A Theory of Shape by Space Carving

Kiriakos N. Kutulakos  Department of Computer Science and Department of Dermatology, University of

Rochester, Rochester, NY

Steven M. Seitz  The Robotics Institute, Carnegie Mellon University, Pittsburgh

Published at theSpecial Issue on Genomic Signal Processing, 2000.

Problem Statement

• Assuming:– Arbitrary (known) camera placement.– Arbitrary scene shape.– Arbitrary scene texture, color and background.– Lambertian.

• Input: N photographs of a scene

• Output: 3D structure of the scene

Context

• Traditional Approach to 3D Reconstruction– Correspondence based

“Many scenes can account for the input images”

Shape by Space Carving

• Scene or volume based

• No correspondences needed!

Picture-Shape Constraint

Photo Hull

• Definition: Maximal volume, V, reproducing all possible silhouettes of an object, S, from viewing region R.

R

S V

Photo Hull in 3D

Shape by Space Carving

• Given a volume containing the object, iteratively carves it out until it converges to the Photo Hull.

Shape by Space Carving Analogy

Shape by Space Carving

True Scene Reconstruction

Least-Commitment Recovery

Carving outHow to decide if a certain voxel belongs to the Photo Hull?

C o n s i s t e

n c y

ConsistencyRendering colored voxels from input viewpoints reproduces original images.

Point photo-consistent: A point (voxel) that can be assigned a color consistent with its projection in all visible cameras.

shape

Consistency (cont.)

Shape Photo-consistent: A shape for which all surface points are photo-consistent.

Photo-Hull: Union of all photo-consistent subsets of initial volume.

VPhoto-hull of V

Photo-consistent subsets of V

Proposed Algorithm

1. Initialize the volume containing the shape;

2. Analyze each visible voxel for point consistency (plane sweep strategy);

3. Repeat step 2 until no voxel is found inconsistent;

4. Merge photo consistent subsets.

Plane Sweep Strategy

Sequence of plane sweeps along 6 principle directions.

Only cameras behind the sweep plane are used for consistency checking.

Experimental Results

Experimental Results

Experimental Results

Experimental Results

Space Carving Discussion

• Least-commitment Reconstruction– No a-priori constraints– Flexible acquisition– Insensitivity to occlusion– Efficient– Scalable

• Setup– Camera calibration– Sensitivity to specularities and transparencies