1. A parking assist system of a vehicle, said parking assist system comprising: a camera configured to be disposed at a vehicle, wherein said camera, when disposed at the vehicle, has a field of view exterior of the vehicle; a control comprising an image processor operable to process image data captured by said camera when said camera is disposed at the vehicle; wherein said control, responsive to processing by said image processor of captured image data, detects parking space markers indicative of a parking space and identifies empty or available parking spaces; wherein said control uses a parking space detection algorithm that detects parking space markers by (i) extracting low level features from captured image data, (ii) classifying pixels as being part of a parking space line or not part of a parking space line, (iii) performing spatial line fitting to find lines in the captured images and to apply parking space geometry constraints, and (iv) detecting and selecting rectangles in the captured images; wherein said parking space detection algorithm employs a recursive temporal stabilization mechanism that predicts parking space markers when the parking space markers of a detected parking space disappear from the field of view of said camera; and wherein said control, responsive to identification of an empty or available parking space, at least in part controls the vehicle to park the vehicle in the identified empty or available parking space.