Methods and Apparatus for Manipulating Images and Objects Within Images

Methods and apparatus for manipulating digital images. A warping module is described that enables the manipulation of a surface by selectively deforming portions of the surface while maintaining local rigidity. The user may position multiple control points on a surface to constrain deformation. The user may specify multiple properties (e.g., translation, rotation, depth, and scale) at each control point. A mesh may be overlaid on the surface. The warping module may perform an initialization in which the properties are propagated other vertices in the mesh to generate an initial deformed mesh. The warping module may then perform an iterative optimization operation on the deformed mesh to improve the deformation while retaining local rigidity. Thus, instead of moving every pixel in the surface, the warping module moves or adjusts coordinates of the vertices of the mesh. The surface is then deformed according to the deformed mesh.