Steering the Steerable Pyramid Transform filters

One of the primary advantages of the Steerable Pyramid transform (see [1]) is that the filter response in an arbitrary direction can be obtained as a linear sum of the filter responses computed for a fixed number of orientations. Equivalently, by taking linear sums of the basis elements, an arbitrary rotated version of the main basis element can be obtained. This property is usually called steerability. Below, a visual illustration is given.

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By using steerable filters for different scales and orientations, a multi-scale and multi-directional transform is obtained. This transform is called the Steerable Pyramid Transform and is presented in [2].

Brief explanation of the parameters: