Intensity- and distortion-invariant object recognition and complex linear morphology (1993)

Our research applies to several important problems in pattern recognition. These problems are training-set selection, distortion- and intensity-invariance, and noise in the background scenery. We chose to use correlation-based filter systems for our research. Model based correlation filters have a combination of important properties which include translation-invariance, high signal-to-noise ratio, and can be implemented numerically using the FFT algorithm or optically using Fourier optical techniques. Because of their linear nature, we can optimize their class discrimination performance for a wide variety of scenery noise. Because their designs use a training set we can combine them into distortion-invariant systems. Complex correlation filters can be designed to perform high level logical operations on the input images. These operations allow us to implement intensity-invariant processing. We demonstrate that the training-set can be selected optimally such that the filter design is trivial while maintaining a good discrimination capability. We formulate a new approach to correlation filter and filter bank design which incorporates all of these important aspects into a single system.
Our approach for training-set selection is original and applies to general out-of-plane rotation distortion and is mathematically related to distortion-invariant filter design. We present a way to select a training-set of objects whose correlation matrix approaches an optimal form. The correlation matrix is approximately partition cyclic Toeplitz. Its eigenvectors are Fourier vectors. The associated filter family is optimized for minimum probability of error.
The intensity-invariance is accomplished by post-processing the output response of the distortion-invariant filter systems. The Hybrid Composite filter bank is distortion-invariant. The Hybrid Composite filters are a unification of several well known synthetic discriminant functions. The HC filter bank target class response result in a small number of features unique to the target class. The target response features are searched and quantified in four new post-processing schemes to achieve intensity-invariance.
We also introduce a unified correlation-based pattern recognition approach. In this approach, complex phasor addition and cancellation are incorporated into the design of filter(s) to perform implicit logical operations. These implicit logical operations are suitable to implement high level gray scale morphological transformations of input images. We apply this approach to implement basic mathematical morphology transformations. We use these transformations to solve an automatic distortion- and intensity-invariant object recognition problem. We introduce a set of shape operators or complex filters, which are logically structured into a filter bank architecture to accomplish the distortion- and intensity-invariant system. The complex filter bank is optimally insensitive to fractal noise representing natural scenery. The insensitivity is optimized for a specific fractal parameter using the Fisher discriminant. We demonstrate the performance of this approach with realistic scenery as well as synthesized images. (Abstract shortened by UMI.)