This site contains: mathematics courses and book; covers: image analysis, data analysis, and discrete modelling; provides: image analysis software. Created and run by Peter Saveliev.

From Intelligent Perception

The following pages link to here:

• Homeomorphism
• Connectedness (redirect page)
  • Cell counting
  • Machine learning
  • Tree representation of images
  • Topology
  • Topology in calculus
  • Homology as an equivalence relation
  • Homology of cubical complexes
  • Continuous functions
  • Continuity of functions of several variables
  • Topological spaces
  • Topological equivalence
  • Product topology
  • Quotient spaces
  • Manifolds
  • Connected component (redirect page)
    • Homology
    • Objects in binary images
    • Connectedness (redirect page)
    • Topological data analysis
    • The topology of data
    • Path-connectedness
    • Component (redirect page)
    • Persistence
    • Persistent homology
    • Can a set to be both open and closed?
    • Objects and holes
    • A graph, non-tree representation of the topology of a gray scale image by Saveliev
    • Topology based method of segmentation of gray scale images by Saveliev
    • Computational Homology by Kaczynski, Mischaikow, Mrozek
    • Robustness of topology of digital images and point clouds by Saveliev
    • The topology of a binary image
    • Configuration spaces
  • Surface
  • Connected sum
  • Hawaiian earring
  • Euler characteristic of graphs
  • Topological invariants
  • Functions of several variables
  • Path-connectedness
  • Path connected (redirect page)
    • Independence of path
  • Connected (redirect page)
    • Grayscale images
    • Is Mobius strip homeomorphic to the cylinder?
    • Topology vs algebra vs geometry
    • Why "preimage" in the definition of continuity?
    • Circle
    • Degree of map
    • Topological circle
    • Integration of differential forms of degree 0 and 1
    • The topology a gray scale image
  • Classification of surfaces
  • Computational Homology by Kaczynski, Mischaikow, Mrozek
  • Topology of Surfaces by Kinsey
  • Connected sets (redirect page)
    • Topology of Surfaces by Kinsey
  • Basic Topology by Armstrong
  • Introduction to Topology by Gamelin and Greene
  • Image Processing Handbook by Russ
  • Topology via Calculus
• Homology as an equivalence relation
• Homology of cubical complexes
• Topological equivalence
• New topological spaces from old
• Quotient spaces
• Quotient sets
• New complexes from old
• Cell complex
• Examples of cell complexes
• Partition
• Quotients of manifolds
• Projective plane
• Orientation of cells
• New sets from old
• New vector spaces from old
• Quotients of vector spaces
• Quotient function
• Homotopy
• Path-connectedness
• Cylinder
• Orientation
• Equivalence class (redirect page)
  • How to compute homology
  • Quotient operator
  • Orientation
  • Integration of differential forms of degree 0 and 1
• Introduction to abstract mathematics: course
• Persistent homology
• Is projection a quotient function?
• Discrete Calculus: Applied Analysis on Graphs for Computational Science by Grady and Polimeni
• Calculus / algebra = topology
• Homotopy equivalence
• Modular arithmetic
• Higher order Nielsen numbers by Saveliev
• Contemporary Abstract Algebra by Gallian
• Algebraic operations with forms and cohomology
• Linear algebra in elementary calculus
• Integration of differential forms of degree 0 and 1
• Matrices as functions
• Eigenvalues and eigenvectors of linear operators
• Linear operators: part 5
• De Rham cohomology
• Bordism
• Relation
• Equivalence (redirect page)
  • Higher order Nielsen numbers by Saveliev
  • Bijection