1. An image processing apparatus for processing images picked up by a camera to detect objects in the images, comprising: a memory for storing image data corresponding to the images picked up by the camera; an image processor for processing said image data stored in said memory and detecting an object in said processed image data; a display for displaying processed image data including the detected object output by said image processor; and a designation unit for receiving setting information including coordinate transformation parameters and area parameters input by a user as a polygon or a circle defining an area in which a detected object is to be indicated to a user, wherein said image processor transforms an image on a first coordinate system representing a coordinate system during pickup to an image on a second coordinate system set up on a plane representing a reference based on the coordinate transformation parameters, said display displaying the transformed image, wherein said designation unit receives said polygon or the circle input by the user on the transformed image being displayed in the screen, wherein said image processor transforms the picked-up image or/and the area parameters by using the coordinate transformation parameters and then detects an object inside the area defined by the area parameters for indicating to the user, and wherein said second coordinate system is an approximation of an orthonormal coordinate system having two axes on a ground surface plane so that said image on the second coordinate system corresponds to a map of a monitoring target area, said coordinate transformation parameters includes three independent parameters corresponding to a depression angle, an installation height and a view field angle of said camera, and said image processor performs mutual transformation between the first coordinate system and the second coordinate system through central projection about the center at a principal point of the camera.