This paper presents a geometrical feature detection framework for use with conventional 2D laser rangefinders. This framework is composed of three main procedures: data pre-processing, breakpoint detection and line extraction. In data pre-processing, low-level data organization and processing are discussed, with emphasis to sensor bias compensation. Breakpoint detection allows to determine sequences of measurements which are not interrupted by scanning surface changing. Two breakpoint detectors are investigated, one based on adaptive thresholding, and the other on Kalman filtering. Implementation and tuning of both detectors are also investigated. Line extraction is performed to each continuous scan sequence in a range image by applying line kernels. We have investigated two classic kernels, commonly used in mobile robots, and our Split-and-Merge Fuzzy (SMF) line extractor. SMF employs fuzzy clustering in a split-and-merge framework without the need to guess the number of clusters. Qualitative and quantitative comparisons using simulated and real images illustrate the main characteristics of the framework when using different methods for breakpoint and line detection. These comparisons illustrate the characteristics of each estimator, which can be exploited according to the platform computing power and the application accuracy requirements.