Rescales

Rescales is the plural form of rescale, referring to multiple rescaling operations or instances of size adjustment. In mathematics and geometry, a rescale (or scaling) is a dilation: a transformation that multiplies every coordinate of points in a space by a common factor about a chosen center. A factor greater than one enlarges the object, while a factor between zero and one reduces it; a factor of one leaves it unchanged. Rescalings preserve shapes and angles, so the transformed figures are similar to the original. When the center is the origin, rescaling corresponds to multiplying position vectors by the factor.

In statistics and data processing, rescales describe transformations that adjust the range or distribution of data variables. Common rescaling methods include min-max scaling to a fixed interval, such as [0, 1], and standardization to zero mean and unit variance. Rescales can preserve monotonic order, but they may alter interpretability and the relationships between variables, depending on the method used.

In image processing and computer graphics, rescaling (often called resampling) changes image or texture dimensions. This involves interpolation to estimate new pixel values, with methods such as nearest neighbor, bilinear, and bicubic. The choice of method affects sharpness, blur, and artifacts in the rescaled image.

In scientific computing, rescales are used to nondimensionalize equations and improve numerical stability by adjusting the magnitudes of variables and parameters. Overall, rescales are a broad concept across disciplines, encompassing any operation that changes the size or scale of objects, data, or models while often preserving essential structure. See also scaling, rescaling, normalization.