Parameter transforms play a very important role in the recognition of geometric features in image data. Local operators devised to compute parametric descriptions of geometric entities using a small neighborhood p(x,y) about points of interest have been succesfully employed. These operators fail to exploit the long distance correlations present in the image (distant points belonging to the same feature). Thus, their accuracy decreases with the order of the parametric properties (e.g., position, direction, curvature, torsion, etc.) and they are very sensitive to noise. This paper presents a generalized neighborhood concept that allows parameter-extraction operators to use the joint information of different portions of the same feature. This produces up to a few orders of magnitude improvement in accuracy (signal/noise ratio) and a smoother response of the transform. A general framework, based on a connectionist approach, is presented to deal with the complex response in parameter space generated by such operators. A layered and concurrent scheme to extract 3D surfaces intersection curves is presented which, exploiting the properties of these operators, is able to reconstruct lines and conic sections in three-space.