Maximum Mean Square Projection Filters

Abstract

The maximum mean square projection (MMSP) filter is proposed for distortion invariant recognition. It classifies images according to the energy projected onto an N-dimensional subspace. The MMSP filter is implemented in an updatable optical correlator where correlations from multiple filters are time integrated on the output detector array.

<title>Application of N-dimensional filters to sequential filtering</title>

“…An example training images is shown in figure 2. The maximum mean square projection formulation [3,4] was used to construct the N-dimensional filter.…”

“…This treatment is rather succinct and the interested reader can find a more in-depth treatment elsewhere. [2][3][4] A signal space formalism is helpful for understanding the formulation of the N-D filter and the distortion invariance problem. In this treatment, the input image and the filter impulse response are treated as vectors in a high dimensional linear vector space and the value of a correlation peak is given by the inner product between the filter vector and the image vector.…”

“…An N-D filter can be related to a second order neural network [3,4] and implements a hyperspheriodal cylinder decision surfacein the signal space. [5] The distortion invariant recognition problem is equivalent to recognizing a set of training images.…”