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UCSD CSE 152 - Photometric Stereo and Shape-from-Shading

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1CSE190-B, Spring 2003Computer VisionPhotometric Stereoand Shape-from-ShadingComputer VisionCSE 190-BLecture 12CSE190-B, Spring 2003Computer VisionShading reveals 3-D surface geometryCSE190-B, Spring 2003Computer VisionLighting variationSingle Light SourceCSE190-B, Spring 2003Computer VisionShading reveals shape Basic idea: 3 or more Basic idea: 3 or more images under slightly images under slightly different lightingdifferent lightingCSE190-B, Spring 2003Computer VisionHow people usually do it :1. Get Sufficiently many images (typically 3 – 7) as needed.2. Relate observed intensity with the normal vector field of the object.1. Reflectance Model.2. Integrability condition.3. Integrate the normal vector field to get the depth map. 1. Noisy dataCSE190-B, Spring 2003Computer Vision2CSE190-B, Spring 2003Computer VisionCSE190-B, Spring 2003Computer VisionReflectance Model is encoded in BRDF : (Bi-directional Reflectance Distribution Function)1. A function of four variables : two variables parameterize incoming light and two for outgoing light.2. Depends on lots of things: wavelengths, structural and optical properties of the object .. Etc.3. Normal vector is implicitly used in the definition of BRDF. (the coordinates frame).4. Some interesting properties of BRDF:1. Reciprocity.2. Isotropic BRDF (observed in many objects). CSE190-B, Spring 2003Computer VisionCSE190-B, Spring 2003Computer VisionCSE190-B, Spring 2003Computer VisionImage FormationAt image location (x,y) the intensity of a pixel I(x,y) isI(x,y) = a(x,y) n(x,y) s where• a(x,y) is the albedo of the surface projecting to (x,y).• n(x,y) is the unit surface normal.• s is the direction and strength of the light source.ns.aI(x,y)CSE190-B, Spring 2003Computer Vision3CSE190-B, Spring 2003Computer VisionCSE190-B, Spring 2003Computer VisionCSE190-B, Spring 2003Computer VisionCSE190-B, Spring 2003Computer VisionReflectance Map of Lambertian SurfaceCSE190-B, Spring 2003Computer VisionCSE190-B, Spring 2003Computer VisionTwo Light SourcesEmeasured1Emeasured24CSE190-B, Spring 2003Computer VisionCSE190-B, Spring 2003Computer VisionCSE190-B, Spring 2003Computer VisionReflectance Map of Lambertian + Specular SurfaceCSE190-B, Spring 2003Computer VisionNormal FieldCSE190-B, Spring 2003Computer VisionPlastic Baby Doll: Normal FieldCSE190-B, Spring 2003Computer VisionSurface after integrating normal field5CSE190-B, Spring 2003Computer VisionRenderings of Reconstruction CSE190-B, Spring 2003Computer VisionAttached and Cast ShadowsnCast shadowAttached shadowsn s = 0.CSE190-B, Spring 2003Computer VisionMovie with Attached ShadowsSingle Light SourceFace MovieCSE190-B, Spring 2003Computer VisionMovie with Cast ShadowsSingle Light SourceFace MovieCSE190-B, Spring 2003Computer VisionReconstruction with albedo mapCSE190-B, Spring 2003Computer VisionWithout the albedo map6CSE190-B, Spring 2003Computer VisionAnother personCSE190-B, Spring 2003Computer VisionNo Albedo mapCSE190-B, Spring 2003Computer Vision• If the light sources s1, s2, and s3are known, then we canrecover B from as few as three images x1, x2, and x3. (Photometric Stereo: Silver 80, Woodham81). [x1 x2 x3 ] = B [s1s2 s3] • If the light sources are unknown, we cannot recover B. For any ,Bs = BAA-1s = B*s*where B* = BA, and s* = A-1s.)3(GL∈AWhat if Light source Directions are unknown?CSE190-B, Spring 2003Computer VisionBas-Relief


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UCSD CSE 152 - Photometric Stereo and Shape-from-Shading

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