Many different edge detectors have been proposed. Most of them output the edge intensity and the edge orientation as edge features. In this paper we state necessity of a measure which can discriminate a clear edge with small edge height from a noisy edge with large edge height. To find such a measure as an edge feature, we analyze variances within a window around the edge and propose an edge-feature extractor based on this analysis. Then it is noticed that the traditional edge intensity can be considered as two elements: edge height and edge reliability. In multiple edge cases, the condition is clarified for calculating accurate edge locations by analyzing the edge-height function. From this analysis we suggest a method for determining edge points by thresholding edge height. Our detector is compared to Canny's detector both in synthetic models and in a real image and it is demonstrated that our method produces better results in edge locations than Canny's. We also show that our method can detect edges with low edge height and high edge reliability.