In the field of applied mathematics , a rotating filter [1] is the core of a convolution according to the choice of direction (expressed as a linear set of states of an object, determined only by its directivity in space, under constant external conditions; for example, a set of illuminance maps of an object depending on its rotation to conditionally stationary light source), which is used to improve image quality and highlight special features in it. An example of a rotating filter is the oriented first derivative of a two-dimensional Gaussian filter : it is equal to the scalar product of the direction given by the unit vector and the gradient. Basic filters are partial derivatives of a two-dimensional Gaussian filter with respect to and .
The process by which an oriented filter is synthesized for any given angle is known as a “steering turn” , which is similar to beam rotation for an antenna array . The use of rotating filters includes: detection of the boundaries of objects , analysis of oriented textures and determination of the volumetric shape of an object from its shading maps.
A new mathematical rotating filter can be created on the basis of the existing one - for example, by approximating its shape (i.e., simplifying it) or, conversely, complicating it - to change the ratio of filtration purity to its computational complexity . [2]
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- ↑ Freeman, WT and Adelson, EH . The design and use of steerable filters, pp. 891–906.
- ↑ Perona, P .. Deformable kernels for early vision ,, IEEE, pp. 488–499.