Morphological methods in image and signal processing
Morphological methods in image and signal processing
Local distances for distance transformations in two and three dimensions
Pattern Recognition Letters
Optimization of length measurements for isotropic distance transformations in three dimension
CVGIP: Image Understanding
Thinning Methodologies-A Comprehensive Survey
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Euclidean distance transform in arbitrary dimensions
Pattern Recognition Letters
On topology preservation in 3D thinning
CVGIP: Image Understanding
On digital distance transforms in three dimensions
Computer Vision and Image Understanding
Sequential Operations in Digital Picture Processing
Journal of the ACM (JACM)
Skeletons in N dimensions using shape primitives
Pattern Recognition Letters
Morphological Image Processing: Architecture and VLSI Design
Morphological Image Processing: Architecture and VLSI Design
A medial-surface oriented 3-d two-subfield thinning algorithm
Pattern Recognition Letters
Digital distance transforms in 3D images using information from neighbourhoods up to 5 × 5 × 5
Computer Vision and Image Understanding
On Skeletonization in 4D Images
SSPR '96 Proceedings of the 6th International Workshop on Advances in Structural and Syntactical Pattern Recognition
Weighted digital distance transforms in four dimensions
Discrete Applied Mathematics
Morphological operations in recursive neighborhoods
Pattern Recognition Letters - Special issue: Discrete geometry for computer imagery (DGCI'2002)
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Hexagonal Parallel Pattern Transformations
IEEE Transactions on Computers
Three-Dimensional Skeletonization: Principle and Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Topology preservation and detection is a well known concept in the processing of 2- and 3-dimensional binary images. These images can be considered as sets that are mapped on square tessellated (hyper cubic) grids. This paper describes how the formalisms derived for 2D and 3D images can be expanded to N-dimensional images, i.e. binary point sets that are aligned on an N-dimensional square tessellated grid. Topology preserving thinning of objects in an image, informally referred to as skeletonization, is based on the successive erosion of the boundary of an object until locally a primitive shape is detected, e.g. in 3D a surface or a curve. The detection of primitive shapes is done using shape primitives. The generation of shape primitive detectors is based on the possibility to describe the primitives for intrinsic or object dimensions N@?=N-1 by quadratic equations of the form x"N=@?(a"nx"x+b"nx"n^2). From this, primitives for lower object dimensions can be derived. A formula is derived that predicts the number of unique shape primitives in each dimension. Their application in measurements on shapes, in conditions for topology detection as used in topology preserving thinning, as well as the determination of standing wave patterns in topological kernels, is described. Finally as on each element of an image at least one of the primitives matches, this can be used to measure the total content of length, area, volume, etc from the objects in the image.