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

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