Solid shape
Holes and genus of 2D and 3D digital images
CVGIP: Graphical Models and Image Processing
Topological Numbers and Singularities in Scalar Images: Scale-Space Evolution Properties
Journal of Mathematical Imaging and Vision
Generic structure of two-dimensional dimages under Gaussian blurring
SIAM Journal on Applied Mathematics
Thinning algorithms on rectangular, hexagonal, and triangular arrays
Communications of the ACM
Alternative tilings for improved surface area estimates by local counting algorithms
Computer Vision and Image Understanding
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
Robot Vision
Journal of Mathematical Imaging and Vision
Generic Sign Systems in Medical Imaging
IEEE Computer Graphics and Applications
Surface Coding Based on Morse Theory
IEEE Computer Graphics and Applications
Constructing a Reeb graph automatically from cross sections
IEEE Computer Graphics and Applications
Proceedings of the Second International Conference on Scale-Space Theories in Computer Vision
SCALE-SPACE '99 Proceedings of the Second International Conference on Scale-Space Theories in Computer Vision
The Relevance of Non-generic Events in Scale Space Models
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
The hierarchical structure of images
IEEE Transactions on Image Processing
A discrete scale space neighborhood for robust deep structure extraction
SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Laplacian eigenimages in discrete scale space
SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
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Although spatial critical points (saddle points and extrema--minima and maxima) are mathematically well-defined, it is non-trivial to detect them on an arbitrary discrete grid. Discretising a continuous method as well as a straightforward discrete neighbourhood based method do not guarantee to return all critical points. Although not all image analysis tasks require the right amount of critical point in mutual relations, it is obviously an advantage to know that all critical points are found. Furthermore, some methods do require the right amount of saddle points in relation to the extrema. The Euler number is an invariant stating explicitly the relation of the number of types of critical points. Using this, one is sure to find the right number of critical points. It is defined on a discrete lattice, so one only has to use the right grid. This appears to be a hexagonal one where each point has six neighbours. An easy way is given to use the hexagonal based critical point detection in a rectangular grid, which is commonly used in computer vision and image analysis tasks.