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. 2010;10(2):1093-118.
doi: 10.3390/100201093. Epub 2010 Jan 29.

Using fuzzy logic to enhance stereo matching in multiresolution images

Marcos D Medeiros  1 , Luiz Marcos G Gonçalves, Alejandro C Frery
Affiliations

Using fuzzy logic to enhance stereo matching in multiresolution images

Marcos D Medeiros et al. Sensors (Basel). 2010.

Abstract

Stereo matching is an open problem in computer vision, for which local features are extracted to identify corresponding points in pairs of images. The results are heavily dependent on the initial steps. We apply image decomposition in multiresolution levels, for reducing the search space, computational time, and errors. We propose a solution to the problem of how deep (coarse) should the stereo measures start, trading between error minimization and time consumption, by starting stereo calculation at varying resolution levels, for each pixel, according to fuzzy decisions. Our heuristic enhances the overall execution time since it only employs deeper resolution levels when strictly necessary. It also reduces errors because it measures similarity between windows with enough details. We also compare our algorithm with a very fast multi-resolution approach, and one based on fuzzy logic. Our algorithm performs faster and/or better than all those approaches, becoming, thus, a good candidate for robotic vision applications. We also discuss the system architecture that efficiently implements our solution.

Keywords: fuzzy rules; image analysis; multiresolution; sensor configuration; stereo matching; vision.

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Figures

Figure 1.
Figure 1.
Creation of a pyramid with wavelet transform.
Figure 2.
Figure 2.
Illustration of the creation of a pyramid with three levels.
Figure 3.
Figure 3.
Cartoon image and δ map.
Figure 4.
Figure 4.
Scheme of the software architecture.
Figure 5.
Figure 5.
Computed pyramids. Left to right: original image, Daubechies wavelet levels, and levels computed by our proposal.
Figure 6.
Figure 6.
Tsukuba data set. From left to right: left image, right image, desired disparity map.
Figure 7.
Figure 7.
Tsukuba data set. From left to right: left image, right image, desired disparity map.
Figure 8.
Figure 8.
Disparity maps generated by multiresolution matching using the detail images at the coarsest level (level), and using always the scale images (right).
Figure 9.
Figure 9.
Errors measured with both algorithms: mean distance d (left) and standard deviation s (right).
Figure 10.
Figure 10.
Disparities obtained by plain correlation (right) and multiresolution (left) with correlation windows of size 3 (top) and 5 (bottom) pixels, using δ = 0.3.
Figure 11.
Figure 11.
Measured errors for multiresolution with variable depth: Tsukuba pair.
Figure 12.
Figure 12.
Measured errors for plain correlation with no search interval: Tsukuba pair.
Figure 13.
Figure 13.
Visual comparison between disparity maps generated by correlation (right column) and multiresolution matching with δ ∈ {0.1, 0.2} (middle and left columns, respectively), Tsukuba data set, using windows of size 3, 5, 9 (top, middle and bottom rows, resp.), 4 pixels search interval.
Figure 14.
Figure 14.
Visual comparison for the Corridor images between disparity maps generated by correlation (right column) and multiresolution matching with δ ∈ {0.1, 0.2} (middle and left columns, respectively), using windows of size 5, 9, 13 (top, middle and bottom rows, resp.), 10 pixels search interval
Figure 15.
Figure 15.
Disparity maps generated by multiresolution matching with δ ∈ {0, 0.2, 0.3, 0.4} (columns from left to right) and windows of size 3, 5, 7 (rows from top to bottom), 6 pixels search interval.
Figure 16.
Figure 16.
Disparity maps generated, Corridor, by generated by correlation (right column) and multiresolution matching multiresolution matching with δ ∈ {0, 0.1, 0.2} (columns from left to right), windows of size 5, 7, 11 (from top to bottom), refinement windows of 4 pixels.
Figure 17.
Figure 17.
Time needed for computing the disparity by our approach in the Corridor pair.
Figure 18.
Figure 18.
Error and standard variation for the Corridor images.
Figure 19.
Figure 19.
Required time.
Figure 20.
Figure 20.
Disparity maps, Kumar and Chatterji algorithm, for window of sizes 3, 5, 7, 9, and 11 (from top to bottom).
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