Image Transformations

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Geometric transformations map pixel coordinates from one space to another:

\[\begin{split}\begin{pmatrix} x' \\ y' \\ 1 \end{pmatrix} = \mathbf{T} \begin{pmatrix} x \\ y \\ 1 \end{pmatrix}\end{split}\]

Common transformations include translation, rotation, scaling, shearing, and affine/perspective warping. These are used extensively in data augmentation (see Classical Augmentation).

Intensity transformations operate point-wise:

• Normalization: rescale intensities to a fixed range, e.g., [0, 1].

• Standardization (z-score): subtract mean and divide by standard deviation.

• Gamma correction: \(s = r^\gamma\) adjusts brightness.

• Log transform: \(s = c \log(1 + r)\) compresses dynamic range.

See also

• Classical Augmentation — geometric transforms used for data augmentation

• Normalization and Standardization — intensity transforms applied as a concrete preprocessing step

• Digital Image Processing Basics — every other basics topic