Recovery of the Three-Dimensional Shape of an Object from a Single View

Abstract

Given a single picture which is a projection of a three-dimensional scene onto the two-dimensional picture plane, we usually have definite ideas about the 3-D shapes of objects. To do this we need to use assumptions about the world and the image formation process, since there exist a large number of shapes which can produce the same picture.

The purpose of this paper is to identify some of these assumptions—mostly geometrical ones—by demonstrating how the theory and techniques which exploit such assumptions can provide a systematic shape-recovery method. The method consists of two parts. The first is the application of the Origami theory which models the world as a collection of plane surfaces and recovers the possible shapes qualitatively. The second is the technique of mapping image regularities into shape constraints for recovering the probable shapes quantitatively.

Actual shape recovery from a single view is demonstrated for the scenes of an object such as a box and a chair. Given a single image, the method recovers the 3-D shapes of an object in it, and generates images of the same object as we would see it from other directions.