Watersheds of functions and picture segmentation

Beucher, Serge

doi:10.1109/icassp.1982.1171424

Cited by 149 publications

(81 citation statements)

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“…The watershed algorithm is widely studied and used for efficient object separation (23)(24)(25)(26)28). It was introduced by Digabel and Lantuejoul (29), extended by Beucher (30), analyzed theoretically by Maisonneuve (31), and formally defined in terms of flooding simulations by Vincent and Soille (32). Its popularity is attributable to its high computational efficiency and ability to extend it to 3D spaces (6,33,34), which makes it amenable to application to data-intensive 3D confocal image stacks.…”

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confidence: 99%

A hybrid 3D watershed algorithm incorporating gradient cues and object models for automatic segmentation of nuclei in confocal image stacks

et al. 2003

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Background: Automated segmentation of fluorescentlylabeled cell nuclei in 3D confocal microscope images is essential to many studies involving morphological and functional analysis. A common source of segmentation error is tight clustering of nuclei. There is a compelling need to minimize these errors for constructing highly automated scoring systems. Methods: A combination of two approaches is presented. First, an improved distance transform combining intensity gradients and geometric distance is used for the watershed step. Second, an explicit mathematical model for the anatomic characteristics of cell nuclei such as size and shape measures is incorporated. This model is constructed automatically from the data. Deliberate initial over-segmentation of the image data is performed, followed by statistical model-based merging. A confidence score is computed for each detected nucleus, measuring

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A hybrid 3D watershed algorithm incorporating gradient cues and object models for automatic segmentation of nuclei in confocal image stacks

et al. 2003

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“…In computational geometry, the Morse complex is often described in terms of a filtration of sub-level sets of f [9,8,35]. The watershed segmentation method [4,27], widely used in image processing, is a variant of the Morse-complex and has been described for image data [3] as well as abstract-graphs and n-dimensional grids [34]. Gradient ascent-based clustering methods, such as mean-shift [10,12], medoid-shift [30], and quick shift [32] clustering, are widely used in machine learning and pattern recognition, and they are also closely related to algorithms for computing and approximating the Morse complex.…”

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Enhanced Topology-Sensitive Clustering by Reeb Graph Shattering

Harvey

Rübel

Pascucci

et al. 2011

Mathematics and Visualization

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Scalar-valued functions are ubiquitous in scientific research. Analysis and visualization of scalar functions defined on low-dimensional and simple domains is a well-understood problem, but complications arise when the domain is high-dimensional or topologically complex. Topological analysis and Morse theory provide tools that are effective in distilling useful information from such difficult scalar functions. A recently proposed topological method for understanding highdimensional scalar functions approximates the Morse-Smale complex of a scalar function using a fast and efficient clustering technique. The resulting clusters (the so-called Morse crystals) are each approximately monotone and are amenable to geometric summarization and dimensionality reduction. However, some Morse crystals may contain loops. This shortcoming can affect the quality of the analysis performed on each crystal, as regions of the domain with potentially disparate geometry are assigned to the same cluster. We propose to use the Reeb graph of each Morse crystal to detect and resolve certain classes of problematic clustering. This provides a simple and efficient enhancement to the previous Morse crystals clustering. We provide preliminary experimental results to demonstrate that our improved topology-sensitive clustering algorithm yields a more accurate and reliable description of the topology of the underlying scalar function.

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“…In the classical watershed, where the segmentation of the image starts from the local minima of the grey tone image, one would obtain an over segmentation. Here, the point is to start from other markers selected as a function of the problem to solve (Beucher, 1982;Beucher and Meyer 1992). Correct results were obtained by using the morphological gradient image filtered by a low-pass (weighted mean obtained by a kernel of convolution of size from 3×3 to 7×7 ).…”

Section: Fig 2 A) Image Presenting Some Small Real and Fake Grains mentioning

confidence: 99%