Gratuitous Picture US Naval Artillery Rangefinder from World War I (1918)!!

Gratuitous Picture US Naval Artillery Rangefinder from World War I (1918)!!

Lecture 10: Depth

Computer Vision, Robert Pless All three vectors in the same plane: y x x y

Computer Vision, Robert Pless F is the “fundamental matrix”. Normalized camera system, epipolar equation. “Uncalibrated” Case, epipolar equation:

Stereo image rectification Reproject image planes onto a common plane parallel to the line between camera centers Pixel motion is horizontal after this transformation Two homographies (3x3 transform), one for each input image reprojection  C. Loop and Z. Zhang. Computing Rectifying Homographies for Stereo Vision. IEEE Conf. Computer Vision and Pattern Recognition, 1999.Computing Rectifying Homographies for Stereo Vision

Planar rectification Bring two views to standard stereo setup (moves epipole (on image) to  )

Standard stereo geometry

Actually searching for disparities.

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’)

Matching cost disparity LeftRight scanline Correspondence search 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

LeftRight scanline Correspondence search SSD

LeftRight scanline Correspondence search Norm. corr

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

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

How can we improve window-based matching? So far, matches are independent for each point What constraints or priors can we add?

Stereo constraints/priors Uniqueness – For any point in one image, there should be at most one matching point in the other image

Stereo constraints/priors Uniqueness – For any point in one image, there should be at most one matching point in the other image Ordering – Corresponding points should be in the same order in both views

Stereo constraints/priors Uniqueness – For any point in one image, there should be at most one matching point in the other image Ordering – Corresponding points should be in the same order in both views Ordering constraint doesn’t hold

Priors and constraints Uniqueness – For any point in one image, there should be at most one matching point in the other image Ordering – Corresponding points should be in the same order in both views Smoothness – We expect disparity values to change slowly (for the most part)

Stereo matching, the computer science approach. Optimal path (dynamic programming ) Similarity measure (SSD or NCC) Constraints epipolar ordering uniqueness disparity limit Trade-off Matching cost (data) Discontinuities (prior) Consider all paths that satisfy the constraints pick best using dynamic programming

Energy minimization (Slide from Pascal Fua)

Graph Cut (Slide from Pascal Fua) (general formulation requires multi-way cut!)

(Roy and Cox ICCV‘98) Simplified graph cut

Pop quiz. What are features of a scene that make it hard to get good stereo depth?

To every vision problem, … there is an engineering solution.

Stereo Triangulation IJ Correspondence is hard!

IJ Structured Light Triangulation Correspondence becomes easier!

Digital Michelangelo Project Example: Laser scanner

Binary Coding Pattern 1 Pattern 2 Pattern 3 Projected over time Example: 3 binary-encoded patterns which allows the measuring surface to be divided in 8 sub-regions Faster: stripes in images.

Binary Coding Assign each stripe a unique illumination code over time [Posdamer 82] Space Time

Binary Coding Pattern 1 Pattern 2 Pattern 3 Projected over time Example: 7 binary patterns proposed by Posdamer & Altschuler … Codeword of this píxel:  identifies the corresponding pattern stripe

More complex patterns Zhang et al Works despite complex appearances Works in real-time and on dynamic scenes Need very few images (one or two). But needs a more complex correspondence algorithm

3D computer vision techniques v.4b37 Kinect Another structure light method Use dots rather than strips

3D computer vision techniques v.4b38 Kinect Hardware

3D computer vision techniques v.4b39 See the IR-dots emitted by KINECT