Topology-based image segmentation using LBP pyramids

Cerman, Martin; Janusch, Ines; González-Dı́az, Rocı́o; Kropatsch, Walter G.

doi:10.1007/s00138-016-0795-1

Cited by 14 publications

(12 citation statements)

References 26 publications

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“…Besides, we plan to prove that MS complexes can be seen as particular cases of slopes complexes. Finally, Cerman et al (2016) can be considered as a first step in the computation of slope complexes and we plan to continue this work in the very near future.…”

Section: Discussionmentioning

confidence: 99%

“…The computation of slope complexes was made in only in the case in which the height map is piecewise linear and slope regions are planar triangles obtained from a triangulation of a 2D continuous surface. In Cerman et al (2016), we produced superpixel hierarchies (combinatorial graph pyramids) that are multiresolution segmentations of the given picture and where critical points are preserved along the pyramid. In , we approached the study of slope complexes from the point of view of the neighborhood graph of a digital picture.…”

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confidence: 99%

“…From the application point of view, Cerman et al (2016) provided an algorithm where the neighborhood graphs were used to represent a digital image. By a sequence of edge contraction and edge removal operations, we reduced the graph and stack them to form an irregular graph pyramid.…”

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confidence: 99%

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Characterizing slope regions

et al. 2021

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This paper provides a theoretical characterization of monotonically connected image surface regions, called slope regions. The characterization is given by several topological properties described in terms of critical points relative to the region. We formally prove the necessary and sufficient conditions that a region needs to satisfy to be a slope region. We also provide a prototype of slope regions which is general and contains, as particular cases, the prototypes studied and published in previous conference papers.

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Characterizing slope regions

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“…The cycle of length 4 corresponds to the well-known checkerboard pattern, the non-well-composed configurations [7]. It "hides" a saddle point inside the cycle (compare with [2]). This is true for all longer cycles of extrema, a cycle of 2n length needs n − 1 saddle vertices to subdivide the interior region completely into slope regions.…”

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Computing and Reducing Slope Complexes

Kropatsch

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Batavia

et al. 2018

Computational Topology in Image Context

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In this paper we provide a new characterization of cell decomposition (called slope complex) of a given 2-dimensional continuous surface. Each patch (cell) in the decomposition must satisfy that there exists a monotonic path for any two points in the cell. We prove that any triangulation of such surface is a slope complex and explain how to obtain new slope complexes with a smaller number of slope regions decomposing the surface. We give the minimal number of slope regions by counting certain bounding edges of a triangulation of the surface obtained from its critical points.

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“…By performing contraction and removal operations on edges, they formed a stack of graphs called graph pyramid. Cerman et al [4] provide a practical application of multi-resolution image segmentation using graph pyramids. Similar approaches are used by Wei in [12] where a hierarchical structure similar to graph pyramid were constructed by using superpixels.…”

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confidence: 99%

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Kropatsch

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et al. 2019

Graph-Based Representations in Pattern Recognition

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A digital image can be perceived as a 2.5D surface consisting of pixel coordinates and the intensity of pixel as height of the point in the surface. Such surfaces can be efficiently represented by the pair of dual plane graphs: neighborhood (primal) graph and its dual. By defining orientation of edges in the primal graph and use of Local Binary Patters (LBPs), we can categorize the vertices corresponding to the pixel into critical (maximum, minimum, saddle) or slope points. Basic operation of contraction and removal of edges in primal graph result in configuration of graphs with different combinations of critical and non-critical points. The faces of graph resemble a slope region after restoration of the continuous surface by successive monotone cubic interpolation. In this paper, we define orientation of edges in the dual graph such that it remains consistent with the primal graph. Further we deliver the necessary and sufficient conditions for merging of two adjacent slope regions.3 There is a topological and a combinatorial isomorphism between G and G and it is a unique pair of graphs embedded in a surface [5, p. 70-80]

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Topology-based image segmentation using LBP pyramids

Cited by 14 publications

References 26 publications

Characterizing slope regions

Characterizing slope regions

Computing and Reducing Slope Complexes

Congratulations! Dual Graphs Are Now Orientated!

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