Refine
Year of publication
Document Type
Way of publication
- Open Access (9)
Keywords
- Laplace interpolation (4)
- Color image (3)
- Matrix field (3)
- partial differential equations (3)
- Inpainting (2)
- M-smoother (2)
- Median filter (2)
- Partial differential equations (2)
- Shape from Shading (2)
- Shape from shading (2)
Institute
- FG Angewandte Mathematik (83)
- FG Numerische Mathematik und Wissenschaftliches Rechnen (4)
- FG Ingenieurmathematik und Numerik der Optimierung (3)
- FG Praktische Informatik / Graphische Systeme (3)
- FG Geopedologie und Landschaftsentwicklung (2)
- FG Hybride Fertigung (2)
- FG Diskrete Mathematik und Grundlagen der Informatik (1)
- Zentrale Analytik der BTU Cottbus-Senftenberg (ZA-BTU) / Zentrales Analytisches Labor (1)
BTU
Quantile filters, or rank-order filters, are local image filters which assign quantiles of intensities of the input image within neighbourhoods as output image values. Combining a multivariate quantile definition developed in matrix-valued morphology with a recently introduced mapping between the RGB colour space and the space of symmetric 2×2 matrices, we state a class of colour image quantile filters, along with a class of morphological gradient filters derived from these. Using amoeba structuring elements, we devise image-adaptive versions of both filter classes. Experiments demonstrate the favourable properties of the filters.
The integration of surface normals for the purpose of computing the shape of a surface in 3D space is a classic problem in computer vision. However, even nowadays it is still a challenging task to devise a method that is flexible enough to work on non-trivial computational domains with high accuracy, robustness, and computational efficiency. By uniting a classic approach for surface normal integration with modern computational techniques, we construct a solver that fulfils these requirements. Building upon the Poisson integration model, we use an iterative Krylov subspace solver as a core step in tackling the task. While such a method can be very efficient, it may only show its full potential when combined with suitable numerical preconditioning and problem-specific initialisation. We perform a thorough numerical study in order to identify an appropriate preconditioner for this purpose. To provide suitable initialisation, we compute this initial state using a recently developed fast marching integrator. Detailed numerical experiments illustrate the benefits of this novel combination. In addition, we show on real-world photometric stereo datasets that the developed numerical framework is flexible enough to tackle modern computer vision applications.
A major task in non-rigid shape analysis is to retrieve correspondences between two almost isometric 3D objects. An important tool for this task are geometric feature descriptors. Ideally, a feature descriptor should be invariant under isometric transformations and robust to small elastic deformations. A successful class of feature descriptors employs the spectral decomposition of the Laplace-Beltrami operator. Important examples are the heat kernel signature using the heat equation and the more recent wave kernel signature applying the Schrödinger equation from quantum mechanics.
In this work we propose a novel feature descriptor which is based on the classic wave equation that describes e.g. sound wave propagation. We explore this new model by discretizing the underlying partial differential equation. Thereby we consider two different time integration methods. By a detailed evaluation at hand of a standard shape data set we demonstrate that our approach may yield significant improvements over state of the art methods for finding correct shape correspondences.