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A drawing of the Heawood graph with three crossings. This is the minimum number of crossings among all drawings of this graph, so the graph has crossing number cr(G) = 3.. In graph theory, the crossing number cr(G) of a graph G is the lowest number of edge crossings of a plane drawing of the graph G.
The zero-crossing based methods search for zero crossings in a second-order derivative expression computed from the image in order to find edges, usually the zero-crossings of the Laplacian or the zero-crossings of a non-linear differential expression.
It supports macOS including Apple Silicon-based. It's a free compiler, though it also has commercial add-ons (e.g. for hiding source code). Numba is used from Python, as a tool (enabled by adding a decorator to relevant Python code), a JIT compiler that translates a subset of Python and NumPy code into fast machine code.
A zero-crossing is a point where the sign of a mathematical function changes (e.g. from positive to negative), represented by an intercept of the axis (zero value) in the graph of the function. It is a commonly used term in electronics, mathematics, acoustics , and image processing .
Thus we can find a graph with at least e − cr(G) edges and n vertices with no crossings, and is thus a planar graph. But from Euler's formula we must then have e − cr(G) ≤ 3n, and the claim follows. (In fact we have e − cr(G) ≤ 3n − 6 for n ≥ 3). To obtain the actual crossing number inequality, we now use a probabilistic argument.
In an unweighted bipartite graph, the optimization problem is to find a maximum cardinality matching. The problem is solved by the Hopcroft-Karp algorithm in time O ( √ V E ) time, and there are more efficient randomized algorithms , approximation algorithms , and algorithms for special classes of graphs such as bipartite planar graphs , as ...
A variational explanation for the main ingredient of the Canny edge detector, that is, finding the zero crossings of the 2nd derivative along the gradient direction, was shown to be the result of minimizing a Kronrod–Minkowski functional while maximizing the integral over the alignment of the edge with the gradient field (Kimmel and ...
NumPy addresses the slowness problem partly by providing multidimensional arrays and functions and operators that operate efficiently on arrays; using these requires rewriting some code, mostly inner loops, using NumPy. Using NumPy in Python gives functionality comparable to MATLAB since they are both interpreted, [18] and they both allow the ...