applied mathematics Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathemat ...

, a steerable filter is an orientation-selective

convolution kernel In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions ( and ) that produces a third function (f*g) that expresses how the shape of one is modified by the other. The term ''convolution'' ...

used for image enhancement and feature extraction that can be expressed via a linear combination of a small set of rotated versions of itself. As an example, the oriented first derivative of a 2D Gaussian is a steerable filter. The oriented first order derivative can be obtained by taking the

dot product In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a scalar as a result". It is also used sometimes for other symmetric bilinear forms, for example in a pseudo-Euclidean space. is an alg ...

of a unit vector oriented in a specific direction with the gradient. The basis filters are the partial derivatives of a 2D Gaussian with respect to

x

and

y

. The process by which the oriented filter is synthesized at any given angle is known as ''steering'', which is used in similar sense as in

beam steering Beam steering is a technique for changing the direction of the main lobe of a radiation pattern. In radio and radar systems, beam steering may be accomplished by switching the antenna elements or by changing the relative phases of the RF signa ...

for antenna arrays. Applications of steerable filters include

edge detection Edge detection includes a variety of mathematical methods that aim at identifying edges, curves in a digital image at which the image brightness changes sharply or, more formally, has discontinuities. The same problem of finding discontinuiti ...

, oriented texture analysis and shape from shading. Steerable filters may be designed as approximations of a given filter shape up to a desired error or computational complexity.

References

Image processing Feature detection (computer vision) {{applied-math-stub