In this paper a new technique for directional analysis of linear patterns in images is proposed based on the notion of scale space. A given image is preprocessed by a sequence of filters which are second derivatives of 2-D Gaussian functions with different scales. This gives a set of zero crossing maps (the scale space) from which a stability map is generated. Significant linear patterns are detected from measurements on the stability map. Information regarding orientation of the linear patterns in the image and the area covered by the patterns in specific directions is then computed. The performance of the method is illustrated through applications to synthetic patters and to scanning electron microscope images of collagen fibrils in rabbit ligaments.