Abstract: In general, small targets always are the extremum pixels in image local area. Based on the feature of targets, a new small target detection algorithm is presented based on the extremum theory for bi-variate cubic function. In this paper, a new model is developed named Zernike-facet model, which is used to fit local image intensity. And coefficients of the model are solved by the Total Least Squares (TLS) method, which performance in resisting noise is better than the Least Squares (LS) method. Then the new small target detection algorithm is proposed. The new algorithm used the Zernike-facet model and the TLS to fit image local intensity surface, and then those extremum points are extracted as targets. The simulations show that the new method is better in resisting noise than others. Several target detection experiments are carried out on visible /infrared image. The results demonstrate that the proposed method is efficient.