1. An image sensing system comprising: an image sensing device for sensing the image of a subject and outputting image data representing the image of the subject; a preliminary-image-sensing control device for controlling said image sensing device so as to perform preliminary image sensing and output image data representing a preliminary image of the subject; a first target-image detecting device for detecting a target image from within the preliminary image of the subject represented by the image data that has been output from said image sensing device under the control of said preliminary-image-sensing control device; an exposure-amount adjustment determination device for determining whether adjustment of amount of exposure is necessary based upon the target image that has been detected by said first target-image detecting device; a first regular-image-sensing control device for controlling said image sensing device so as to perform regular image sensing and output image data, which represents a regular sensed image of the subject, in response to a determination by said exposure-amount adjustment determination device that adjustment of amount of exposure is unnecessary; an exposure-amount adjusting device for adjusting amount of exposure, in response to a determination by said exposure-amount adjustment determination device that adjustment of amount of exposure is necessary, in such a manner that the amount of exposure of the target image detected by said first target-image detecting device will result in a brightness in the vicinity of an appropriate brightness; and a second regular-image-sensing control device for controlling said image sensing device so as to perform regular image sensing and output image data, which represents a regular sensed image of the subject, based upon the amount of exposure obtained by the adjustment performed by said exposure-amount adjusting device.