Separable Distance Transformation and Its Applications

Cœurjolly, David; Vacavant, Antoine

doi:10.1007/978-94-007-4174-4_7

Cited by 9 publications

(7 citation statements)

References 51 publications

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“…The initial works on distance transforms focused on rasterscan methods on binary images for computing Manhattan and Chessboard distances [46,47], followed by more refined weighted (Chamfer mask) distance transforms [7,15] which approximate the Euclidean distance transform (EDT) with smaller error than previous methods. Fast, separable algorithms have since then been developed which eliminate approximation errors and compute the exact Euclidean distance transform in linear time [16,24,40] and which are parallelizable and fast in practice.…”

Section: Distance Transformsmentioning

confidence: 99%

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%

Stochastic Distance Transform: Theory, Algorithms and Applications

2020

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“…The smoothed data set is copied into a 3D texture (1 byte per voxel) to enable hardware-accelerated trilinear filtering during ray casting. To enable empty space leaping, i.e., sphere casting, a 3D distance map is computed 48 , the voxel intensities of which provide the distance to the closest opaque voxel, a distance which can be safely skipped in any direction during ray casting 42 . The distance map is computed using the same algorithm as for the segmentation operations described above.…”

Section: Segmentation Visualizationmentioning

confidence: 99%

Imalytics Preclinical: Interactive Analysis of Biomedical Volume Data

et al. 2016

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A software tool is presented for interactive segmentation of volumetric medical data sets. To allow interactive processing of large data sets, segmentation operations, and rendering are GPU-accelerated. Special adjustments are provided to overcome GPU-imposed constraints such as limited memory and host-device bandwidth. A general and efficient undo/redo mechanism is implemented using GPU-accelerated compression of the multiclass segmentation state. A broadly applicable set of interactive segmentation operations is provided which can be combined to solve the quantification task of many types of imaging studies. A fully GPU-accelerated ray casting method for multiclass segmentation rendering is implemented which is well-balanced with respect to delay, frame rate, worst-case memory consumption, scalability, and image quality. Performance of segmentation operations and rendering are measured using high-resolution example data sets showing that GPU-acceleration greatly improves the performance. Compared to a reference marching cubes implementation, the rendering was found to be superior with respect to rendering delay and worst-case memory consumption while providing sufficiently high frame rates for interactive visualization and comparable image quality. The fast interactive segmentation operations and the accurate rendering make our tool particularly suitable for efficient analysis of multimodal image data sets which arise in large amounts in preclinical imaging studies.

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“…[5,11]). In digital geometry, the intersection of the closest-point Voronoi diagram with the fundamental lattice Z 2 and the associated Euclidean distance transform have also been deeply studied (see [3] for a survey). This paper is a step towards the study of the Voronoi diagrams and Delaunay triangulations of analytical subsets of the fundamental lattice in order to understand their geometry.…”

Section: Introductionmentioning

confidence: 99%

Euclidean farthest-point Voronoi diagram of a digital edge

Roussillon

2015

Discrete Applied Mathematics

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a b s t r a c tA digital edge is a digitization of a straight segment joining two points of integer coordinates. Such a digital set may be analytically defined by the rational slope of the straight segment. We show in this paper that the convex hull, the Euclidean farthest-point Voronoi diagram as well as the dual farthest-point Delaunay triangulation of a digital edge can be fully described by the continued fraction expansion of its slope.

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Separable Distance Transformation and Its Applications

Cited by 9 publications

References 51 publications

Stochastic Distance Transform: Theory, Algorithms and Applications

Stochastic Distance Transform: Theory, Algorithms and Applications

Imalytics Preclinical: Interactive Analysis of Biomedical Volume Data

Euclidean farthest-point Voronoi diagram of a digital edge

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