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

, a steerable filter is an orientation-selective

convolution kernel In mathematics (in particular, functional analysis), convolution is a mathematical operation on two functions f and g that produces a third function f*g, as the integral of the product of the two functions after one is reflected about the y-ax ...

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 (mathematics), scalar as a result". It is also used for other symmetric bilinear forms, for example in a pseudo-Euclidean space. N ...

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 si ...

for antenna arrays. Applications of steerable filters include

edge detection Edge or EDGE may refer to: Technology Computing * Edge computing, a network load-balancing system * Edge device, an entry point to a computer network * Adobe Edge, a graphical development application * Microsoft Edge, a web browser developed b ...

, 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