trellis-based parallel stereo matching

Media Processor Lab.Media Processor Lab.

Trellis-based Parallel Stereo Matching

2007. 4. 9.Media Processor Lab. Sejong univ.

E-mail : [email protected] Kim

# 2.Media Processor Lab.Media Processor Lab.

Contents

Introduction Stereo Vision Model Center-referenced space Constraints on disparity Estimating optimal disparity Experimental results Conclusion


Introduction

Stereo vision is an inverse process that attempts to restore the original scene from a pair of images.

In this paper a new basis for disparity based on center-referenced coordinates is presented that is concise and complete in terms of constraint representation.


Stereo Vision Model (1)

Projection Model Assumption : coplanar image planes, parallel optical axes,

equal focal lengths l, and matching epipolar lines The inverse match space I is the finite set of points, repres

ented by solid dots, that are reconstructable by matching image pixels.

Left image scan line : fl = [fl1 ··· fl

N] Right image scan line : fr = [fr

1 ··· frN]


Stereo Vision Model (2)

Representation of Correspondence Each element of each scan line can

have a corresponding element in the other image scan line, denoted (fl

i, frj)

be occluded in the other image scan line, denoted (fli, Ø) for a left

image element (right occlusion) and (Ø, fri) for a right image elem

ent (left occlusion)

Left-referenced disparity map : dl = [dl1 ··· dl

N] Disparity value : dl

i ⇔ (fli, fr

i+dli)

Right-referenced disparity map : dr = [dr1 ··· dr

N] Disparity value : dr

j ⇔ (fli+dr

j ,fr

j)

.


Center-referenced space (1)

Using only left- or right-referenced disparity, it is difficult to represent common matching constraints with respect to both images.

An alternate center-referenced projection The focal point pc located at the midpoint between the foca

l points for the left and right image plane Plane with 2N + 1 and focal length of 2l The projection lines intersect with the horizontal iso-dispar

ity lines forms the inverse space D.



Center-referenced disparity vector d = [d0 ··· d2N] disparity value di indicates the depth index of a real world

point along the projection line from site i on the center image plane

If di is a match point : (fl(i – dj + 1)/2

, fr(i + dj + 1)/2

)

(fli , fr

j) is denoted by the disparity di + j – 1 = j – i

The odd function o(x) is used to indicate if di is a match point, that is o(i + di) = 1 when di is a match point.



Represent occlusions by assigning the highest possible disparity (Fig. 3)

The correspondence (fl

5 , fr

8) creates a right

occlusion for which the real object could lie anywhere in the triangular Right Occlusion Region (ROR)

If only I is used, then the match points (solid dots) in the ROR are used.

D contains additional occlusion points (open dots) in the ROR that are further to the right, which are used instead.


Constraints on disparity

Parallel axes : di ≥ 0

Endpoints : d0 = d2N = 0

Cohesiveness : di – di – 1 ∈ {–1, 0, 1}

Uniqueness : o(i + di) = 1⇒ di–1 = di = di+1


Estimating optimal disparity DP techniques progressing through the trellis from left to right (site i = 0,

…, 2N). In recursive form, the shortest path algorithm for disparity is formally given by: Initialization : Endpoint has zero disparity

Recursion : At each site i = 1, … 2N, find the best path into each node j. if i+j is even,

otherwise

Termination : i = 2N and j = 0.

Reconstruction : Backtrack the decisions..


Experimental results


Conclusion

We have used a center-referenced projection to represent the discrete inverse space for stereo correspondence.

This space D contains additional occlusion points which we exploit to create a concise representation of correspondence and occlusion.

The algorithm was tested on both real and synthetic image pairs with good results.

trellis-based parallel stereo matching

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