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# From Images to Voxels

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SIGGRAPH 2000 Course on 3D Photography From Images to Voxels Steve Seitz Carnegie Mellon University University of Washington http www cs cmu edu seitz 3D Reconstruction from Calibrated Images Scene Volume V Input Images Calibrated Goal Determine transparency radiance of points in V Discrete Formulation Voxel Coloring Discretized Scene Volume Input Images Calibrated Goal Assign RGBA values to voxels in V photo consistent with images Complexity and Computability Discretized Scene Volume N C 3 voxels colors True Scene Photo ConsistentAll Scenes C Scenes N3 Issues Theoretical Questions Identify class of all photo consistent scenes Practical Questions How do we compute photo consistent models Voxel Coloring Solutions 1 C 2 silhouettes Volume intersection Martin 81 Szeliski 93 2 C unconstrained viewpoint constraints Voxel coloring algorithm Seitz Dyer 97 3 General Case Space carving Kutulakos Seitz 98 Reconstruction from Silhouettes C 2 Binary Images Approach Backproject each silhouette Intersect backprojected volumes Volume Intersection Reconstruction Contains the True Scene But is generally not the same In the limit get visual hull Complement of all lines that don t intersect S Voxel Algorithm for Volume Intersection Color voxel black if on silhouette in every image O MN3 for M images N3 voxels Don t have to search 2N3 possible scenes Properties of Volume Intersection Pros Easy to implement fast Accelerated via octrees Szeliski 1993 Cons No concavities Reconstruction is not photo consistent Requires identification of silhouettes Voxel Coloring Solutions 1 C 2 silhouettes Volume intersection Martin 81 Szeliski 93 2 C unconstrained viewpoint constraints Voxel coloring algorithm Seitz Dyer 97 3 General Case Space carving Kutulakos Seitz 98 Voxel Coloring Approach 1 2 3 Choose voxel Project and correlate Color if consistent Visibility Problem in which images is each voxel visible The Global Visibility Problem Which points are visible in which images Known Scene Unknown

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