Circular-harmonic function, minimum average correlation energy filters

Circular harmonic filters for the recognition of marine microorganisms

We present an application of circular-harmonic filters (CHF's) for the recognition of planktonic microorganisms. CHF's discriminated both genera Acartia and Calanus. The symmetry of genus Acartia permitted discrimination to the species and sex levels, whereas the asymmetry of the genus Calanus permitted discrimination only to the generic level. The differences among organisms of different sex of the genus Calanus could not be detected by these particular CHF's. More research needs to be carried out with more complex CHF's to enhance their performance and to permit the implementation of an automated optodigital system to identify and count marine microorganisms.

Multiple circular-harmonic-function correlation filter providing specified response to in-plane rotation

The circular-harmonic-function correlation filter originally proposed by Hsu and Arsenault [Appl. Opt. 21, 4016 (1982)] for in-plane rotation invariance uses only one harmonic, which results in poor discrimination capability of the filter. Various methods to use multiple harmonics were explored previously by different researchers. We present a new method to combine multiple circular harmonics into a single filter that can provide the desired correlation response to in-plane rotation while minimizing the correlation-plane energy. Since multiple harmonics are included, the filter can discriminate well, and since correlation-plane energy is minimized, correlation peaks tend to be sharp. Since the designer can specify the desired in-plane rotation response, a variety of filter behaviors (including complete invariance to input rotations) can be obtained. Underlying theory is discussed, and simulation results are presented.

Automatic spatial frequency selection algorithm for pattern recognition by correlation

We describe an approach to compute filters that automatically performs a spatial frequency selection to improve interclass discrimination and to reduce intraclass sensitivity. This approach is achieved by using as input to the filter synthesis a set of reference images to compute the filters and a set of distorted images to introduce the distortion or noise model of the reference images. Simulation results of correlation examples are provided for two pattern-recognition problems and are compared with the ones obtained with the standard minimum average correlation energy filters.

Fast design of circular-harmonic filters using simulated annealing

A new method is presented for determining the proper center of the circular-harmonic filter using an analytical expression for circular-harmonic expansion about an arbitrary center and simulated annealing for the automatic search of the maximum. The new method is two orders of magnitude faster than the previous method.

Tutorial survey of composite filter designs for optical correlators

A tutorial survey is presented of the many composite filter designs proposed for distortion-invariant optical pattern recognition. Remarks are made throughout regarding areas for further investigation.