvature estimation are discussed, along with algorithms for digital plane recognition. The book emphasizes morphological analysis, constrained connectivity, and applications in structural recognition and image segmentation,