The paper presents a new parametric model-based approach to high-precision composite edge detection using orthogonal Zernike moment-based operators. It deals with two types of composite edges: (a) generalized step and (b) pulse/staircase edges. A 2-D generalized step edge is modeled in terms of five parameters: two gradients on two sides of the edge, the distance from the center of the candidate pixel, the orientation of the edge and the step size at the location of the edge. A 2-D pulse/staircase edge is modeled in terms of two steps located at two positions within the mask, and the edge orientation. A pulse edge is formed if the steps are of opposite polarities whereas a staircase edge results from two steps having the same polarity. Two complex and two real Zernike moment-based masks are designed to determine parameters of both the 2-D edge models. For a given edge model, estimated parameter values at a point are used to detect the presence or absence of that type of edge. Extensive noise analysis is performed to demonstrate the robustness of the proposed operators. Experimental results with intensity and range images are included to demonstrate the efficacy of the proposed edge detection technique as well as to compare its performance with the geometric moment-based step edge detection technique and Canny's (1986) edge detector.