Scale Space Implementation

Scale Space Implementation

The linear scale-space representation of an N-dimensional continuous signal is obtained by convolving with an N-dimensional Gaussian kernel

begin{align} L(x_1, x_2, dots, x_N, t) = int_{u_1=-infty}^{infty} int_{u_2=-infty}^{infty} dots int_{u_N=-infty}^{infty} &f_C(x_1-u_1, x_2-u_2, dots, x_N-u_N, t)\ , cdot , &g_N(u_1, u_2, dots, u_N, t) , du_1 , du_2 dots du_N end{align}

However, for implementation, this definition is impractical, since it is continuous. When applying the scale space concept to a discrete signal, different approaches can be taken. This article is a brief summary of some of the most frequently used methods.

Read more about Scale Space Implementation:  Separability, The Sampled Gaussian Kernel, The Discrete Gaussian Kernel, Recursive Filters, Finite-impulse-response (FIR) Smoothers, Real-time Implementation Within Pyramids and Discrete Approximation of Scale-normalized Derivatives, Other Multi-scale Approaches, See Also

Other articles related to "scale space implementation":

Scale Space Implementation - See Also
... scale space pyramid (image processing) multi-scale approaches Gaussian filter. ...

Famous quotes containing the words scale and/or space:

    “The Humanity of men and women is inversely proportional to their Numbers. A Crowd is no more human than an Avalanche or a Whirlwind. A rabble of men and women stands lower in the scale of moral and intellectual being than a herd of Swine or of Jackals.”
    —Aldous Huxley (1894–1963)

    “For tribal man space was the uncontrollable mystery. For technological man it is time that occupies the same role.”
    —Marshall McLuhan (1911–1980)