In this paper, we present a nonlinear algorithm for critical point detection (CPD) of 2D digital shapes. The algorithm eliminates the problems arising from curvature approximation and Gaussian filtering in the existing algorithms. Based on the definition of "critical level," we establish a set of criteria for the design of an effective CPD algorithm for the first time. By quantifying the critical level to the modified area confined by three consecutive "pseudocritical points," a simple but very effective algorithm is developed. The comparison of our experimental results with those of many other CPD algorithms shows that the proposed algorithm is superior in that it provides a sequence of figures at every detail level, and each has a smaller integral error than the others with the same number of critical points. The experimental results on shapes with various complexities also show the algorithm is reliable and robust with regard to noise. >