FEATURE EXTRACTION CASE STUDIES

Many linear algebra operations, matrix inversions, etc. are required in pattern recogni­ tion as well as in signal processing. In this paper, we concentrate on feature extraction pattern recognition techniques (specifically a chord distribution and a moment feature space). For these two case studies, we note the various linear algebra operations required in distortion- invariant pattern recognition. Systolic processors can easily perform all required linear algebra functions. Linear algebra operations are required in many signal processing applications and these have been extensively discussed elsewhere in this volume. In this paper, I note that similar operations are also required in many pattern recognition and object identification applica­ tions. In this paper, specific attention is given to feature extraction or feature space based pattern recognition problems and to viable applications such as achieving object rec­ ognition in the face of geometrical distortions in the input image. The two feature extrac­ tion case studies considered are the use of a chord distribution and a moment feature space. Each of these results in considerably different linear algebra operations required on the object features to achieve the desired object identification. Sections 2 and 3 address the chord distribution feature space and Section 4 addresses the moment feature space case study. As background, we briefly discuss the general concept and approach to feature extraction using Figure 1. In this figure, we show that multiple scalar image features are computed for a given input object. These features are then operated upon by a classifier whose out­ puts tell us: the class of the input object, often its location (position) and orientation (distortion parameters) in the input field of view, and the confidence of the above esti­ mates. The basic premise associated with feature extraction is to reduce the large space bandwidth product (SBWP) of the input image to a few scalar features or numbers (1). Many different image features are possible and have and are being used (2), These include: Fourier coefficients, Mellin coefficients (3,4), geometrical features (such as object area, perimeter, etc.) (2), chord distributions (5-8), geometrical moments (9-12), invariant moments (13) and many other possible image features. In this paper, we consider only the chord distribution and geometrical moment feature spaces. Earlier papers (8,11) discuss several ways to compute such features. This present paper concentrates on the linear algebra operations required to process such features to achieve distortion-invariant intra and inter- class object recognition. We also note the role that systolic processors can have in such image pattern recognition applications. Many other pattern recognition techniques and algorithms (besides feature-space based ones) exist. These include the use of synthetic discriminant functions in correlator archi­ tectures. Such approaches also require linear algebra operations and can likewise benefit from systolic array processors. Such approaches are described elsewhere (14). As will be seen, the two feature extraction methods described here result in considerably different classifier requirements.