We present a new approach to training set selection for general out-of-plane rotation distortion. This approach is mathematically related to distortion-invariant filter design and acts to simplify filter design and improve discrimination performance. It is also applicable to most other model based rotation-invariant filter designs. We develop the approach in a 3-D space with 3-D objects. Given a target object, it is first uniformly rotated about a coordinate axis and sampled. This is denoted as an in- plane rotation set. The set is then rotated in spherical coordinates corresponding in direction to the vertices of a platonic solid. All the rotated objects are correlated to obtain a correlation matrix. The correlation matrix is approximately cyclic Toeplitz dependent on the training set ordering. Its eigenvectors are approximately the Kronecker product of subsets of Fourier Vectors. The training set is intended to be orthographically projected to 2-D images. A filter family is defined by multiplying the training set matrix times the eigenvector matrix. The resulting correlation response at the origin is constant magnitude and linear in phase. As with linear phase coefficient composite filters, we expect such a filter family to demonstrate inherent discrimination against clutter and high signal-to-noise ration in detection.
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