Shape-from-shading analysis for reconstructing 3D object shape using an image scanner

An image scanner is usually used to take 2D images of documents, pictures, photographs, and so on. If 3D shape information is acquired with an image scanner, the shading and geometric distortion in the unfolded book surface image can be restored and an image scanner can be used as a low-cost and easy-to-operate 3D measurement device. This study addresses problems related to the methods of recovering the 3D shape of an object from a scanned image and developing a new advantage for use of an image scanner. Many shape-recovering methods with use of images have been proposed, such as the stereo method, the shape-from-shading method, the texture analysis method, the shapefrom-focus method, etc. Among these methods, the shape-from-shading method, that is a method of reconstruction shape from a shading information in an image, is the most appropriate for a method of recovering object shape from a scanned image. Because an image scanner normally has only one CCD sensor, taking only a single image makes it difficult to use another CCD like an stereo method. But it is possible to recover the object shape from a single image by using the shape-from-shading method. Moreover, having no assumptions about the texture on the object surface makes it possible to pick up various objects as a target. In implementing a shape-from-shading method, it is necessary to formulate the relation between the shape and shading information. But, the shape-from-shading method is an ill-posed problem because formulating the fundamental relation alone cannot determine the unique surface orientation from one shading measurement. To solve this particular problem and recover shape, therefore, we must take into account the object properties as constraint conditions for the shape reconstruction and formulate the problem based on these conditions. Accordingly, what is going to be important in solving the problem associated with the shape-from-shading method are what object to use as a target, what properties to use to recover its shape, and how to formulate the relation between shape and shading. The object properties are classified into two types; the photometric and geometric properties. In this study, we pick up two objects whose properties differ with each other as the targets for the shape reconstruction with the use of an image scanner. One of the objects is unfolded book surface and the other, the arbitrary 3D shape whose albedo on the surface is constant like a plaster figure. Since the book surface shape is simple in terms of cross section and is assumed to be a smooth curved one, naturally it leads to the recovery of a simpler 2D cross section shape than 3D shape. However, book surface, because of the interreflections and the non-uniform albedo distribution, presents complex photometric properties. On the other hand, as for the arbitrary 3D shape reconstruction, no-interreflections and a Lambertian surface with constant albedo are assumed. Hence, its photometric properties are simpler than book surface, whereas its geometric properties are complex because there are no constraints for its shape. In this study, we are going to examine shape reconstruction methods for two targets as described above. To estimate any object shape from its shading information, we must formulate the relation between the shape and its shading. The fundamental model of this relation is a physically-based one concerning the brightness at a certain point on the surface. However, coupled with object properties, the light source in an image scanner is modeled as the linear light source, which naturally complexes the reflectance model. Hence, when