1. MSU CSE 803 Stockman1 CV: Perceiving 3D from 2D Many cues from 2D images enable interpretation of the structure of the 3D world producing them

2. MSU CSE 803 Stockman2 Topic roadmap Labeling 3D structure in a 2D image Labeling constraints on edge graphs Huffman-Clowes-Waltz labeling Other cues motion parallax shape from texture or shading stereo from two 2d images

3. MSU CSE 803 Stockman3 Topic roadmap: mathematical models Shape from shading Depth from stereo Depth from focus Perspective transformation (review)

4. MSU CSE 803 Stockman4 Many 3D cues How can humans and other machines reconstruct the 3D nature of a scene from 2D images? What other world knowledge needs to be added in the process?

5. MSU CSE 803 Stockman5 Vocabulary for image labeling Interpret the local structure of the scene in the image space

6. MSU CSE 803 Stockman6 Some terms for local 3D structure Crease: (convex + or concave -) formed by an abrupt change to a surface or the joining of two surfaces. Surface on both sides of the crease can be sensed Blade: ( > ) as in the blade of a knife, where the normal to the occluding surface element. Occluding and occluded surfaces unrelated. (left) intensity image of 3 blocks (right) result of 5x5 Prewitt operator

7. MSU CSE 803 Stockman7 Limb: smooth object contour Limb: (>>) formed by viewing a smooth 3D object, such as an arm or a soup can: when approaching the contour, the surface normal becomes perpendicular to the line of sight. (Right side of arrow is the occluding surface.) egg Soup can

8. MSU CSE 803 Stockman8 Albedo and lighting mark: (M) surface mark or change of “albedo” (reflectance) and not the 3d surface, creating an intensity contour in the image shading: (S) illumination change due to a change in lighting or shadow on the surface, creating an intensity contour in the image

9. MSU CSE 803 Stockman9 Labeling image contours interprets the 3D scene structure + An egg and a thin cup on a table top lighted from the top right Logo on cup is a “mark” on the material “shadow” relates to illumination, not material

10. MSU CSE 803 Stockman10 “Intrinsic Image” stores 3D info in “pixels” and not intensity. For each point of the image, we want depth to the 3D surface point, surface normal at that point, albedo of the surface material, and illumination of that surface point.

11. MSU CSE 803 Stockman11 Practice labeling the contours (left) an unopened can of Brand X soda is a solid blue can with a bright orange block ‘X’. (right) an empty box with all four flaps open so even the bottom of the box is visible.

12. MSU CSE 803 Stockman12 3D scene versus 2D image Creases Corners Faces Occlusions (for some viewpoint) Edges Junctions Regions Blades, limbs, T’s

13. MSU CSE 803 Stockman13 Labeling of simple polyhedra Labeling of a block floating in space. BJ and KI are convex creases. Blades AB, BC, CD, etc model the occlusion of the background. Junction K is a convex trihedral corner. Junction D is a T- junction modeling the occlusion of blade CD by blade JE.

14. MSU CSE 803 Stockman14 Trihedral Blocks World Image Junctions: only 16 cases! Only 16 possible junctions in 2D formed by viewing 3D corners formed by 3 planes and viewed from a general viewpoint! From top to bottom: L-junctions, arrows, forks, and T-junctions.

15. MSU CSE 803 Stockman15 Challenge ! Create a scene shot of no more than 2 blocks that creates all 16 junctions in the image

16. MSU CSE 803 Stockman16 How do we obtain the catalog? think about solid/empty assignments to the 8 octants about the X-Y-Z-origin think about non-accidental viewpoints account for all possible topologies of junctions and edges then handle T-junction occlusions

17. MSU CSE 803 Stockman17 Blocks world labeling Left: block floating in space Right: block glued to a wall at the back

18. MSU CSE 803 Stockman18 Try labeling these: interpret the 3D structure, then label parts What does it mean if we can’t label them? If we can label them?

19. MSU CSE 803 Stockman19 Waltz filtering discards edge interpretations spanning junctions

20. MSU CSE 803 Stockman20 1975 researchers very excited very strong constraints on interpretations several hundred in catalogue when cracks and shadows allowed (Waltz): algorithm works very well with them but, world is not made of blocks! later on, curved blocks world work done but not as interesting

21. MSU CSE 803 Stockman21 Backtracking or interpretation tree

22. MSU CSE 803 Stockman22 Interpretation tree search

23. MSU CSE 803 Stockman23 “Necker cube” has multiple interpretations A human staring at one of these cubes typically experiences changing interpretations. The interpretation of the two forks (G and H) flip-flops between “front corner” and “back corner”. What is the explanation? Label the different interpretations

24. MSU CSE 803 Stockman24 Depth cues in 2D images

25. MSU CSE 803 Stockman25 “Interposition” cue Def: Interposition occurs when one object occludes another object, thus indicating that the occluding object is closer to the viewer than the occluded object.

26. MSU CSE 803 Stockman26 interposition T-junctions indicate occlusion: top is occluding edge while bar is the occluded edge Bench occludes lamp post leg occludes bench lamp post occludes fence railing occludes trees trees occlude steeple

27. MSU CSE 803 Stockman27 Perspective scaling: railing looks smaller at the left; bench looks smaller at the right; 2 steeples are far away Forshortening: the bench is sharply angled relative to the viewpoint; image length is affected accordingly

28. MSU CSE 803 Stockman28 Texture gradient reveals surface orientation Texture Gradient: change of image texture along some direction, often corresponding to a change in distance or orientation in the 3D world containing the objects creating the texture. ( In East Lansing, we call it “corn” not “maize’. ) Note also that the rows appear to converge in 2D

29. MSU CSE 803 Stockman29 3D Cues from Perspective

30. MSU CSE 803 Stockman30 3D Cues from perspective

31. MSU CSE 803 Stockman31 More 3D cues Virtual linesFalsely perceived interposition

32. MSU CSE 803 Stockman32 More 3D cues 2D alignment usually means 3d alignment 2D image curves create perception of 3D surface

33. MSU CSE 803 Stockman33 “structured light” can enhance surfaces in industrial vision Sculpted object Potatoes with light stripes

34. MSU CSE 803 Stockman34 Shape (normals) from shading Cylinder with white paper and pen stripes Intensities plotted as a surface Clearly intensity encodes shape in this case

35. MSU CSE 803 Stockman35 Shape (normals) from shading Plot of intensity of one image row reveals the 3D shape of these diffusely reflecting objects.