Region Growing Segmentation Based on Region Dissimilarity

The region dissimilarity approach to region growing is an improvement over Logical Predicate region growing in which the segmentation result may be attained more efficiently via the use of a region dissimilarity function based on aggregated region features. Let d(Xi, Xj). be the dissimilarity function that is zero when region feature values of regions Xi and Xj are identical, and becomes larger as these regions become more dissimilar. This function surpercedes the logical predicate function which is based on the individual pixels contained in the region. However, just as before with the logical predicate region growing approach, this version of region growing segmentation can be accomplished through repeated scans through the image until no further region merges can occur.

Following from the above summary, in the first scan of the image, each pixel, xp, is placed in a neigboring region, Xj, from the previous scan line or column if d(xp, Xj) < d(xp, Xk) for all the regions adjacent to xp with j≠k and d(xp, Xj)threshold, T. (Here the pixel, xp, is treated as a single pixel region when computing the dissimilarity function. Also, if the pixel attains the minimum value of the dissimilarity function, d() ≤ T, for more than one region, the pixel is merged with the region with the smallest region label.) In the event, the pixel, xp , is not merged with an adjacent region, it forms a new one-pixel region. In the ensuing scans through the image, the image is scanned region-by-region instead of pixel-by-pixel. Throughout these scans, spatially adjacent regions Xi and Xj are merged if d(Xi, Xj ) < d(Xi, Xk ) for all regions adjacent to region Xi with j≠k and d(Xi, Xj )T. The process terminates when no merges occur in a complete image scan.

The spatial structure of the image segmentation resulting from this approach corresponds much more closely to the original image. In addition, the scan order dependence apparent in the logical predicate region growing results, is much reduced or eliminated. Even though the scanning process was not changed, the overall improvement in the image segmentation result brings about the reduction or elimination of scan order dependence in the result. Moreover, since the merge decisions are made based on region-by-region comparisons rather than computations involving individual image pixels, region growing based on region dissimilarity is much more computationally efficient.

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Fig. 2. (a) Region mean image for the 203 region segmentation result produced by using region growing with dissimilarity based segmentation with threshold, T, equal to 26.0. The global dissimilarity value from the logical predicate segmentation is 10.0344. (b) Boundary map for (a).

Another dissimilarity criterion, the more commonly used Mean Squared Error (MSE) method, is based on selecting merges that minimize the increase in the mean squared error between the region mean image and ther original image. Nevertheless, there are two approaches the MSE approach: (1) Band Sum Mean Squared Error, which sums over the spectral bands in determining the region dissimilarity, whereas (2) Band Maximum Mean Squared Error, takes the maximum over the spectral bands.

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Fig. 3. (a) Region mean image for the 162 region segmentation result produced by using region growing with BSMSE dissimilarity based segmentation with threshold, T, equal to 3200. The global dissimilarity value from the BSMSE segmentation is 9.98618. (b) Boundary map for (a). (c) Region mean image for the 151 region segmentation result produced by using region growing with BSMSE dissimilarity based segmentation with threshold, T, equal to 1850. The global dissimilarity value from the BSMSE segmentation is 9.96472. (d) Boundary for (c).

Using the BSME dissimilarity function for region growing, the results produced a spatial structure much closer to the original image; better than the logical predicate region growing results. Also, the results show finer details than the logical predicate region growing results with less than half the regions. However, a reappearance of scan order preference was present but to a much lesser degree.

Even though the segmentation result produced with this approach is much improved, even more improvement in segmentation quality can be obtained through Hierarchical Step-Wise Optimization, as described in the next section.