1. An image processing apparatus comprising: a memory that stores instructions, and a controller configured to execute the instructions stored in the memory to: control a projection device that projects an image on a projection surface to project a correction image; acquire captured image data obtained by capturing the correction image projected by the projection device; calculate (i) a distance between the correction image and a line expressed by a function representing a straight line and (ii) a distance the correction image and a line expressed by a function representing a curved line; judge, when the correction image expressed by the acquired captured image data is placed in a place with a coordinate system, which of the following functions: a function representing a straight line; and a function representing a curved line is used to make image correction based on both (i) the distance between the correction image and the line expressed by the function representing a straight line and (ii) the distance between the correction image and the line expressed by the function representing a curved line; present a user with an operation screen for correction using the judged function to be used for the image correction, the operation screen including first correction points to adjust positions of two vertexes and a second correction point to adjust a middle point of a line connecting two vertexes; and allow the user to adjust only the first correction points when the controller judges that the function representing a straight line is used to make image correction.