1. A driving support apparatus to support driving of a vehicle based on a vicinity state that is a state of vicinity of the vehicle while cooperating with a display apparatus, comprising: an information acquisition section to acquire vicinity information expressing the vicinity state of the vehicle; a recognition section to recognize at least one object in the vicinity of the vehicle based on the vicinity information acquired, and a predetermined target object that is included in the at least one object recognized in the vicinity of the vehicle; a drawing section to display in the display apparatus a vicinity image that expresses the vicinity state of the vehicle based on the vicinity information acquired; a visibility reduction section to reduce a visibility of the predetermined target object when the predetermined target object is displayed within the vicinity image in the display apparatus, wherein: the at least one object recognized by the recognition section includes a pedestrian and a different object other than the pedestrian; and the pedestrian that is recognized as the at least one object by the recognition section becomes the predetermined target object whose visibility is reduced in the vicinity image by the visibility reduction section; and an automatic driving section to drive the vehicle automatically while noticing the pedestrian corresponding to the target object whose visibility is reduced by the visibility reduction section in the vicinity image in the display apparatus based on a recognition result by the recognition section, (i) the visibility of the predetermined target object is reduced by the visibility reduction section to indicate that the predetermined target object is already noticed as a pedestrian by the automatic driving section, (ii) the visibility of an object other than the predetermined target object is not reduced by the visibility reduction section to indicate that a driver of the vehicle should pay attention to the predetermined target object which is unseen by the automatic driving section as the pedestrian.