The Scale Space Formulation of Pyramid Data Structures
The Scale Space Formulation of Pyramid Data Structures
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More precisely, vix, y, t) = du(x, y, t)/dt .
Recall, however, that the Gaussian pyramid function u(x, y, t) is a solution to the Heat Equation. Thus v(x, y, t) = -—ix, y, t) = Au(x, y, t) .
01 So the Laplacian pyramid contains data that is simply the Laplacian of values in the Gaussian pyramid. Moreover, u is obtained by convolution of the original data / with the Heat kernel K: u=^K*f. We may use properties of convolutions to write v(, x, y, t) in three forms: v{x, y, t) = Au(x, y, 0 = AK * f... = K * Af .
Thus the Laplacian pyramid data can be formed from the Laplacian of the Gaussian pyramid, or by filtering the original data / with the Laplacian-of-Gaussian kernel AK, or by filtering the Laplacian of the original data by a Gaussian.
The last equation shows that v itself is a solution to the Heat Equation: with initial data A/. This implies a rapid method of constructing v, by blurring A/ data. However, in practice, blurring A/ can lead to numerical precision difficulties, and so one of the other forms is generally used for construction of v.
What to read after The Scale Space Formulation of Pyramid Data Structures?
You can find similar books in the "Read Also" column, or choose other free books by Robert a Hummel to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
More precisely, vix, y, t) = du(x, y, t)/dt .
Recall, however, that the Gaussian pyramid function u(x, y, t) is a solution to the Heat Equation. Thus v(x, y, t) = -—ix, y, t) = Au(x, y, t) .
01 So the Laplacian pyramid contains data that is simply the Laplacian of values in the Gaussian pyramid. Moreover, u is obtained by convolution of the original data / with the Heat kernel K: u=^K*f. We may use properties of convolutions to write v(, x, y, t) in three forms: v{x, y, t) = Au(x, y, 0 = AK * f... = K * Af .
Thus the Laplacian pyramid data can be formed from the Laplacian of the Gaussian pyramid, or by filtering the original data / with the Laplacian-of-Gaussian kernel AK, or by filtering the Laplacian of the original data by a Gaussian.
The last equation shows that v itself is a solution to the Heat Equation: with initial data A/. This implies a rapid method of constructing v, by blurring A/ data. However, in practice, blurring A/ can lead to numerical precision difficulties, and so one of the other forms is generally used for construction of v.
What to read after The Scale Space Formulation of Pyramid Data Structures?
You can find similar books in the "Read Also" column, or choose other free books by Robert a Hummel to read onlineMoreLess
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