Journal of Computational Physics
Structured spatial domain image and data comparison metrics
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
Low-storage, explicit Runge-Kutta schemes for the compressible Navier-Stokes equations
Applied Numerical Mathematics
Competent, Compact, Comparative Visualization of a Vortical Flow Field
IEEE Transactions on Visualization and Computer Graphics
FG '98 Proceedings of the 3rd. International Conference on Face & Gesture Recognition
Stochastic differential algebraic equations of index 1 and applications in circuit simulation
Journal of Computational and Applied Mathematics
Comparative Flow Visualization
IEEE Transactions on Visualization and Computer Graphics
Local and Global Comparison of Continuous Functions
VIS '04 Proceedings of the conference on Visualization '04
Clifford Fourier Transform on Vector Fields
IEEE Transactions on Visualization and Computer Graphics
Clifford Convolution And Pattern Matching On Vector Fields
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
VisTrails: visualization meets data management
Proceedings of the 2006 ACM SIGMOD international conference on Management of data
Three-dimensional flow characterization using vector pattern matching
IEEE Transactions on Visualization and Computer Graphics
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part II
Scale and rotation invariant detection of singular patterns in vector flow fields
SSPR&SPR'10 Proceedings of the 2010 joint IAPR international conference on Structural, syntactic, and statistical pattern recognition
Modeling design and flow feature interactions for automotive synthesis
IDEAL'11 Proceedings of the 12th international conference on Intelligent data engineering and automated learning
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We present a novel approach for analyzing two-dimensional (2D) flow field data based on the idea of invariant moments. Moment invariants have traditionally been used in computer vision applications, and we have adapted them for the purpose of interactive exploration of flow field data. The new class of moment invariants we have developed allows us to extract and visualize 2D flow patterns, invariant under translation, scaling, and rotation. With our approach one can study arbitrary flow patterns by searching a given 2D flow data set for any type of pattern as specified by a user. Further, our approach supports the computation of moments at multiple scales, facilitating fast pattern extraction and recognition. This can be done for critical point classification, but also for patterns with greater complexity. This multi-scale moment representation is also valuable for the comparative visualization of flow field data. The specific novel contributions of the work presented are the mathematical derivation of the new class of moment invariants, their analysis regarding critical point features, the efficient computation of a novel feature space representation, and based upon this the development of a fast pattern recognition algorithm for complex flow structures.