60 research outputs found
Mathematical Imaging and Surface Processing
Within the last decade image and geometry processing have become increasingly rigorous with solid foundations in mathematics. Both areas are research fields at the intersection of different mathematical disciplines, ranging from geometry and calculus of variations to PDE analysis and numerical analysis. The workshop brought together scientists from all these areas and a fruitful interplay took place. There was a lively exchange of ideas between geometry and image processing applications areas, characterized in a number of ways in this workshop. For example, optimal transport, first applied in computer vision is now used to define a distance measure between 3d shapes, spectral analysis as a tool in image processing can be applied in surface classification and matching, and so on. We have also seen the use of Riemannian geometry as a powerful tool to improve the analysis of multivalued images.
This volume collects the abstracts for all the presentations covering this wide spectrum of tools and application domains
Variational image fusion
The main goal of this work is the fusion of multiple images to a single composite that offers more information than the individual input images. We approach those fusion tasks within a variational framework. First, we present iterative schemes that are well-suited for such variational problems and related tasks. They lead to efficient algorithms that are simple to implement and well-parallelisable. Next, we design a general fusion technique that aims for an image with optimal local contrast. This is the key for a versatile method that performs well in many application areas such as multispectral imaging, decolourisation, and exposure fusion. To handle motion within an exposure set, we present the following two-step approach: First, we introduce the complete rank transform to design an optic flow approach that is robust against severe illumination changes. Second, we eliminate remaining misalignments by means of brightness transfer functions that relate the brightness values between frames. Additional knowledge about the exposure set enables us to propose the first fully coupled method that jointly computes an aligned high dynamic range image and dense displacement fields. Finally, we present a technique that infers depth information from differently focused images. In this context, we additionally introduce a novel second order regulariser that adapts to the image structure in an anisotropic way.Das Hauptziel dieser Arbeit ist die Fusion mehrerer Bilder zu einem Einzelbild, das mehr Informationen bietet als die einzelnen Eingangsbilder. Wir verwirklichen diese Fusionsaufgaben in einem variationellen Rahmen. ZunĂ€chst prĂ€sentieren wir iterative Schemata, die sich gut fĂŒr solche variationellen Probleme und verwandte Aufgaben eignen. Danach entwerfen wir eine Fusionstechnik, die ein Bild mit optimalem lokalen Kontrast anstrebt. Dies ist der SchlĂŒssel fĂŒr eine vielseitige Methode, die gute Ergebnisse fĂŒr zahlreiche Anwendungsbereiche wie Multispektralaufnahmen, BildentfĂ€rbung oder Belichtungsreihenfusion liefert. Um Bewegungen in einer Belichtungsreihe zu handhaben, prĂ€sentieren wir folgenden Zweischrittansatz: Zuerst stellen wir die komplette Rangtransformation vor, um eine optische Flussmethode zu entwerfen, die robust gegenĂŒber starken BeleuchtungsĂ€nderungen ist. Dann eliminieren wir verbleibende Registrierungsfehler mit der Helligkeitstransferfunktion, welche die Helligkeitswerte zwischen Bildern in Beziehung setzt. ZusĂ€tzliches Wissen ĂŒber die Belichtungsreihe ermöglicht uns, die erste vollstĂ€ndig gekoppelte Methode vorzustellen, die gemeinsam ein registriertes Hochkontrastbild sowie dichte Bewegungsfelder berechnet. Final prĂ€sentieren wir eine Technik, die von unterschiedlich fokussierten Bildern Tiefeninformation ableitet. In diesem Kontext stellen wir zusĂ€tzlich einen neuen Regularisierer zweiter Ordnung vor, der sich der Bildstruktur anisotrop anpasst
Variational image fusion
The main goal of this work is the fusion of multiple images to a single composite that offers more information than the individual input images. We approach those fusion tasks within a variational framework. First, we present iterative schemes that are well-suited for such variational problems and related tasks. They lead to efficient algorithms that are simple to implement and well-parallelisable. Next, we design a general fusion technique that aims for an image with optimal local contrast. This is the key for a versatile method that performs well in many application areas such as multispectral imaging, decolourisation, and exposure fusion. To handle motion within an exposure set, we present the following two-step approach: First, we introduce the complete rank transform to design an optic flow approach that is robust against severe illumination changes. Second, we eliminate remaining misalignments by means of brightness transfer functions that relate the brightness values between frames. Additional knowledge about the exposure set enables us to propose the first fully coupled method that jointly computes an aligned high dynamic range image and dense displacement fields. Finally, we present a technique that infers depth information from differently focused images. In this context, we additionally introduce a novel second order regulariser that adapts to the image structure in an anisotropic way.Das Hauptziel dieser Arbeit ist die Fusion mehrerer Bilder zu einem Einzelbild, das mehr Informationen bietet als die einzelnen Eingangsbilder. Wir verwirklichen diese Fusionsaufgaben in einem variationellen Rahmen. ZunĂ€chst prĂ€sentieren wir iterative Schemata, die sich gut fĂŒr solche variationellen Probleme und verwandte Aufgaben eignen. Danach entwerfen wir eine Fusionstechnik, die ein Bild mit optimalem lokalen Kontrast anstrebt. Dies ist der SchlĂŒssel fĂŒr eine vielseitige Methode, die gute Ergebnisse fĂŒr zahlreiche Anwendungsbereiche wie Multispektralaufnahmen, BildentfĂ€rbung oder Belichtungsreihenfusion liefert. Um Bewegungen in einer Belichtungsreihe zu handhaben, prĂ€sentieren wir folgenden Zweischrittansatz: Zuerst stellen wir die komplette Rangtransformation vor, um eine optische Flussmethode zu entwerfen, die robust gegenĂŒber starken BeleuchtungsĂ€nderungen ist. Dann eliminieren wir verbleibende Registrierungsfehler mit der Helligkeitstransferfunktion, welche die Helligkeitswerte zwischen Bildern in Beziehung setzt. ZusĂ€tzliches Wissen ĂŒber die Belichtungsreihe ermöglicht uns, die erste vollstĂ€ndig gekoppelte Methode vorzustellen, die gemeinsam ein registriertes Hochkontrastbild sowie dichte Bewegungsfelder berechnet. Final prĂ€sentieren wir eine Technik, die von unterschiedlich fokussierten Bildern Tiefeninformation ableitet. In diesem Kontext stellen wir zusĂ€tzlich einen neuen Regularisierer zweiter Ordnung vor, der sich der Bildstruktur anisotrop anpasst
Dynamical models and machine learning for supervised segmentation
This thesis is concerned with the problem of how to outline regions of interest in medical images, when
the boundaries are weak or ambiguous and the region shapes are irregular. The focus on machine learning
and interactivity leads to a common theme of the need to balance conflicting requirements. First,
any machine learning method must strike a balance between how much it can learn and how well it
generalises. Second, interactive methods must balance minimal user demand with maximal user control.
To address the problem of weak boundaries,methods of supervised texture classification are investigated
that do not use explicit texture features. These methods enable prior knowledge about the image to
benefit any segmentation framework. A chosen dynamic contour model, based on probabilistic boundary
tracking, combines these image priors with efficient modes of interaction. We show the benefits of the
texture classifiers over intensity and gradient-based image models, in both classification and boundary
extraction.
To address the problem of irregular region shape, we devise a new type of statistical shape model
(SSM) that does not use explicit boundary features or assume high-level similarity between region
shapes. First, the models are used for shape discrimination, to constrain any segmentation framework
by way of regularisation. Second, the SSMs are used for shape generation, allowing probabilistic segmentation
frameworks to draw shapes from a prior distribution. The generative models also include
novel methods to constrain shape generation according to information from both the image and user
interactions.
The shape models are first evaluated in terms of discrimination capability, and shown to out-perform
other shape descriptors. Experiments also show that the shape models can benefit a standard type of
segmentation algorithm by providing shape regularisers. We finally show how to exploit the shape
models in supervised segmentation frameworks, and evaluate their benefits in user trials
International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book
The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions.
This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more
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