Edge feature analysis by a vectorized feature extractor and in multiple edges

In this paper we propose a method to generalize a 1-D edge feature extractor to 2-D and clarifies its properties for the edges located closely each other (i.e., multiple edges). In a previous paper (1995) we stated necessity of a measure which can discriminate a clear edge with small edge height from a noisy edge with large edge height. Then we claimed that the edge features be viewed as a composition of edge height and edge reliability, based on the analysis of variances within a window around the edge. From this analysis, we constructed an edge feature extractor in 1-D. In this paper we generalize our 1-D edge feature extractor to a 2-D vectorized edge extractor and prove it able to calculate an edge orientation and edge height accurately and also to reduce computation time. Experiments show this clearly. The same vectorization technique is also applicable to the Canny's operator (1986). In multiple edges case, we made the conditions clear for calculating accurate edge locations. Since most edge detection methods use local maximums of the edge height function to detect edge points, we found the conditions by differentiating the edge height function.