A three-layered neural network is described for transforming two-dimensional discrete signals into generalized representations which need not necessarily be either orthogonal or complete, for image analysis, segmentation, and compression. One such transform of particular interest is a conjoint spatial/spectral 2-D "Gabor ~ transform, which provides a complete image description in terms of locally windowed 2-D spectral coordinates embedded within global 2-D spatial coordinates. Because intrinsic redundancies within images are extracted, the resulting image codes in this and related transforms can be very compact. However, these conjolnt transforms are inherently difficult to compute because the elementary expansion functions in general are not orthogonal. One orthosonalizing approach developed for I-D signals by Bastisans based on bi-orthonormal expansions is restricted by constraints on the conjoint sampling rates and invariance of the windowing function, as well as by the fact that the required auxiliary orthe~onalising functions are nonlocal infinite series. In the present simple 'neural network' approach, based upon inter-|amlnar interactions involving two layers with fixed weights and one layer with adjustable weighs, the network finds coe~cients for complete conjoint 2-D Gabor transforms without these restrictive conditions. For arbitrary non-complete transforms, in which the coefficients might be interpreted simply as signifying the presence of certain features in the image, the