This paper introduces LOCAL LINES––a robust, high-resolution line detector that operates in linear time. LOCAL LINES tolerates noisy images well and can be optimized for various specialized applications by adjusting the values of configurable parameters, such as mask values and mask size. As described in this paper, the resolution of LOCAL LINES is the maximum that can be justified for pixelized data. Despite this high resolution, LOCAL LINES is of linear asymptotic complexity in terms of number of pixels in an image. This paper also provides a comparison of LOCAL LINES with the prevalent Hough Transform Line Detector.