1. 3D Vision

2. 3D Perception: Illusions Block & Yuker

3. 3D Perception: Illusions Block & Yuker

4. 3D Perception: Illusions Block & Yuker

5. 3D Perception: Illusions Block & Yuker

6. 3D Perception: Illusions Block & Yuker

7. 3D Perception: Illusions Block & Yuker

8. 3D Perception: Illusions Block & Yuker

9. 3D Perception: Illusions Block & Yuker

10. 3D Perception: Illusions Block & Yuker

11. 3D Perception: Illusions Block & Yuker

12. 3D Perception: Conclusions Perspective is assumedPerspective is assumed Relative depth orderingRelative depth ordering Occlusion is importantOcclusion is important Local consistencyLocal consistency

13. 3D Perception: Stereo Experiments show that absolute depth estimation not very accurateExperiments show that absolute depth estimation not very accurate – Low “relief” judged to be deeper than it is Relative depth estimation very accurateRelative depth estimation very accurate – Can judge which object is closer for stereo disparities of a few seconds of arc

14. 3D Computer Vision Accurate (or not) shape reconstructionAccurate (or not) shape reconstruction SegmentationSegmentation Easier (?) to match in 3D than in 2DEasier (?) to match in 3D than in 2D – Occlusion – Shading – Smaller database of examples

15. 3D Data Types Point DataPoint Data Volumetric DataVolumetric Data Surface DataSurface Data

16. 3D Data Types: Point Data “Point clouds”“Point clouds” Advantage: simplest data typeAdvantage: simplest data type Disadvantage: no information on adjacency / connectivityDisadvantage: no information on adjacency / connectivity

17. 3D Data Types: Volumetric Data Regularly-spaced grid in (x,y,z): “voxels”Regularly-spaced grid in (x,y,z): “voxels” For each grid cell, storeFor each grid cell, store – Occupancy (binary: occupied / empty) – Density – Other properties Popular in medical imagingPopular in medical imaging – CAT scans – MRI

18. 3D Data Types: Volumetric Data Advantages:Advantages: – Can “see inside” an object – Uniform sampling: simpler algorithms Disadvantages:Disadvantages: – Lots of data – Wastes space if only storing a surface – Most “vision” sensors / algorithms return point or surface data

19. 3D Data Types: Surface Data PolyhedralPolyhedral – Piecewise planar – Polygons connected together – Most popular: “triangle meshes” SmoothSmooth – Higher-order (quadratic, cubic, etc.) curves – Bézier patches, splines, NURBS, subdivision surfaces, etc.

20. 3D Data Types: Surface Data Advantages:Advantages: – Usually corresponds to what we see – Usually returned by vision sensors / algorithms Disadvantages:Disadvantages: – How to find “surface” for translucent objects? – Parameterization often non-uniform – Non-topology-preserving algorithms difficult

21. 3D Data Types: Surface Data Implicit surfaces (cf. parametric)Implicit surfaces (cf. parametric) – Zero set of a 3D function – Usually regularly sampled (voxel grid) Advantage: easy to write algorithms that change topologyAdvantage: easy to write algorithms that change topology Disadvantage: wasted space, timeDisadvantage: wasted space, time

22. 2½-D Data Image: stores an intensity / color along each of a set of regularly-spaced rays in spaceImage: stores an intensity / color along each of a set of regularly-spaced rays in space Range image: stores a depth along each of a set of regularly-spaced rays in spaceRange image: stores a depth along each of a set of regularly-spaced rays in space Not a complete 3D description: does not store objects occluded (from some viewpoint)Not a complete 3D description: does not store objects occluded (from some viewpoint) View-dependent scene descriptionView-dependent scene description

23. 2½-D Data This is what most sensors / algorithms really returnThis is what most sensors / algorithms really return AdvantagesAdvantages – Uniform parameterization – Adjacency / connectivity information DisadvantagesDisadvantages – Does not represent entire object – View dependent

24. 2½-D Data Range imagesRange images Range surfacesRange surfaces Depth imagesDepth images Depth mapsDepth maps Height fieldsHeight fields 2½-D images2½-D images Surface profilesSurface profiles xyz maps xyz maps …

25. Range Acquisition Taxonomy Range acquisition Contact Transmissive Reflective Non-optical Optical Industrial CT Mechanical (CMM, jointed arm) Radar Sonar Ultrasound MRI Ultrasonic trackers Magnetic trackers Inertial (gyroscope, accelerometer)

26. Range Acquisition Taxonomy Optical methods Passive Active Shape from X: stereomotionshadingtexturefocusdefocus Active variants of passive methods Stereo w. projected texture Active depth from defocus Photometric stereo Time of flight Triangulation

27. Optical Range Acquisition Methods Advantages:Advantages: – Non-contact – Safe – Usually inexpensive – Usually fast Disadvantages:Disadvantages: – Sensitive to transparency – Confused by specularity and interreflection – Texture (helps some methods, hurts others)

28. Stereo Find feature in one image, search along epipole in other image for correspondenceFind feature in one image, search along epipole in other image for correspondence

29. Stereo Advantages:Advantages: – Passive – Cheap hardware (2 cameras) – Easy to accommodate motion – Intuitive analogue to human vision Disadvantages:Disadvantages: – Only acquire good data at “features” – Sparse, relatively noisy data (correspondence is hard) – Bad around silhouettes – Confused by non-diffuse surfaces Variant: multibaseline stereo to reduce ambiguityVariant: multibaseline stereo to reduce ambiguity

30. Shape from Motion “Limiting case” of multibaseline stereo“Limiting case” of multibaseline stereo Track a feature in a video sequenceTrack a feature in a video sequence For n frames and f features, have 2  n  f knowns, 6  n +3  f unknownsFor n frames and f features, have 2  n  f knowns, 6  n +3  f unknowns

31. Shape from Motion Advantages:Advantages: – Feature tracking easier than correspondence in far- away views – Mathematically more stable (large baseline) Disadvantages:Disadvantages: – Does not accommodate object motion – Still problems in areas of low texture, in non-diffuse regions, and around silhouettes

32. Shape from Shading Given: image of surface with known, constant reflectance under known point lightGiven: image of surface with known, constant reflectance under known point light Estimate normals, integrate to find surfaceEstimate normals, integrate to find surface Problem: ambiguityProblem: ambiguity

33. Shape from Shading Advantages:Advantages: – Single image – No correspondences – Analogue in human vision Disadvantages:Disadvantages: – Mathematically unstable – Can’t have texture “Photometric stereo” (active method) more practical than passive version“Photometric stereo” (active method) more practical than passive version

34. Shape from Texture Mathematically similar to shape from shading, but uses stretch and shrink of a (regular) textureMathematically similar to shape from shading, but uses stretch and shrink of a (regular) texture

35. Shape from Texture Analogue to human visionAnalogue to human vision Same disadvantages as shape from shadingSame disadvantages as shape from shading

36. Shape from Focus and Defocus Shape from focus: at which focus setting is a given image region sharpest?Shape from focus: at which focus setting is a given image region sharpest? Shape from defocus: how out-of-focus is each image region?Shape from defocus: how out-of-focus is each image region? Passive versions rarely usedPassive versions rarely used Active depth from defocus can be made practicalActive depth from defocus can be made practical

37. Active Optical Methods Advantages:Advantages: – Usually can get dense data – Usually much more robust and accurate than passive techniques Disadvantages:Disadvantages: – Introduces light into scene (distracting, etc.) – Not motivated by human vision

38. Terminology Range acquisition, shape acquisition, rangefinding, range scanning, 3D scanningRange acquisition, shape acquisition, rangefinding, range scanning, 3D scanning Alignment, registrationAlignment, registration Surface reconstruction, 3D scan merging, scan integration, surface extractionSurface reconstruction, 3D scan merging, scan integration, surface extraction 3D model acquisition3D model acquisition

39. Related Fields Computer VisionComputer Vision – Passive range sensing – Rarely construct complete, accurate models – Application: recognition MetrologyMetrology – Main goal: absolute accuracy – High precision, provable errors more important than scanning speed, complete coverage – Applications: industrial inspection, quality control, as-built models

40. Related Fields Computer GraphicsComputer Graphics – Often want complete model – Low noise, geometrically consistent model more important than absolute accuracy – Application: animated CG characters