1. Vision: Inferring Information from Clues
Outline:
Stereo vision as an AI problem
Stereograms
Geometry of stereograms
Computing correspondences
Letting cues vote for hypotheses
Polar representation of a line
Hough transform
Gestalt grouping
CSE (c) S. Tanimoto, Inference in Vision

2. Stereo Vision as an AI Problem
Projection from 3 dimension to 2 loses information.
With 2 projections, we can gain back some of that information.
Recovering the missing information is an inference problem.
The missing information is constrained by knowledge about the real world and assumptions about the scene.
The use of knowledge and assumptions to make inferences is a standard approach in artificial intelligence.
CSE (c) S. Tanimoto, Inference in Vision

3. CSE 415 -- (c) S. Tanimoto, 2002 Inference in Vision
Stereograms
Two-view stereograms:
1. spatially separated left-eye/right-eye pair
(including virtual-reality goggles)
2. superimposed, with separation using color filters.
3. superimposed, with temporal shuttering.
4. superimposed, with separation using polarizing filters.
Single-view stereograms:
1. Magic-eye pictures with depth-modulated carrier.
2. Wallpaper offering depth effects due to its periodicity.
CSE (c) S. Tanimoto, Inference in Vision

4. Geometry of Stereograms
CSE (c) S. Tanimoto, Inference in Vision

5. Computing Correspondence
Approach 1: Extract features and find a consistent matching of features in each view.
Approach 2: Directly compute a disparity map, performing local correlations of the views.
CSE (c) S. Tanimoto, Inference in Vision

6. Inferring Trends via Voting Methods
The classical Hough Transform identifies prominent lines in a scene by letting each edge point vote for the line(s) it is on.
Voting methods can do well under noisy conditions.
Votes are tallied in an array of accumulators, indexed by theta and rho (polar parameters of a line).
ρ = x cos θ + y sin θ.
CSE (c) S. Tanimoto, Inference in Vision

7. Letting a Point Vote for all the Lines that Pass Through It
CSE (c) S. Tanimoto, Inference in Vision

8. Hough Transform: Polar representation
ρ = x cos θ + y sin θ.
(x, y) ρ
(0, 0) θ
CSE (c) S. Tanimoto, Inference in Vision

9. Hough Transform (Cont.)
nondirectional, unweighted Hough Transform:
H(θ,ρ) = Σ Σ f(x,y) δ(x cos θ + y sin θ - ρ).
δ(x) = if | x | < 1
otherwise
CSE (c) S. Tanimoto, Inference in Vision

10. CSE 415 -- (c) S. Tanimoto, 2002 Inference in Vision
Gestalt Grouping
CSE (c) S. Tanimoto, Inference in Vision

11. CSE 415 -- (c) S. Tanimoto, 2002 Inference in Vision
Gestalt Grouping
Texture element = “texel”
Texel directionality
Texel granularity
Alignments of endpoints
Spacing of texels
Groups cue for surfaces, objects.
CSE (c) S. Tanimoto, Inference in Vision