Stochastic Distance Transform: Theory, Algorithms and Applications

Distance transforms (DTs) are standard tools in image analysis, with applications in image registration and segmentation. The DT is based on extremal (minimal) distance values and is therefore highly sensitive to noise. We present a stochastic distance transform (SDT) based on discrete random sets ,...

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Vydáno v:Journal of mathematical imaging and vision Ročník 62; číslo 5; s. 751 - 769
Hlavní autoři: Öfverstedt, Johan, Lindblad, Joakim, Sladoje, Nataša
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.06.2020
Springer Nature B.V
Témata:
Accuracy
Algorithms
Applications of Mathematics
Computer Science
Computer simulation
Computerized Image Processing
Datoriserad bildbehandling
Deterministic algorithm
Discrete random set
Disks
Distance transform
Image analysis
Image Processing and Computer Vision
Image registration
Image segmentation
Mathematical Methods in Physics
Microscopy
Monte-Carl
Noise sensitivity
Probability theory
Robust distance
Signal,Image and Speech Processing
Special Issue on Discrete Geometry for Computer Imagery 2019
Three dimensional models
Discrete random set
Image segmentation
Monte-Carlo method
Robust distance
Deterministic algorithm
Distance transform
ISSN:0924-9907, 1573-7683, 1573-7683
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Shrnutí:Distance transforms (DTs) are standard tools in image analysis, with applications in image registration and segmentation. The DT is based on extremal (minimal) distance values and is therefore highly sensitive to noise. We present a stochastic distance transform (SDT) based on discrete random sets , in which a model of element-wise probability is utilized and the SDT is computed as the first moment of the distance distribution to the random set. We present two methods for computing the SDT and analyze them w.r.t. accuracy and complexity. Further, we propose a method, utilizing kernel density estimation, for estimating probability functions and associated random sets to use with the SDT. We evaluate the accuracy of the SDT and the proposed framework on images of thin line structures and disks corrupted by salt and pepper noise and observe excellent performance. We also insert the SDT into a segmentation framework and apply it to overlapping objects, where it provides substantially improved performance over previous methods. Finally, we evaluate the SDT and observe very good performance, on simulated images from localization microscopy, a state-of-the-art super-resolution microscopy technique which yields highly spatially localized but noisy point-clouds.
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ISSN:0924-9907
1573-7683
1573-7683
DOI:10.1007/s10851-020-00964-7