2018 25th IEEE International Conference on Image Processing (ICIP) 2018
DOI: 10.1109/icip.2018.8451395
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Abstract: We extend recent work on mathematical morphology for signal processing on weighted graphs, based on discrete tropical algebra. The framework is general and can be applied to any scalar function defined on a graph. We show applications in structure tensors analysis and the regularisation of greyscale images.

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Cited by 9 publications
(12 citation statements)
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“…It would also be interesting to compare these models with the invariance obtained from data augmentation and possibly combine the two approaches in a complementary way. Additionally, future works will explore the use of the proposed morphological scale-spaces on other types of data like 3D point clouds [1], graphs [2], and high dimensional images.…”
Section: Discussionmentioning
confidence: 99%
“…It would also be interesting to compare these models with the invariance obtained from data augmentation and possibly combine the two approaches in a complementary way. Additionally, future works will explore the use of the proposed morphological scale-spaces on other types of data like 3D point clouds [1], graphs [2], and high dimensional images.…”
Section: Discussionmentioning
confidence: 99%
“…In the present paper, we focus on complete lattices of the type [a, b] n , where a and b represent the minimal and maximal possible signal values (typically a = 0 and b = 255 for 8-bits images), and n is an integer representing the size of the signal (typically, the number of pixels of an image, reshaped as a column vector). This is a theoretical contribution that can be viewed as a companion paper to previous studies where this framework has been successfully applied to adaptive anisotropic filtering [2,3] 3 . In Section 2 we introduce the matrix-based morphological setting and prove simple but fundamental results: in particular, we characterise the adjunctions that can be represented by matrices and show that these matrices need to be doubly-0-astic.…”
Section: Introductionmentioning
confidence: 92%
“…Proposition 2 Let W ∈ M n and ε W be the function defined by (2). Then ε W is an erosion mapping L to L if and only if W is column-0-astic.…”
Section: Erosions and Adjunctionsmentioning
confidence: 99%
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