An algebraic model for fast corner detection

This paper revisits the classical problem of detecting interest points, popularly known as “corners,” in 2D images by proposing a technique based on fitting algebraic shape models to contours in the edge image. Our method for corner detection is targeted for use on structural images, i.e., images that contain man-made structures for which corner detection algorithms are known to perform well. Further, our detector seeks to find image regions that contain two distinct linear contours that intersect. We define the intersection point as the corner, and, in contrast to previous approaches such as the Harris detector, we consider the spatial coherence of the edge points, i.e., the fact that the edge points must lie close to one of the two intersecting lines, an important aspect to stable corner detection. Comparisons between results for the proposed method and that for several popular feature detectors are provided using input images exhibiting a number of standard image variations, including blurring, affine transformation, scaling, rotation, and illumination variation. A modified version of the repeatability rate is proposed for evaluating the stability of the detector under these variations which requires a 1-to-1 mapping between matched features. Using this performance metric, our method is found to perform well in contrast to several current methods for corner detection. Discussion is provided that motivates our method of evaluation and provides an explanation for the observed performance of our algorithm in contrast to other algorithms. Our approach is distinct from other contour-based methods since we need only compute the edge image, from which we explicitly solve for the unknown linear contours and their intersections that provide image corner location estimates. The key benefits to this approach are: (1) performance (in space and time); since no image pyramid (space) and no edge-linking (time) is required and (2) compactness; the estimated model includes the corner location, and direction of the incoming contours in space, i.e., a complete model of the local corner geometry.