shapefrom

Shape from is a term used in computer vision and graphics to describe a family of methods for reconstructing the three-dimensional shape of a scene or object from two-dimensional observations. The common goal is to infer geometry that is not directly visible in a single image by exploiting cues such as shading, texture, silhouettes, motion, or combinations of these. The umbrella term covers several subfields, including shape from shading, shape from texture, shape from silhouettes (visual hull), shape from motion (structure from motion), as well as related approaches in stereo and photometric methods.

Shape from shading derives surface orientation from variations in image brightness caused by lighting and surface curvature. With a reflectance model (often Lambertian) and known lighting, local surface normals can be estimated and integrated to recover depth. This approach is intrinsically ill-posed and sensitive to non-Lambertian materials, shadows, and lighting uncertainty.

Shape from texture uses patterns on a surface to infer its orientation and depth from perspective-induced distortions or texture scaling. It requires a detectable, regular texture and some knowledge of the camera parameters; otherwise, depth estimates can be ambiguous.

Shape from silhouettes, or visual hull reconstruction, uses object outlines from multiple views to generate a volume that is consistent with all silhouettes. It yields a coarse approximation of shape and cannot reveal internal structure or concavities not visible in any silhouette.

Shape from motion leverages parallax across several images to estimate camera motion and reconstruct 3D structure. It typically produces a sparse or dense 3D model up to a scale and is robust to lighting changes but depends on accurate feature matching and motion estimation.

Applications include robotics, cultural heritage digitization, 3D modeling, and medical imaging. Limitations include assumptions about lighting, texture, and object rigidity, plus sensitivity to noise and occlusions.