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The recognition in image data of viewed patches of spheres, cylinders, and planes in the 3-D world is discussed as a first step to complex object recognition or complex object location and orientation estimation. Accordingly, an image is partitioned into small square windows, each of which is a view of a piece of a sphere, or of a cylinder, or of a plane. Windows are processed in parallel for recognition of content. New concepts and techniques include approximations of the image within a window by 2-D quadric polynomials where each approximation is constrained by one of the hypotheses that the 3-D surface shape seen is either planar, cylindrical, or spherical; a recognizer based upon these approximations to determine whether the object patch viewed is a piece of a sphere, or a piece of a cylinder, or a piece of a plane; lowpass filtering of the image by the approximation. The shape recognition is computationally simple, and for large windows is approximately Bayesian minimum-probability-of-error recognition. These classifications are useful for many purposes. One such purpose is to enable a following processor to use an appropriate estimator to estimate shape, and orientation and location parameters for the 3-D surface seen within a window.