Royal Institute of Technology (KTH), NADA, S-100 44 Stockholm, Sweden.
IEEE Trans Pattern Anal Mach Intell. 1987 Jun;9(6):726-41. doi: 10.1109/tpami.1987.4767980.
Edge detection in a gray-scale image at a fine resolution typically yields noise and unnecessary detail, whereas edge detection at a coarse resolution distorts edge contours. We show that ``edge focusing'', i.e., a coarse-to-fine tracking in a continuous manner, combines high positional accuracy with good noise-reduction. This is of vital interest in several applications. Junctions of different kinds are in this way restored with high precision, which is a basic requirement when performing (projective) geometric analysis of an image for the purpose of restoring the three-dimensional scene. Segmentation of a scene using geometric clues like parallelism, etc., is also facilitated by the algorithm, since unnecessary detail has been filtered away. There are indications that an extension of the focusing algorithm can classify edges, to some extent, into the categories diffuse and nondiffuse (for example diffuse illumination edges). The edge focusing algorithm contains two parameters, namely the coarseness of the resolution in the blurred image from where we start the focusing procedure, and a threshold on the gradient magnitude at this coarse level. The latter parameter seems less critical for the behavior of the algorithm and is not present in the focusing part, i.e., at finer resolutions. The step length of the scale parameter in the focusing scheme has been chosen so that edge elements do not move more than one pixel per focusing step.
在高分辨率的灰度图像中进行边缘检测通常会产生噪声和不必要的细节，而在低分辨率下进行边缘检测则会扭曲边缘轮廓。我们表明，“边缘聚焦”，即在连续的方式中进行从粗到细的跟踪，将高精度与良好的降噪相结合。这在几个应用中非常重要。不同类型的交点就是以这种方式高精度恢复的，这是为了恢复三维场景而对图像进行（射影）几何分析时的基本要求。使用平行等几何线索对场景进行分割也会受到算法的促进，因为不需要的细节已经被过滤掉了。有迹象表明，聚焦算法的扩展可以在某种程度上将边缘分类为扩散和非扩散（例如扩散照明边缘）。边缘聚焦算法包含两个参数，即模糊图像中分辨率的粗糙程度，以及在该粗糙级别上梯度幅度的阈值。后一个参数对算法的行为不太关键，并且在聚焦部分（即更精细的分辨率）中不存在。聚焦方案中尺度参数的步长选择为使得边缘元素在每个聚焦步骤中移动不超过一个像素。
