Browsing by Author "Hildebrandt, Klaus"
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Item EUROGRAPHICS 2018: CGF 37-2 STARs Frontmatter(The Eurographics Association and John Wiley & Sons Ltd., 2018) Hildebrandt, Klaus; Theobalt, Christian; Hildebrandt, Klaus; Theobalt, Christian-Item A Geometric Optimization Approach for the Detection and Segmentation of Multiple Aneurysms(The Eurographics Association and John Wiley & Sons Ltd., 2019) Lawonn, Kai; Meuschke, Monique; Wickenhöfer, Ralph; Preim, Bernhard; Hildebrandt, Klaus; Gleicher, Michael and Viola, Ivan and Leitte, HeikeWe present a method for detecting and segmenting aneurysms in blood vessels that facilitates the assessment of risks associated with the aneurysms. The detection and analysis of aneurysms is important for medical diagnosis as aneurysms bear the risk of rupture with fatal consequences for the patient. For risk assessment and treatment planning, morphological descriptors, such as the height and width of the aneurysm, are used. Our system enables the fast detection, segmentation and analysis of single and multiple aneurysms. The method proceeds in two stages plus an optional third stage in which the user interacts with the system. First, a set of aneurysm candidate regions is created by segmenting regions of the vessels. Second, the aneurysms are detected by a classification of the candidates. The third stage allows users to adjust and correct the result of the previous stages using a brushing interface. When the segmentation of the aneurysm is complete, the corresponding ostium curves and morphological descriptors are computed and a report including the results of the analysis and renderings of the aneurysms is generated. The novelty of our approach lies in combining an analytic characterization of aneurysms and vessels to generate a list of candidate regions with a classifier trained on data to identify the aneurysms in the candidate list. The candidate generation is modeled as a global combinatorial optimization problem that is based on a local geometric characterization of aneurysms and vessels and can be efficiently solved using a graph cut algorithm. For the aneurysm classification scheme, we identified four suitable features and modeled appropriate training data. An important aspect of our approach is that the resulting system is fast enough to allow for user interaction with the global optimization by specifying additional constraints via a brushing interface.Item Locally Supported Tangential Vector, n-Vector, and Tensor Fields(The Eurographics Association and John Wiley & Sons Ltd., 2020) Nasikun, Ahmad; Brandt, Christopher; Hildebrandt, Klaus; Panozzo, Daniele and Assarsson, UlfWe introduce a construction of subspaces of the spaces of tangential vector, n-vector, and tensor fields on surfaces. The resulting subspaces can be used as the basis of fast approximation algorithms for design and processing problems that involve tangential fields. Important features of our construction are that it is based on a general principle, from which constructions for different types of tangential fields can be derived, and that it is scalable, making it possible to efficiently compute and store large subspace bases for large meshes. Moreover, the construction is adaptive, which allows for controlling the distribution of the degrees of freedom of the subspaces over the surface. We evaluate our construction in several experiments addressing approximation quality, scalability, adaptivity, computation times and memory requirements. Our design choices are justified by comparing our construction to possible alternatives. Finally, we discuss examples of how subspace methods can be used to build interactive tools for tangential field design and processing tasks.Item Nonlinear Deformation Synthesis via Sparse Principal Geodesic Analysis(The Eurographics Association and John Wiley & Sons Ltd., 2020) Sassen, Josua; Hildebrandt, Klaus; Rumpf, Martin; Jacobson, Alec and Huang, QixingThis paper introduces the construction of a low-dimensional nonlinear space capturing the variability of a non-rigid shape from a data set of example poses. The core of the approach is a Sparse Principal Geodesic Analysis (SPGA) on the Riemannian manifold of discrete shells, in which a pose of a non-rigid shape is a point. The SPGA is invariant to rigid body motions of the poses and supports large deformation. Since the Riemannian metric measures the membrane and bending distortions of the shells, the sparsity term forces the modes to describe largely decoupled and localized deformations. This property facilitates the analysis of articulated shapes. The modes often represent characteristic articulations of the shape and usually come with a decomposing of the spanned subspace into low-dimensional widely decoupled subspaces. For example, for human models, one expects distinct, localized modes for the bending of elbow or knee whereas some more modes are required to represent shoulder articulation. The decoupling property can be used to construct useful starting points for the computation of the nonlinear deformations via a superposition of shape submanifolds resulting from the decoupling. In a preprocessing stage, samples of the individual subspaces are computed, and, in an online phase, these are interpolated multilinearly. This accelerates the construction of nonlinear deformations and makes the method applicable for interactive applications. The method is compared to alternative approaches and the benefits are demonstrated on different kinds of input data.Item Solving Variational Problems Using Nonlinear Rotation-invariant Coordinates(The Eurographics Association, 2019) Sassen, Josua; Heeren, Behrend; Hildebrandt, Klaus; Rumpf, Martin; Bommes, David and Huang, HuiWe consider Nonlinear Rotation-Invariant Coordinates (NRIC) representing triangle meshes with fixed combinatorics as a vector stacking all edge lengths and dihedral angles. Previously, conditions for the existence of vertex positions matching given NRIC have been established. We develop the machinery needed to use NRIC for solving geometric optimization problems. Moreover, we introduce a fast and robust algorithm that reconstructs vertex positions from close-to integrable NRIC. Our experiments underline that NRIC-based optimization is especially effective for near-isometric problems.Item Spectral Processing of Tangential Vector Fields(© 2017 The Eurographics Association and John Wiley & Sons Ltd., 2017) Brandt, Christopher; Scandolo, Leonardo; Eisemann, Elmar; Hildebrandt, Klaus; Chen, Min and Zhang, Hao (Richard)We propose a framework for the spectral processing of tangential vector fields on surfaces. The basis is a Fourier‐type representation of tangential vector fields that associates frequencies with tangential vector fields. To implement the representation for piecewise constant tangential vector fields on triangle meshes, we introduce a discrete Hodge–Laplace operator that fits conceptually to the prominent discretization of the Laplace–Beltrami operator. Based on the Fourier representation, we introduce schemes for spectral analysis, filtering and compression of tangential vector fields. Moreover, we introduce a spline‐type editor for modelling of tangential vector fields with interpolation constraints for the field itself and its divergence and curl. Using the spectral representation, we propose a numerical scheme that allows for real‐time modelling of tangential vector fields.We propose a framework for the spectral processing of tangential vector fields on surfaces. The basis is a Fourier‐type representation of tangential vector fields that associates frequencies with tangential vector fields. To implement the representation for piecewise constant tangential vector fields on triangle meshes, we introduce a discrete Hodge–Laplace operator that fits conceptually to the prominent discretization of the Laplace–Beltrami operator. Based on the Fourier representation, we introduce schemes for spectral analysis, filtering and compression of tangential vector fields.Item Symposium on Geometry Processing 2017: Frontmatter(Eurographics Association, 2017) Bærentzen, Jakob Andreas; Hildebrandt, Klaus; Bærentzen, Jakob Andreas and Hildebrandt, KlausItem Symposium on Geometry Processing 2017: Frontmatter(Eurographics Association, 2017) Bærentzen, Jakob Andreas; Hildebrandt, Klaus; Bærentzen, Jakob Andreas and Hildebrandt, Klaus