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Each iteration of the Sierpinski triangle contains triangles related to the next iteration by a scale factor of 1/2. In affine geometry, uniform scaling (or isotropic scaling [1]) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions (isotropically).
The geometric transformation represented by a diagonalizable matrix is an inhomogeneous dilation (or anisotropic scaling). That is, it can scale the space by a different amount in different directions. The direction of each eigenvector is scaled by a factor given by the corresponding eigenvalue.
More general is scaling with a separate scale factor for each axis direction. Non-uniform scaling (anisotropic scaling, inhomogeneous dilation) is obtained when at least one of the scaling factors is different from the others; a special case is directional scaling or stretching (in one direction).
The construction of continuous shearlet systems is based on parabolic scaling matrices = [/], > as a mean to change the resolution, on shear matrices = [], as a means to change the orientation, and finally on translations to change the positioning.
An image size can be changed in several ways. Consider resizing a 160x160 pixel photo to the following 40x40 pixel thumbnail and then scaling the thumbnail to a 160x160 pixel image. Also consider doubling the size of the following image containing text.
Anisotropy is also used to describe situations where properties vary systematically, dependent on direction. Isotropic radiation has the same intensity regardless of the direction of measurement , and an isotropic field exerts the same action regardless of how the test particle is oriented.
In image processing and computer vision, anisotropic diffusion, also called Perona–Malik diffusion, is a technique aiming at reducing image noise without removing significant parts of the image content, typically edges, lines or other details that are important for the interpretation of the image.
Image scaling can be interpreted as a form of image resampling or image reconstruction from the view of the Nyquist sampling theorem.According to the theorem, downsampling to a smaller image from a higher-resolution original can only be carried out after applying a suitable 2D anti-aliasing filter to prevent aliasing artifacts.