An Adaptive Window Based Polynomial Fitting Approach for Pixel Matching in Stereo Images

With the advances in 3D technology, digital photogrammetry and computer vision, solving the correspondence problem accurately and efficiently has gained popularity. Locating the position of corresponding pixel in target image for given pixel in reference image is referred as Correspondence problem in stereo-image matching. A number of stereo image matching approaches are available at present, but there has been trade-off between density of match, speed and accuracy. Techniques that are capable of producing dense disparity maps are prone to higher computational complexity thereby, requires longer time, however techniques that are fast are not capable of producing dense disparity maps. On the basis of density of disparity maps generated, we can broadly classify image matching methods as area-based image matching or feature-based image matching.
^[1]
An alternative approach has been proposed in this paper in order to match pixels accurately using a mathematical approach referred as Polynomial Fitting which requires identification of minimum of 6 control points in the locality or neighborhood. If the number of control points for a given region or locality is less than 6, than window size increases automatically to accommodate more control points. Window continues to grow in size until number of control points in the region becomes 6 or exceeds 6. When the number of control points are greater than 6, all possible combination of 6 points are used to calculate and the combination that gives least Sum of Squared Error is used for further calculation. A statistical algorithm referred as Random Sample Consensus is applied in order to select 6 control points for calculation. The algorithm randomly selects any 6 pair of control points for calculation. We can divide this algorithm into two segments-1)Determination of control points 2) Determination of match points. The percentage of accurately matched pixels in stereo pairs was found to be 93.48% in one of the test data set, which was very high compared to standard Normalized Cross Correlation based approach (77.89%).