Stochastic Distance Transform

Öfverstedt, Johan; Lindblad, Joakim; Sladoje, Nataša

doi:10.1007/978-3-030-14085-4_7

Cited by 1 publication

(9 citation statements)

References 16 publications

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“…1b. Figure 1g, h shows the DT resulting from the k-distance as well as the proposed SDT method with a uniform certainty map [45]. The two results are similar; the impact of noise is reduced compared to the results of using a classic DT (Fig.…”

Section: Introductionmentioning

confidence: 78%

“…This work extends [45], where we introduced the SDT, a mathematical tool based on the theory of DRSs, for computing robust distances in the presence of noise. In the here-presented study, we include general definitions of the transform as well as two methods for its efficient computation: one based on Monte-Carlo simulation and one based on ordered sequences of nearest points.…”

Section: Contributions Of the Papermentioning

confidence: 83%

“…in the uniform case, which is similar to the form of the deterministic formulation introduced in [45].…”

Section: The Uniform Probability Modelmentioning

confidence: 89%

“…We perform analysis of the approximation accuracy and computational complexity for both methods. We expand the discussion of advantages and limitations of the special case of the SDT presented in [45], where coverage probability functions are restricted to be uniform and incorporate this case into the more general version of the framework. Further, we propose a method, based on KDE, to estimate coverage probability functions from noisy input images.…”

Section: Contributions Of the Papermentioning

confidence: 99%

“…The uniform model is noteworthy, first and foremost for its simplicity, where a single probability value, together with an input binary imageŶ on domain I characterizes the entire DRS. Our initial study of the SDT [45] focused on this special case. Inserting Eq.…”

Section: The Uniform Probability Modelmentioning

confidence: 99%

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Stochastic Distance Transform: Theory, Algorithms and Applications

2020

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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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Section: Introductionmentioning

confidence: 78%

Section: Contributions Of the Papermentioning

confidence: 83%

“…in the uniform case, which is similar to the form of the deterministic formulation introduced in [45].…”

Section: The Uniform Probability Modelmentioning

confidence: 89%

Section: Contributions Of the Papermentioning

confidence: 99%

Section: The Uniform Probability Modelmentioning

confidence: 99%