Technical Reports

UBC CS TR-85-13 Summary

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Coaxial Stereo \& Scale Based Matching'', September 1985 Itzhak Katz

The past decade has seen a growing interest in {\em computer stereo vision}: the recovery of the depth map of a scene from two-dimensional images. The main problem of computer stereo is in establishing correspondence between features or regions in two or more images. This is referred to as the {\em correspondence problem}.

One way to reduce the difficulty of the above problem is to constrain the {\em camera modeling}. Conventional stereo systems use two or more cameras, which are positioned in space at a uniform distance from the scene. These systems use {\em epipolar geometry} for their camera modeling, in order to curb the search space to be one-dimensional --- along {\em epipolar lines}.

Following Jain's approach, this thesis exploits a non-conventional camera modeling: the cameras are positioned in space one behind the other, such that their optical axes are collinear (hence the name {\em coaxial stereo}), and their distance apart is known. This approach complies with a simple case of epipolar geometry which further reduces the magnitude of the correspondence problem.

The displacement of the projection of a stationary point occurs along a {\em radial line}, and depends only on its spatial depth and the distance between the cameras. Thus, to simplify (significantly) the recovery of depth from {\em disparity}, complex logarithmic mapping is applied to the original images. The logarithmic part of the transformation introduces great distortion to the image's resolution. Therefore, to minimize this distortion, it is applied to the features used in the matching process.

The search for matching features is conducted along radial lines. Following Mokhtarian and Mackworth's approach, a {\em scale-space} image is constructed for each radial line by smoothing its intensity profile with a {\em Gaussian filter} and finding {\em zero-crossings} in the second derivative at varying scale levels. Scale-space images of corresponding radial lines are then matched, based on a modified uniform cost algorithm. The matching algorithm is written with generality in mind. As a consequence, it can be easily adopted to other stereoscopic systems.

Some new results on the structure of scale-space images of one dimensional functions are presented.