In order to recognize an object and determine its spatial position, 180 training images are divided into four image sets, and the feature vectors of all image sets are calculated. It is shown that each image set can be represented with three feature vectors, so the total four feature spaces can be constructed with only twelve feature vectors. The object decomposition and reconstruction are simplified greatly. Based on the relation between object vector and its reconstructed vector, the object can be determined as true or false, and its spatial position can be located. Simulation results show that the method of constructing multiple feature spaces and the object recognition rule are effective, and object recognizing and spatial position determining under out-of-plane rotation can be achieved.