In object recognition from a three-dimensional image such as a spatio-temporal image or a range image, detecting edge planes correctly at accurate positions is important. In this work, we propose a method of edge plane detection in three-dimensional images by utilizing features of edge vector and edge reliability. This method can detect only reliable edge planes against noise influences. For the two-dimensional case, we proposed an edge detection method, which calculates edge vectors and edge reliabilities and can detect reliable edges at more accurate positions than Canny's method. This 2-D edge vector detector is generalized to the 3-D case, that is, pixels are vectorized in 3-D and its weighting function is extended to 3-D. In applying this method to a 3-D image, edge vectors and edge reliabilities are calculated first. For finding edge surfaces (i.e., 3-D boundaries), then, connected components of edge points detected from those features are composed by labeling. Finally, each edge surface is classified into edge planes using the directions of edge vectors. The proposed method was applied to spatio-temporal images and the depths of ridges in the 3-D scene were estimated from the detected edge planes.