Effective Component Tree Computation with Application to Pattern Recognition in Astronomical Imaging

Berger, Ch.; Géraud, Thierry; Levillain, Roland; Widynski, Nicolas; Baillard, A.; Bertin, Emmanuel

doi:10.1109/icip.2007.4379949

Cited by 82 publications

(112 citation statements)

References 5 publications

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“…The algorithm presented in [2] to compute the max-tree is surprisingly also able to compute the tree of shapes. The skeleton, or canvas, of this algorithm is the routine compute tree given in the right part of Algorithm 1; it is composed of three steps: sort the image elements (pixels); then run the modified unionfind algorithm to compute a tree encoded by a parent function; last modify the parent function to give that tree its canonical form.…”

Section: Computing the Max-tree And The Tree Of Shapesmentioning

confidence: 99%

“…The union-by-rank procedure that guaranties quasi-linear complexity. So that the Union-Find routine (given in [2] and recalled in Algorithm 1) remains short, its code does not feature tree balancing; yet it is explained in [3]. A formal proof of our algorithm.…”

Section: About Union-find and Component Treesmentioning

confidence: 99%

“…The routine union find, given in Algorithm 1, is the classical "union-find" algorithm [19] but modified so that it computes the expected morphological tree [2] while browsing pixels following R −1 , i.e., from leaves to root (let us recall that we do not feature here the union-by-rank version). Its result is a parent function that fulfills those first four properties.…”

Section: About Union-find and Component Treesmentioning

confidence: 99%

“…This section shows that the max-tree algorithm presented in [2] is actually an algorithmic "canvas" [7], that is, a kind of meta-algorithm that can be "filled in" so that it can serve different aims. In the present paper it gives an algorithm to compute the tree of shapes.…”

Section: Algorithmic Scheme and The Need For Continuitymentioning

confidence: 99%

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A Quasi-linear Algorithm to Compute the Tree of Shapes of nD Images

Géraud

Carlinet

Crozet

et al. 2013

Lecture Notes in Computer Science

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Abstract. To compute the morphological self-dual representation of images, namely the tree of shapes, the state-of-the-art algorithms do not have a satisfactory time complexity. Furthermore the proposed algorithms are only effective for 2D images and they are far from being simple to implement. That is really penalizing since a self-dual representation of images is a structure that gives rise to many powerful operators and applications, and that could be very useful for 3D images. In this paper we propose a simple-to-write algorithm to compute the tree of shapes; it works for nD images and has a quasi-linear complexity when data quantization is low, typically 12 bits or less. To get that result, this paper introduces a novel representation of images that has some amazing properties of continuity, while remaining discrete.

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Section: Computing the Max-tree And The Tree Of Shapesmentioning

confidence: 99%

Section: About Union-find and Component Treesmentioning

confidence: 99%

Section: About Union-find and Component Treesmentioning

confidence: 99%

Section: Algorithmic Scheme and The Need For Continuitymentioning

confidence: 99%

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A Quasi-linear Algorithm to Compute the Tree of Shapes of nD Images

Géraud

Carlinet

Crozet

et al. 2013

Lecture Notes in Computer Science

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“…Alternative methods were presented in [49][50][51][52]. The recursive method discussed in [19] separates the construction of the tree from the computation of attributes and the actual filtering.…”

Section: The Max-tree Algorithm and The One-pass Methodsmentioning

confidence: 99%

An Efficient Parallel Algorithm for Multi-Scale Analysis of Connected Components in Gigapixel Images

Wilkinson

Pesaresi

Ouzounis³

2016

IJGI

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Differential Morphological Profiles (DMPs) and their generalized Differential Attribute Profiles (DAPs) are spatial signatures used in the classification of earth observation data. The Characteristic-Salience-Leveling (CSL) is a model allowing the compression and storage of the multi-scale information contained in the DMPs and DAPs into raster data layers, used for further analytic purposes. Computing DMPs or DAPs is often constrained by the size of the input data and scene complexity. Addressing very high resolution remote sensing gigascale images, this paper presents a new concurrent algorithm based on the Max-Tree structure that allows the efficient computation of CSL. The algorithm extends the "one-pass" method for computation of DAPs, and delivers an attribute zone segmentation of the underlying trees. The DAP vector field and the set of multi-scale characteristics are computed separately and in a similar fashion to concurrent attribute filters. Experiments on test images of 3.48 to 3.96 Gpixel showed an average computational speed of 59.85 Mpixel per second, or 3.59 Gpixel per minute on a single 2U rack server with 64 opteron cores. The new algorithms could be extended to morphological keypoint detectors capable of handling gigascale images.

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