1. An image coding apparatus, comprising: a slice modeling unit to designate portions of each image into designated slices, the designated slices including at least two independent rectangular slices of at least two respective regions that partially overlap and at least one slice of a region that surrounds at least one of the at least two partially overlapping regions; a picture header coding unit to code respective information on positions and sizes of the designated slices into a picture header; and a slice coding unit to code an image in units of slices by referring to the picture header.