N-th Power Non-linear Transforms

1. Which is non-linear transforms?
2. Can matrices represent non-linear transformations?
3. What is non-linear transformation in image processing?

Which is non-linear transforms?

Linear Transformation: Preserves linear relationship between variables. Therefore, correlation between x and y would be unchanged after a linear transformation. Nonlinear Transformation: Changes linear relationship between variables, and thus, changes the correlation between variables.

Can matrices represent non-linear transformations?

Linear transformations are not the only ones that can be represented by matrices. Some transformations that are non-linear on an n-dimensional Euclidean space Rⁿ can be represented as linear transformations on the n+1-dimensional space Rⁿ⁺¹.

What is non-linear transformation in image processing?

A novel non-linear transformation for sharpening digitized gray-level images is defined. The transformation replaces the gray level value at a point by either the minimum or the maximum of gray levels in its neighborhood, the choice depending on which one is closer in value to the original gray level.