Recursive implementation of erosions and dilations along discrete lines at arbitrary angles

Soille, Pierre; Breen, Edmond J.; Jones, Ronald

doi:10.1109/34.494646

Cited by 103 publications

(74 citation statements)

References 14 publications

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“…One of the first algorithms to compute horizontal, vertical and diagonal strel for extraction of linear image structures was van Herk's method [16,17]. He proposed an efficient implementation of erosions and dilations of gray-scale images using only three min/max operations per pixel from 2D images.…”

Section: Detecting Local-linear Structuresmentioning

confidence: 99%

“…Limitations include requiring that the size of the buffers be a multiple of k and padding the end of the buffer with negative numbers. Soille et al [17] generalizes van Herk's algorithm to alleviate some of these limitations, and to allow lines at arbitrary angles. The main contributions in [17] consist of a periodic line to define arbitrary directions and a new recursive algorithm to calculate erosions and dilations, with complexity independent of the k. Both approaches explore the efficiency gained by avoiding unnecessary computer cycles, however they instead rely on memory utilization.…”

Section: Detecting Local-linear Structuresmentioning

confidence: 99%

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Structure recognition from high resolution images of ceramic composites

Ushizima

Perciano

Krishnan

et al. 2014

2014 IEEE International Conference on Big Data (Big Data)

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Fibers provide exceptional strength-to-weight ratio capabilities when woven into ceramic composites, transforming them into materials with exceptional resistance to high temperature, and high strength combined with improved fracture toughness. Microcracks are inevitable when the material is under strain, which can be imaged using synchrotron X-ray computed micro-tomography (µ-CT) for assessment of material mechanical toughness variation. An important part of this analysis is to recognize fibrillar features. This paper presents algorithms for detecting and quantifying composite cracks and fiber breaks from high-resolution image stacks. First, we propose recognition algorithms to identify the different structures of the composite, including matrix cracks and fibers breaks. Second, we introduce our package F3D for fast filtering of large 3D imagery, implemented in OpenCL to take advantage of graphic cards. Results show that our algorithms automatically identify micro-damage and that the GPU-based implementation introduced here takes minutes, being 17x faster than similar tools on a typical image file.

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Section: Detecting Local-linear Structuresmentioning

confidence: 99%

Section: Detecting Local-linear Structuresmentioning

confidence: 99%

Structure recognition from high resolution images of ceramic composites

Ushizima

Perciano

Krishnan

et al. 2014

2014 IEEE International Conference on Big Data (Big Data)

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“…It is interesting and important to find more efficient accurate algorithms for this problem, with and without assuming that pixel values are bounded. (Previous results [1], [22] give approximations to this problem.) 2.…”

Section: Conclusion and Open Problemsmentioning

confidence: 99%

“…The partitioning information is then used for an efficient implementation of the preprocessing stage in which prefix-and suffix-minima are computed. It follows from (22) that the preprocessing stage can be done in Oðlg 2 pÞ comparisons. Since the merge step can be done in Oðlg pÞ comparisons, we obtain: Theorem 4.…”

Section: An Efficient Algorithm For the Opening And Closing Filtersmentioning

confidence: 99%

Efficient Dilation, Erosion, Opening and Closing Algorithms

Gil

Kimmel

Mathematical Morphology and Its Applications to Image and Signal Processing

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Abstract-We propose an efficient and deterministic algorithm for computing the one-dimensional dilation and erosion (max and min) sliding window filters. For a p-element sliding window, our algorithm computes the 1D filter using 1:5 þ oð1Þ comparisons per sample point. Our algorithm constitutes a deterministic improvement over the best previously known such algorithm, independently developed by van Herk [25] and by Gil and Werman [12] (the HGW algorithm). Also, the results presented in this paper constitute an improvement over the Gevorkian et al. [9] (GAA) variant of the HGW algorithm. The improvement over the GAA variant is also in the computation model. The GAA algorithm makes the assumption that the input is independently and identically distributed (the i.i.d. assumption), whereas our main result is deterministic. We also deal with the problem of computing the dilation and erosion filters simultaneously, as required, e.g., for computing the unbiased morphological edge. In the case of i.i.d. inputs, we show that this simultaneous computation can be done more efficiently then separately computing each. We then turn to the opening filter, defined as the application of the min filter to the max filter and give an efficient algorithm for its computation. Specifically, this algorithm is only slightly slower than the computation of just the max filter. The improved algorithms are readily generalized to two dimensions (for a rectangular window), as well as to any higher finite dimension (for a hyperbox window), with the number of comparisons per window remaining constant. For the sake of concreteness, we also make a few comments on implementation considerations in a contemporary programming language.Index Terms-Mathematical morphology, running maximum filter, min-max filter, computational efficiency.

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“…The implementation of such an operator with actual lines as structuring elements is inefficient, however using recursive implementations of openings at arbitrary angles yields a linear time algorithm [17] with respect to the length of the structuring elements. Note that this algorithm is not translation-invariant.…”

Section: Morphological Operators For Thin Structuresmentioning

confidence: 99%

Efficient Path Openings and Closings

Appleton

Talbot

Computational Imaging and Vision

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Path openings and closings are algebraic morphological operators using families of thin and oriented structuring elements that are not necessarily perfectly straight. These operators are naturally translation invariant and can be used in filtering applications instead of operators based on the more standard families of straight line structuring elements. They give similar results to area or attributebased operators but with more flexibility in the constraints. Trivial implementations of this idea using actual suprema or infima of morphological operators with paths as structuring elements would imply exponential complexity. Fortunately a linear complexity algorithm exists in the literature, which has similar running times as an efficient implementation of algebraic operators using straight lines as structuring elements.However even this implementation is sometimes not fast enough, leading practitioners to favour some attribute-based operators instead, which in some applications is not optimal.In this paper we propose an implementation of path-based morphological operators which has logarithmic complexity and comparable computing times with those of attribute-based operators.

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Recursive implementation of erosions and dilations along discrete lines at arbitrary angles

Cited by 103 publications

References 14 publications

Structure recognition from high resolution images of ceramic composites

Structure recognition from high resolution images of ceramic composites

Efficient Dilation, Erosion, Opening and Closing Algorithms

Efficient Path Openings and Closings

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