CSE 185 Introduction to Computer Vision

1. CSE 185 Introduction to Computer Vision Stereo

2. Multiple views • Taken at the same time or sequential in time • stereo vision • structure from motion • optical flow

3. Why multiple views? • Structure and depth are inherently ambiguous from single views.

4. Why multiple views? • Structure and depth are inherently ambiguous from single views. P1 P2 P1’=P2’ Optical center

5. Shape from X • What cues help us to perceive 3d shape and depth? • Many factors • Shading • Motion • Occlusion • Focus • Texture • Shadow • Specularity • …

6. Shading For static objects and known light source, estimate surface normals

7. Focus/defocus Images from same point of view, different camera parameters far focused near focused 3d shape / depth estimates estimated depth map

8. Texture estimate surface orientation

9. Perspective effects perspective, relative size, occlusion, texture gradients contribute to 3D appearance of the scene

10. Motion Motion parallax: as the viewpoint moves side to side, the objects at distance appear to move slower than the ones close to the camera

11. Occlusion and focus

12. Estimating scene shape “Shape from X”: Shading, Texture, Focus, Motion… Stereo: shape from motion between two views infer 3d shape of scene from two (multiple) images from different viewpoints scene point Main idea: image plane optical center

13. Outline • Human stereopsis • Stereograms • Epipolar geometry and the epipolar constraint • Case example with parallel optical axes • General case with calibrated cameras

14. Human eye Rough analogy with human visual system: Pupil/Iris – control amount of light passing through lens Retina - contains sensor cells, where image is formed Fovea – highest concentration of cones

15. Human eyes fixate on point in space – rotate so that corresponding images form in centers of fovea. Human stereopsis: disparity

16. Human stereopsis: disparity Disparity occurs when eyes fixate on one object; others appear at different visual angles

17. Random dot stereograms Julesz 1960: Do we identify local brightness patterns before fusion (monocular process) or after (binocular)? To test: pair of synthetic images obtained by randomly spraying black dots on white objects

18. Random dot stereograms

19. Random dot stereograms 1. Create an image of suitable size. Fill it with random dots. Duplicate the image. 2. Select a region in one image. 3. Shift this region horizontally by a small amount. The stereogram is complete.

20. Random dot stereograms When viewed monocularly, they appear random; when viewed stereoscopically, see 3d structure. Conclusion: human binocular fusion not directly associated with the physical retinas; must involve the central nervous system Imaginary “cyclopean retina”that combines the left and right image stimuli as a single unit High level scene understanding not required for Stereo

21. Invented by Sir Charles Wheatstone, 1838 Stereo photograph and viewer Take two pictures of the same subject from two slightly different viewpoints and display so that each eye sees only one of the images. Image from fisher-price.com

22. http://www.johnsonshawmuseum.org

23. http://www.johnsonshawmuseum.org

24. Public Library, Stereoscopic Looking Room, Chicago, by Phillips, 1923

25.  present stereo images on the screen by simply putting the right and left images in an animated gif http://www.well.com/~jimg/stereo/stereo_list.html

26. Autostereograms Exploit disparity as depth cue using single image. (Single image random dot stereogram, Single image stereogram)

27. Autosteoreogram Designed to create the visual illusion of a 3D scene Using smooth gradients

28. Stereo: shape from motion between two views We’ll need to consider: Info on camera pose (“calibration”) Image point correspondences Estimating depth with stereo scene point image plane optical center

29. Stereo vision Two cameras, simultaneous views Single moving camera and static scene

30. Camera frame 1 Camera parameters Camera frame 2 Extrinsic parameters: Camera frame 1  Camera frame 2 Intrinsic parameters: Image coordinates relative to camera  Pixel coordinates • Extrinsic params: rotation matrix and translation vector • Intrinsic params: focal length, pixel sizes (mm), image center point, radial distortion parameters We’ll assume for now that these parameters are given and fixed.

31. Outline • Human stereopsis • Stereograms • Epipolar geometry and the epipolar constraint • Case example with parallel optical axes • General case with calibrated cameras

32. Geometry for a stereo system • First, assuming parallel optical axes, known camera parameters (i.e., calibrated cameras):

33. World point Depth of p image point (left) image point (right) Focal length optical center (right) optical center (left) baseline

34. Assume parallel optical axes, known camera parameters (i.e., calibrated cameras). What is expression for Z? Geometry for a stereo system Similar triangles (pl, P, pr) and (Ol, P, Or): disparity

35. Depth from disparity image I´(x´,y´) image I(x,y) Disparity map D(x,y) (x´,y´)=(x+D(x,y), y) So if we could find the corresponding points in two images, we could estimate relative depth…

36. Basic stereo matching algorithm • If necessary, rectify the two stereo images to transform epipolar lines into scanlines • For each pixel x in the first image • Find corresponding epipolar scanline in the right image • Examine all pixels on the scanline and pick the best match x’ • Compute disparity x-x’ and set depth(x) = fB/(x-x’)

37. Correspondence search Left Right • Slide a window along the right scanline and compare contents of that window with the reference window in the left image • Matching cost: SSD or normalized correlation scanline Matching cost

38. Correspondence search Left Right scanline SSD

39. Correspondence search Left Right scanline Norm. corr

40. Effect of window size W = 3 W = 20 • Smaller window + More detail • More noise • Larger window + Smoother disparity maps • Less detail

41. Failures of correspondence search Occlusions, repetition Textureless surfaces Non-Lambertian surfaces, specularities

42. Results with window search Data Window-based matching Ground truth

43. Beyond window-based matching • So far, matches are independent for each point • What constraints or priors can we add?

44. Summary • Depth from stereo: main idea is to triangulate from corresponding image points. • Epipolar geometry defined by two cameras • We’ve assumed known extrinsic parameters relating their poses • Epipolar constraint limits where points from one view will be imaged in the other • Makes search for correspondences quicker • Terms: epipole, epipolar plane / lines, disparity, rectification, intrinsic/extrinsic parameters, essential matrix, baseline