Determining Cylindrical Shape from Contour and Shading

1 . I N T R O D U C T I O N Recent studies on computer vision have exploited many methods for interpret ing a brightness pattern in an image as a shape in 3-D space using physical constraints on the l ight source, object class, surface properties of the object and mul t i ­ ple views (Brady 1975) Especially, contour and shading in the image have a very impor tant role in recovering surface shape in both computer vision and human perception (Marr 1982). Shape f rom shading methods obtain surface properties by exploit ing photometric constraints on the image formation process (Horn 1975, Woodham 1977) The diff iculty in these methods is to characterize the l ighting geometry, because most of them cannot recover the surface shape unless the l ight ing conditions are given. Al though Pentland (Pentland 1984) has tried to extract information on shape locally wi thout knowing the l ight ing conditions, his method requires strong assump­ tions, e.g. that the surface is spherical. Interpretat ion of line drawings has been one focal point of vision work, and there are successful results in the polyhedral world (Mackworth 1973, Huffman 1977 and Sugihara 1984). Outside this wor ld, only qual i tat ive description is obtained (Barrow and Tenebaum 1981, Mar r 1977), such as extremal boundaries and sur­ face discontinuit ies, or a strong assumption is necessary to recover the surface or ientat ion, e.g. the extremum principle (Brady and Yui l le 1984). The first quanti tat ive approach to recovering surface shape f rom contour and shading was developed by Horn (Horn 1977). In his method, the reflectance This work was supported by the Defense Advanced Research Projects Agency and the U S Army Center for Night Vision and Electro-Optics under Grant DAAB07-85-K-F073 •Permanent address Department of Control Engineering, Osaka University, Toyonaka, Osaka 560, Japan map is effectively used to infer the surface normals of the planes of a block in gradient space. Also Ikeuchi and Horn (Ikeuchi and Horn 1981) used the occluding boundaries as boundary condit ions on their relaxation method to infer the surface structure. Both methods, however, assume that the the l ight ing condit ions and the surface albedo are known. In those methods, the surface type is planar (in the polyhedral world) or doubly curved (for shading analysis). Between them is the class of objects that have singly curved surfaces. The most representative object in this class is a cyl indrical object which can be often seen in daily life. Cyl indr ical models have been popular for describing many kinds of objects in terms of generalized cylinders since Binford (Binford 1971) introduced them as a useful method of volume description for 3-D objects. A l though several papers have been published which at tempt to describe cyl indrical shape parameters f rom range data (Nevat ia and Binford 1977, Rao and Nevat ia 1986) or which examine geometrical properties of gen­ eralized cylinders w i th shadows and occluding boundaries (Shafer 1983), there are few papers dealing wi th the problem of reconstructing cyl indrical shapes from images. Asada et al. (Asada and Tsu j i 1983a,b) proposed two approaches to recon­ struct ing a cyl indrical shape f rom the viewpoint of dynamic scene analysis. One approach is to analyze shading information to obtain the normals of surfaces, which are useful for finding the correspondence of base planes between consecutive frames. Local shading analysis (Pentland 1984) is not applicable to estimating the normal at a point on a cyl indrical surface unless the l ight ing conditions are known. W i t h knowledge of the l ight ing conditions, the motion between frames can be deter­ mined by the extended reflectance map method. The other approach is to analyze changes in contour shape between frames. If the base planes of an object are perpendicular to its cyl indrical surface, the 3-D geometry of the object can be recovered f rom two views. The first approach cannot recon­ struct the cyl indrical shape w i thou t knowledge of the l ight ing conditions; the second approach needs two frames and assumes perpendicularity of the base plane to the cyl indrical surface. We consider the image understanding problem of infer­ r ing the shape of a cyl indrical object f rom an image such as Figure 1. Th is paper presents a new method which determines the shape of a cyl indrical object using the contour of the base plane and the intensities on the cyl indrical surface wi thout knowledge about the l ight ing condit ions of the scene or the albedo. Local shading analysis enables us to segment the input image in to planar, cyl indr ical and spherical surfaces and tells us the direction of the generating line f rom which the cyl indr i­ cal surface is produced. The brightest generating line, like singular points and occluding boundaries which play a impor­ tant role in shape f rom shading methods (Ikeuchi and Horn 1981, Brooks and Horn 1985), provides strong constraints on