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Documents authored by Breuß, Michael

Document
DOI: 10.4230/DagRep.8.10.87
Shape Analysis: Euclidean, Discrete and Algebraic Geometric Methods (Dagstuhl Seminar 18422)

Authors: Michael Breuß, Alfred M. Bruckstein, Christer Oscar Kiselman, and Petros Maragos

Published in: Dagstuhl Reports, Volume 8, Issue 10 (2019)

Abstract
In computer vision, geometric processing and image analysis, the notation of a shape of a 3-D object has been studied either by an embedded manifold for the continuous stetting or as a collection of a discrete set of marker positions on the manifold. Within the last years, there have been many rapid developments in the field of shape representation, shape correspondence and shape manipulation with technical applications ranging from laser-range scanners to 3-D printing. Classic shape analysis tools from differential geometry have a fresh influence in the field, often powered by modern methods from optimization and numerical computing. At the same time, discrete geometric methods and related techniques such as from mathematical morphology have evolved significantly. Moreover, techniques like deep learning gained a significant influence in the development of corresponding methods and tools. New developments from tropical geometry have a high potential for use in shape analysis. The topics in our seminar addressed the sketched challenges and developments that will be useful for shape analysis. Especially we aimed to discuss the possibilities of combining fields like tropical geometry with more classical techniques as for instance from mathematical morphology. We discussed possibilities of applying machine learning methods in this context and considered recent advances from more classical fields like differential geometry and partial differential equations that can be useful for setting up and understanding shape analysis methods in all of these approaches. This seminar brought together 26 researchers from North America and Europe engaged in recent and upcoming developments in shape analysis who view these challenges from different perspectives and who together discussed the pressing open problems and novel solutions to them.
Cite as

Michael Breuß, Alfred M. Bruckstein, Christer Oscar Kiselman, and Petros Maragos. Shape Analysis: Euclidean, Discrete and Algebraic Geometric Methods (Dagstuhl Seminar 18422). In Dagstuhl Reports, Volume 8, Issue 10, pp. 87-103, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@Article{breu_et_al:DagRep.8.10.87,
  author =	{Breu{\ss}, Michael and Bruckstein, Alfred M. and Kiselman, Christer Oscar and Maragos, Petros},
  title =	{{Shape Analysis: Euclidean, Discrete and Algebraic Geometric Methods (Dagstuhl Seminar 18422)}},
  pages =	{87--103},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2019},
  volume =	{8},
  number =	{10},
  editor =	{Breu{\ss}, Michael and Bruckstein, Alfred M. and Kiselman, Christer Oscar and Maragos, Petros},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.8.10.87},
  URN =		{urn:nbn:de:0030-drops-103499},
  doi =		{10.4230/DagRep.8.10.87},
  annote =	{Keywords: algebraic geometry, mathematical morphology, optimization, shape analysis, shape reconstruction}
}
Document
DOI: 10.4230/DagRep.4.2.60
New Perspectives in Shape Analysis (Dagstuhl Seminar 14072)

Authors: Michael Breuß, Alfred M. Bruckstein, Petros Maragos, and Stefanie Wuhrer

Published in: Dagstuhl Reports, Volume 4, Issue 2 (2014)

Abstract
Over the last decade, it has become increasingly affordable to digitize 2D and 3D shape information using multiple modalities, such as (video) cameras, image-based reconstruction systems, laser-range scanners, or depth cameras. If these dense models can be processed and described in an efficient and informative way, they can be used in applications, such as ergonomic design, virtual shopping, scientific and medical visualization, realistic simulation, photo-realistic rendering, the design of natural user interfaces, and semantic scene understanding. Traditionally, the notion of shape has been studied either by analyzing projections of shapes in images or by analyzing a sparse set of marker positions on 3D shapes. Typical tasks in 2D shape analysis include segmenting objects in images and tracking objects across a sequence of images, and typical tasks in 3D shape analysis include reconstructing the three-dimensional object depth from input images and identifying corresponding points on different 3D models. The analysis and processing of shape data becomes especially challenging because of the increasing amount of data captured by sensors used to acquire shapes, and because modern applications such as natural user interfaces require real-time processing of the input shapes. Meeting these challenges requires models of shape analysis that are compact and informative, thereby allowing the development of algorithms that can process large datasets efficiently. To achieve these goals, interdisciplinary approaches are needed that use concepts from a variety of research areas, including numerical computing, differential geometry, deformable shape modeling, sparse data representation, and machine learning. On the algorithmic side, many shape analysis tasks are modeled using partial differential equations, which can be solved using tools from the field of numerical computing. The fields of differential geometry and deformable shape modeling have recently begun to influence shape analysis methods. Furthermore, tools from the field of sparse representations, which aim to describe input data using a compressible representation with respect to a set of carefully selected basis elements, have the potential to significantly reduce the amount of data that needs to be processed in shape analysis tasks. The related field of machine learning offers similar potential. This seminar brought together 28 researchers from North America and Europe engaged in recent and upcoming developments in shape analysis who view these challenges from different perspectives and who together discussed the pressing open problems and novel solutions to them.
Cite as

Michael Breuß, Alfred M. Bruckstein, Petros Maragos, and Stefanie Wuhrer. New Perspectives in Shape Analysis (Dagstuhl Seminar 14072). In Dagstuhl Reports, Volume 4, Issue 2, pp. 60-78, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@Article{breu_et_al:DagRep.4.2.60,
  author =	{Breu{\ss}, Michael and Bruckstein, Alfred M. and Maragos, Petros and Wuhrer, Stefanie},
  title =	{{New Perspectives in Shape Analysis (Dagstuhl Seminar 14072)}},
  pages =	{60--78},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2014},
  volume =	{4},
  number =	{2},
  editor =	{Breu{\ss}, Michael and Bruckstein, Alfred M. and Maragos, Petros and Wuhrer, Stefanie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.4.2.60},
  URN =		{urn:nbn:de:0030-drops-45452},
  doi =		{10.4230/DagRep.4.2.60},
  annote =	{Keywords: shape analysis, mathematical morphology, shape reconstruction, sparsity, machine learning, numerical computing, level set methods, optimisation method}
}
Document
DOI: 10.4230/DagRep.1.4.23
Innovations for Shape Analysis: Models and Algorithms (Dagstuhl Seminar 11142)

Authors: Michael Breuß, Alfred M. Bruckstein, and Petros Maragos

Published in: Dagstuhl Reports, Volume 1, Issue 4 (2011)

Abstract
This report documents the program and the results of Dagstuhl Seminar 11142 "Innovations for Shape Analysis: Models and Algorithms", taking place April 3-8 in 2011. The focus of the seminar was to discuss modern and emerging topics in shape analysis by researchers from different scientific communities, as there is no conference specifically devoted to this field.
Cite as

Michael Breuß, Alfred M. Bruckstein, and Petros Maragos. Innovations for Shape Analysis: Models and Algorithms (Dagstuhl Seminar 11142). In Dagstuhl Reports, Volume 1, Issue 4, pp. 23-40, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@Article{breu_et_al:DagRep.1.4.23,
  author =	{Breu{\ss}, Michael and Bruckstein, Alfred M. and Maragos, Petros},
  title =	{{Innovations for Shape Analysis: Models and Algorithms (Dagstuhl Seminar 11142)}},
  pages =	{23--40},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2011},
  volume =	{1},
  number =	{4},
  editor =	{Breu{\ss}, Michael and Bruckstein, Alfred M. and Maragos, Petros},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.1.4.23},
  URN =		{urn:nbn:de:0030-drops-31966},
  doi =		{10.4230/DagRep.1.4.23},
  annote =	{Keywords: Shape analysis, mathematical morphology, shape reconstruction, numerical computing, level set methods, fast marching methods}
}
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