1. An image processing device comprising: a candidate point extracting unit configured to extract a plurality of candidate points belonging to a predetermined structure from image data; a shape model storing unit configured to store a shape model representing a known shape of the predetermined structure, the shape model being formed by a plurality of model labels having a predetermined connection relationship; and a corresponding point selecting unit configured to select a mapping relationship between the candidate points and the model labels from a set of candidate mapping relationships satisfying constraints (a) to (c) below: (a) each model label is mapped with only one of the candidate points or none of the candidate points; (b) each candidate point is mapped with only one of the model labels or none of the model labels; and (c) when a path between two candidate points which are mapped with each pair of the model labels connected with each other is determined, each candidate point which is mapped with none of the model labels is included in only one of the determined paths or none of the determined paths.