Many computer vision applications require robust model estimation from a set of observed data. However, these data usually contain outliers, due to imperfect data acquisition or pre-processing steps, which can reduce the performance of conventional model-fitting methods. Robust fitting is thus critical to make the model estimation robust against outliers and reach stable performance. All of the contributions made in this thesis are for maximum consensus. In robust model fitting, maximum consensus is one of the most popular criteria, which aims to estimate the model that is consistent to as many observations as possible, i.e. obtain the highest consensus. The thesis makes contributions in two aspects of maximum consensus, one is non-learning...