In the dissertation a new robust estimation technique for range image segmentation and fitting has been developed. The performance of the algorithm has been considerably improved by incorporating the genetic algorithm.  The new robust estimation method randomly samples range image points and solves equations determined by these points for parameters of selected primitive type. From K samples we measure RESidual Consensus (RESC) to choose one set of sample points which determines an equation best fitting the largest homogeneous surface patch in the current processing region. The residual consensus is measured by a compressed histogram method which can be used at various noise levels. After obtaining surface parameters of the best fitting and the residuals of each point in the current processing region, a boundary list searching method is used to extract this surface patch out of the processing region and to avoid further computation. Since the RESC method can tolerate more than 80% of outliers, it is a substantial improvement over the least median squares method. The method segments range image into planar and quadratic surfaces, and works very well even in smoothly connected curve regions.  A genetic algorithm is used to accelerate the random search. A large number of offline average performance experiments on GA are carried out to investigate different types of GAs and the influence of control parameters. A steady state GA works better than a generational replacement GA.  The algorithms have been validated on the large set of synthetic and real range images.