Exact Linear Time Euclidean Distance Transforms of Grid Line Sampled Shapes

Lindblad, Joakim; Sladoje, Nataša

doi:10.1007/978-3-319-18720-4_54

Cited by 7 publications

(4 citation statements)

References 19 publications

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“…Works belonging to category (i) include the anti-aliased distance transform [28,30], which improves the sub-pixel error of distances to continuous structures (discretized in a grid) and the exact EDT for grid sampled signals [38]. Another study investigates models for imprecision in the precise location of digital objects [54].…”

Section: Distance Transformsmentioning

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: Distance Transformsmentioning

confidence: 99%

“…3). If a kernel satisfies (37), it can be inserted into (38) and further into (41). This yields the distance transform…”

Section: Coverage Probability Estimation Using Kernel Density Estimatmentioning

confidence: 99%

Stochastic Distance Transform: Theory, Algorithms and Applications

2020

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“…In our data, the pore space is only a few pixels thin which leads to overly rough estimated distributions when using conventional distance transform algorithms. Using a sub-pixel precision leads to better resolved distributions (Lindblad and Sladoje, 2015;Godehardt et al, 2019). Figure 11 shows the spherical contact distribution at 600 and 1200 nm for both samples.…”

Section: Structural Analysismentioning

confidence: 99%

Three-dimensional structural comparison of tantalum glancing angle deposition thin films by FIB-SEM

Ott

Roldán

Redenbach

et al. 2019

J. Sens. Sens. Syst.

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Abstract. Thin tantalum films generated by glancing angle deposition serve as functional optical layers, for instance as absorption layers for ultrathin infrared sensors. They consist of nano-rods whose dimensions and distribution influence the optical properties of the thin film. Serial sectioning by a focused ion beam combined with scanning electron microscopy of the slices generates stacks of highly resolved images of this nanostructure. Dedicated image processing reconstructs the spatial structure from this stack such that 3-D image analysis yields geometric information that can be related to the optical performance.

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“…The properties of DT have been explored extensively, and several aspects of their performance have been improved by a sequence of important studies: their optimization for efficient approximation of Euclidean DT by local computations [5], fast algorithms for the exact Euclidean DT [15], DT with sub-pixel precision [9,13], and extension of DT to grey-scale and fuzzy images [10,19]. Exact algorithms eliminate approximation errors, and sub-pixel precision methods can reduce the inaccuracy of distances introduced by digitization of objects.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Distance Transform

Öfverstedt,

Lindblad,

Sladoje

2018

Preprint

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The distance transform (DT) and its many variations are ubiquitous tools for image processing and analysis. In many imaging scenarios, the images of interest are corrupted by noise. This has a strong negative impact on the accuracy of the DT, which is highly sensitive to spurious noise points. In this study, we consider images represented as discrete random sets and observe statistics of DT computed on such representations. We, thus, define a stochastic distance transform (SDT), which has an adjustable robustness to noise. Both a stochastic Monte Carlo method and a deterministic method for computing the SDT are proposed and compared. Through a series of empirical tests, we demonstrate that the SDT is effective not only in improving the accuracy of the computed distances in the presence of noise, but also in improving the performance of template matching and watershed segmentation of partially overlapping objects, which are examples of typical applications where DTs are utilized.

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Exact Linear Time Euclidean Distance Transforms of Grid Line Sampled Shapes

Cited by 7 publications

References 19 publications

Stochastic Distance Transform: Theory, Algorithms and Applications

Stochastic Distance Transform: Theory, Algorithms and Applications

Three-dimensional structural comparison of tantalum glancing angle deposition thin films by FIB-SEM

Stochastic Distance Transform

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