Scale Space Implementation - Separability

Separability

Using the separability property of the Gaussian kernel

the N-dimensional convolution operation can be decomposed into a set of separable smoothing steps with a one-dimensional Gaussian kernel along each dimension

where

and the standard deviation of the Gaussian is related to the scale parameter according to .

Separability will be assumed in all that follows, even when the kernel is not exactly Gaussian, since separation of the dimensions is the most practical way to implement multidimensional smoothing, especially at larger scales. Therefore, the rest of the article focuses on the one-dimensional case.

Read more about this topic:  Scale Space Implementation

Other articles related to "separability":

Multipartite Entanglement - Full and Partial Separability
... states is convex and closed with respect to trace norm, and separability is preserved under -separable operations which are a straightforward generalization of the bipartite ones As ...
Scale Space Implementation - Separability
... Using the separability property of the Gaussian kernel the N-dimensional convolution operation can be decomposed into a set of separable smoothing steps with a one-dimensional Gaussian kernel ... Separability will be assumed in all that follows, even when the kernel is not exactly Gaussian, since separation of the dimensions is the most practical way to ...
Separability Problem
... The separability problem is a concept from the field of social choice theory that describes the situation where two or more issues up for vote on a ballot either are, or are perceived as, related ... The separability problem commonly manifests itself most intensely in referendums and in voting on multiple charges before juries or panels of judges, where simultaneous voting is employed ... The solution to the separability problem for referendums would be set-wise voting, where the voter can express preferences for outcomes of related ...
Separable State - Separability Criterion
... The problem of deciding whether a state is separable in general is sometimes called the separability problem in quantum information theory ... The separability problem is a subject of current research ... A separability criterion is a necessary condition a state must satisfy to be separable ...