In vector analysis, it is important to classify three flow primitives as translation, rotation and divergence. These three primitives can be detected utilizing line integral and surface integral according to the knowledge of vector analysis. In this paper, we introduce a method for extracting these three primitives utilizing edges in an image based on vector analysis, namely edge field analysis. The edge has the information of inclination. However, the edge has no information of the direction unlike vector. Hence, line integral and surface integral can not be directly applied to detect these three primitives utilizing edges. We firstly formulate the problem and describe the algorithm for detecting the three primitives in vector analysis. We then propose an algorithm for estimating three primitives regarding edge image as pseudo-vector field. For illustration, we apply edge field analysis to quasi-motion extraction and feature extraction. We also show the experimental results in terms of estimating the center of the flowers, the cell body of neuron, the eye of the storm, the center of the explosion and so on.