Fast and robust obstacle detection is a crucial task for autonomous mobile robots. Current approaches for obstacle detection in autonomous cars are based on the use of LIDAR or computer vision. In this thesis computer vision is selected due to its low-power and passive nature. This thesis proposes the use of edges in images to reduce the required storage and processing. Most current approaches are based on dense maps, where all the pixels in the image are used, but this places a heavy load on the storage and processing capacity of the system. This makes dense approaches unsuitable for embedded systems, for which only limited amounts of memory and processing power are available. This motivates us to use sparse maps based on the edges in an image. Typically edge pixels represent a small percentage of the input image yet they are able to represent most of the image semantics. In this thesis two approaches for the use of edges to obtain disparity maps are proposed and one approach for identifying obstacles given edge-based disparities. The first approach proposes a modification to the Census Transform in order to incorporate a similarity measure. This similarity measure behaves as a threshold on the gradient, resulting in the identification of high gradient areas. The identification of these high gradient areas helps to reduce the search space in an area-based stereo-matching approach. Additionally, the Complete Rank Transform is evaluated for the first time in the context of stereo-matching. An area-based local stereo-matching approach is used to evaluate and compare the performance of these pixel descriptors. The second approach proposes a new approach for the computation of edge-disparities. Instead of first detecting the edges and then reducing the search space, the proposed approach detects the edges and computes the disparities at the same time. The approach extends the fast and robust Edge Drawing edge detector to run simultaneously across the stereo pair. By doing this the number of matched pixels and the required operations are reduced as the descriptors and costs are only computed for a fraction of the edge pixels (anchor points). Then the image gradient is used to propagate the disparities from the matched anchor points along the gradients, resulting in one-voxel wide chains of 3D points with connectivity information. The third proposed algorithm takes as input edge-based disparity maps which are compact and yet retain the semantic representation of the captured scene. This approach estimates the ground plane, clusters the edges into individual obstacles and then computes the image stixels which allow the identification of the free and occupied space in the captured stereo-views. Previous approaches for the computation of stixels use dense disparity maps or occupancy grids. Moreover they are unable to identify more than one stixel per column, whereas our approach can. This means that it can identify partially occluded objects. The proposed approach is tested on a public-domain dataset. Results for accuracy and performance are presented. The obtained results show that by using image edges it is possible to reduce the required processing and storage while obtaining accuracies comparable to those obtained by dense approaches.