5,791 research outputs found
Symmetry-guided nonrigid registration: the case for distortion correction in multidimensional photoemission spectroscopy
Image symmetrization is an effective strategy to correct symmetry distortion
in experimental data for which symmetry is essential in the subsequent
analysis. In the process, a coordinate transform, the symmetrization transform,
is required to undo the distortion. The transform may be determined by image
registration (i.e. alignment) with symmetry constraints imposed in the
registration target and in the iterative parameter tuning, which we call
symmetry-guided registration. An example use case of image symmetrization is
found in electronic band structure mapping by multidimensional photoemission
spectroscopy, which employs a 3D time-of-flight detector to measure electrons
sorted into the momentum (, ) and energy () coordinates. In
reality, imperfect instrument design, sample geometry and experimental settings
cause distortion of the photoelectron trajectories and, therefore, the symmetry
in the measured band structure, which hinders the full understanding and use of
the volumetric datasets. We demonstrate that symmetry-guided registration can
correct the symmetry distortion in the momentum-resolved photoemission
patterns. Using proposed symmetry metrics, we show quantitatively that the
iterative approach to symmetrization outperforms its non-iterative counterpart
in the restored symmetry of the outcome while preserving the average shape of
the photoemission pattern. Our approach is generalizable to distortion
corrections in different types of symmetries and should also find applications
in other experimental methods that produce images with similar features
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Visual Encoding of Dissimilarity Data via Topology-Preserving Map Deformation
We present an efficient technique for topology-preserving map deformation and apply it to the visualization of dissimilarity data in a geographic context. Map deformation techniques such as value-by-area cartograms are well studied. However, using deformation to highlight (dis)similarity between locations on a map in terms of their underlying data attributes is novel. We also identify an alternative way to represent dissimilarities on a map through the use of visual overlays. These overlays are complementary to deformation techniques and enable us to assess the quality of the deformation as well as to explore the design space of blending the two methods. Finally, we demonstrate how these techniques can be useful in several—quite different—applied contexts: travel-time visualization, social demographics research and understanding energy flowing in a wide-area power-grid
Bending invariant meshes and application to groupwise correspondences
We introduce a new bending invariant representation of a triangular mesh S. The bending invariant mesh X of S is a deformation of S that has the property that the geodesic distance between each pair of vertices on S is approximated well by the Euclidean distance between the corresponding vertices on X. Furthermore, X is intersection-free. The main advantage of the bending invariant mesh compared to previous approaches is that mesh-based features on X can be used to facilitate applications such as shape recognition or shape registration. We apply bending invariant meshes to find dense point-to-point correspondences between a number of deformed surfaces corresponding to different postures of the same non-rigid object in a fully automatic way. 1
A Low-Dimensional Representation for Robust Partial Isometric Correspondences Computation
Intrinsic isometric shape matching has become the standard approach for pose
invariant correspondence estimation among deformable shapes. Most existing
approaches assume global consistency, i.e., the metric structure of the whole
manifold must not change significantly. While global isometric matching is well
understood, only a few heuristic solutions are known for partial matching.
Partial matching is particularly important for robustness to topological noise
(incomplete data and contacts), which is a common problem in real-world 3D
scanner data. In this paper, we introduce a new approach to partial, intrinsic
isometric matching. Our method is based on the observation that isometries are
fully determined by purely local information: a map of a single point and its
tangent space fixes an isometry for both global and the partial maps. From this
idea, we develop a new representation for partial isometric maps based on
equivalence classes of correspondences between pairs of points and their
tangent spaces. From this, we derive a local propagation algorithm that find
such mappings efficiently. In contrast to previous heuristics based on RANSAC
or expectation maximization, our method is based on a simple and sound
theoretical model and fully deterministic. We apply our approach to register
partial point clouds and compare it to the state-of-the-art methods, where we
obtain significant improvements over global methods for real-world data and
stronger guarantees than previous heuristic partial matching algorithms.Comment: 17 pages, 12 figure
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