Parsimonious Path Openings and Closings

Morard, Vincent; Dokládal, Petr; Decencière, Étienne

doi:10.1109/tip.2014.2303647

Cited by 20 publications

(19 citation statements)

References 30 publications

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“…Finally, we implemented a variant of the parsimonious path opening (PPO) [13]. The parsimonious path opening is an approximation of the path opening [6], which preselects one-dimensional paths, based on intensity, which are then opened.…”

Section: Resultsmentioning

confidence: 99%

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Mathematical Morphology on Irregularly Sampled Data in One Dimension

Asplund

Hendriks²,

Thurley

et al. 2017

Mathematical Morphology - Theory and Applications

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Mathematical morphology (MM) on grayscale images is commonly performed in the discrete domain on regularly sampled data. However, if the intention is to characterize or quantify continuous-domain objects, then the discrete-domain morphology is a ected by discretization errors that may be alleviated by considering the underlying continuous signal. Given a band-limited image, for example, a real image projected through a lens system, which has been correctly sampled, the continuous signal may be reconstructed. Using information from the continuous signal when applying morphology to the discrete samples can then aid in approximating the continuous morphology. Additionally, there are a number of applications where MM would be useful and the data is irregularly sampled. A common way to deal with this is to resample the data onto a regular grid. Often this creates problems where data is interpolated in areas with too few samples. In this paper, an alternative way of thinking about the morphological operators is presented. This leads to a new type of discrete operators that work on irregularly sampled data. These operators are shown to be morphological operators that are consistent with the regular, morphological operators under the same conditions, and yield accurate results under certain conditions where traditional morphology performs poorly.

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Section: Resultsmentioning

confidence: 99%

“…We only use two adjacency graphs, namely the south-north, and the east-west ones [13], and therefore avoid using more extreme angles in our test images. These line segments have a varying intensity I such that the intensity values are given by…”

Section: Resultsmentioning

confidence: 99%

Mathematical Morphology on Irregularly Sampled Data in One Dimension

Asplund

Hendriks²,

Thurley

et al. 2017

Mathematical Morphology - Theory and Applications

View full text Add to dashboard Cite

show abstract

“…2]. It follows that α 1,l ( f ) and ρ 1,l ( f ) are just as efficient as traditional (binary) path openings, with a time complexity in O(|V | + |E|), and amenable to many of the same tweaks and adaptations [6,16,20].…”

Section: Binary Graphsmentioning

confidence: 99%

“…Note that in addition to using the algorithm above on sequences, one should also be able to use the above algorithm with the technique introduced by Morard et al [20] to compute the so-called "parsimonious path openings" on 2D images (and directed acyclic graphs in general). The idea here is to apply a 1D filter to a cleverly selected [3] subset of paths, giving an approximation to the full path-based filter.…”

Section: Hand If C(a B) < L Then We Do Know That V(b) Is Too Highmentioning

confidence: 99%

Efficient and Robust Path Openings Using the Scale-Invariant Rank Operator

2016

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Some basic properties of a slightly generalized version of the scale-invariant rank operator are given, and it is shown how this operator can be used to create a nearly scale-invariant generalization of path openings that is robust to noise. Efficient algorithms are given for sequences and directed acyclic graphs with binary values, as well as sequences with real (greyscale) values. An algorithm is also given for directed acyclic graphs with real weights. It is shown that the given algorithms might be extended even further by allowing for scores based on a totally ordered semigroup.

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“…The path opening filter explores all the potential paths in an image, leading to low efficiency when applied to large remotely sensed imagery. To address this problem, a newly proposed parsimonious path opening (PPO) was employed in this study [53]. This operator only identifies a subset of the paths considered by the conventional path opening, thus achieving a substantial speed-up while obtaining very similar results as the complete path opening operator.…”

Section: Path Openingmentioning

confidence: 99%

River Detection in Remotely Sensed Imagery Using Gabor Filtering and Path Opening

Yang

Liu

et al. 2015

Remote Sensing

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Detecting rivers from remotely sensed imagery is an initial yet important step in space-based river studies. This paper proposes an automatic approach to enhance and detect complete river networks. The main contribution of this work is the characterization of rivers according to their Gaussian-like cross-sections and longitudinal continuity. A Gabor filter was first employed to enhance river cross-sections. Rivers are better discerned from the image background after filtering but they can be easily corrupted owing to significant gray variations along river courses. Path opening, a flexible morphological operator, was then used to lengthen the river channel continuity and suppress noise. Rivers were consistently discerned from the image background after these two-step processes. Finally, a global threshold was automatically determined and applied to create binary river masks. River networks of the Yukon Basin and the Greenland Ice Sheet were successfully detected in two Landsat 8 OLI panchromatic images using the proposed method, yielding a high accuracy (~97.79%), a high true positive rate (~94.33%), and a low false positive rate (~1.76%). Furthermore, experimental tests validated the high capability of the proposed method to preserve river network continuity.

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Parsimonious Path Openings and Closings

Cited by 20 publications

References 30 publications

Mathematical Morphology on Irregularly Sampled Data in One Dimension

Mathematical Morphology on Irregularly Sampled Data in One Dimension

Efficient and Robust Path Openings Using the Scale-Invariant Rank Operator

River Detection in Remotely Sensed Imagery Using Gabor Filtering and Path Opening

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