Top 10 similar words or synonyms for laplacian
sobel 0.780941
bilinear 0.728697
regularized 0.728379
hessian 0.726311
gabor 0.711152
haar 0.701284
convolution 0.699752
regularization 0.693705
multiscale 0.666857
wavelet 0.666358
Top 30 analogous words or synonyms for laplacian
Article | Example |
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Infinity Laplacian | While the equation involves second derivatives, usually (generalized) solutions are not twice differentiable, as evidenced by the well-known Aronsson solution formula_6. For this reason the correct notion of solutions is that given by the viscosity solutions. |
Infinity Laplacian | A defining property of the usual formula_10-harmonic functions is the mean value property. That has a natural and important discrete version: a real-valued function formula_11 on a finite or infinite graph formula_12 is discrete harmonic on a subset formula_13 if |
Infinity Laplacian | In this equation, we used sup and inf instead of max and min because the graph formula_12 does not have to be locally finite (i.e., to have finite degrees): a key example is when formula_18 is the set of points in a domain in formula_19, and formula_20 if their Euclidean distance is at most formula_21. The importance of this example lies in the following. |
Infinity Laplacian | There is a game theory approach to the p-Laplacian, too, interpolating between simple random walk and the above random tug-of-war game. |
Laplacian smoothing | Where formula_2 is the number of adjacent vertices to node formula_3, formula_4 is the position of the formula_5-th adjacent vertex and formula_6 is the new position for node formula_3. |
Laplacian matrix | The symmetric normalized Laplacian matrix is defined as: |
Laplacian matrix | The (symmetric) normalized Laplacian is defined as |
Laplacian matrix | where "L" is the (unnormalized) Laplacian, "A" is the adjacency matrix and "D" is the degree matrix. Since the degree matrix "D" is diagonal and positive, its reciprocal square root formula_36 is just the diagonal matrix whose diagonal entries are the reciprocals of the positive square roots of the diagonal entries of "D". The symmetric normalized Laplacian is a symmetric matrix. |
Laplacian matrix | where we use the inner product formula_46, a sum over all vertices v, and formula_47 denotes the sum over all unordered pairs of adjacent vertices {u,v}. The quantity |
Laplacian matrix | is called the "Dirichlet sum" of f, whereas the expression |