Obtaining 3-D shape from Silhouette Informations Interpolated by Photometric Stereo

The idea of photometric stereo is to serially vary the direction of incident illumination on the state of the holded view point, but it can locally reconstruct only the front surface to a view point. However the silhouette informations obtained by plural viewing directions provide the entire 3D structure of an object surface, but the 3D information of the region whose edge is unexposed to the viewing direction cannot be obtained. Therefore the two methods make up the demerits each other. In this paper, the possibility of complete three dimensional shape reconstruction was investigated using photometric stereo and silhouette informations. For the entire 3D reconstruction, a chicken bone is used as an experimental object and the reconstructed result is presented and discussed. the other hand, the stereo pair matching by two camera is not a completed method because its running cost and the unstable matching algorithm. The photometric stereo method [6][7][8] can offer the continuous depth informations of surface as pixel unit, so that it can level up the precision locally in accordance with the magnification of lenz of CCD camera, and needs the simple equipments comparing other methods. But its demerit is that it has the possibility to get a twisted result due to specular reflection and the cumulation process for depth conversion. Otherwise the silhouette information can offer a stable and precise result only to the edges exposed to viewer 191. It means that the twisted result obtained by the photometric stereo can be corrected by the silhouette informations. It is the reason we use the photometric stereo and silhouette information. INTRODUCTION SILHOUETTE In accordance with the development of computerized automatic manufacturing, more and more increases the need for sensing and reconstructing 3 dimensional structure. Many traditional method for 3D sensing and reconstruction thereby have been developed and presented in the field of computer vision and sensing, such as the methods scanning slit ray beam [I], interpreting the patterns projected 121131 and using stereo pair images by 2 cameras on the basis of principle of triangulation [4][5]. The methods using slit ray beam have the merit of which can produce precise result but it needs the complex and expensive equipments comparing the proposed method of this paper and has the difficulty to match the discreted slit lines on a very indented irregular surface. The methods interpreting the projected patterns such as binary encoded light pattern, grid pattern and the moire method offer the stable reconstructed results but the resolution depends on the width of a projected pattern or a contour line, especially in the reconstruction using imThe silhouette information from a view point includes partly the 3D information of an object as an edge information of 2D projected image. Therefore the silhouette informations obtained by plural viewing directions include 3D informations reconstructed by the edges exposed t o the viewing points. The line of sight passing through the edge of silhouette is othgonal to the surface normal of an object if it has smooth surface. Assuming a point (X(0, ye), Z(0, ye)) represents an edge point of the silhouette rotated with viewing direction of azimuth 0 on an height ye, and (x,, ze) represent an edge point of silhouette on image plane, the point can be computed as Then the function of line of sight LF(x, z : ye, 0) to the point (X(0, ye), Z(0, ye)) can be computed as, ages obtained CCD camera the precision goes down. It LF(x,z : Y, 0) = {(xrf, zlf)lxrf = 2, . . . is caused by the spacing between patterns or contours, which is needed for intepretation. Also it has the diffiZrf = (-l/tan(O))(x X(0, ye)) + Z(0, ye)). (2) c111ty of interpretation caused by the discrete lines. On where x represents all x values on image plane.